the behaviour of intertidal sandwaves during neap-spring tide cycles and the relevance for...

Sedimentology (1986) 33, 1-3 1

The behaviour of intertidal sandwaves during neap-spring tide cycles and the relevance for palaeoflow reconstructions

JOOST H . J . T E R W I N D T and M A R G U E R I T E J . N . B R O U W E R *

Department of Physical Geography, State University, P .O . Box 80.115,3508 TC Utrecht, The Netherlands

ABSTRACT

Variations in migration distances and shape characteristics of sandwaves in relation to flow conditions were studied on the Ossenisse intertidal shoal in the Westerschelde estuary. The purpose was to analyse bedform behaviour, to establish the threshold and the time lags involved, to find differences in two- and three-dimensional sandwaves and to determine the implications for palaeoflow reconstructions.

Sandwave migration is well correlated with the peak depth-averaged flow velocity of the dominant tide. Thus the latter parameter may be estimated from the thickness of the tidal bundles. Other flow parameters such as shear velocity, Chezy C or roughness length do not show a correlation with the migration and cannot be used in palaeoflow analysis.

Flow depth does not correlate with sandwave height or with length. Consequently, neither sandwave height and length nor set height and length can be used for palaeoflow depth determination.

Sandwaves start moving when the peak dominant flow velocity exceeds 0.5-0.6 m s- ', and appreciable changes in shape occur at 0.75-0.8 m s- ' . Complete reversal of sandwaves is accomplished if both the dominant and subordinate peak depth-averaged current velocities exceed 0.85 m s- '.

Two- and 3-D sandwaves appeared to have different stability fields in the velocity-depth diagram and in the diagram of the Froude number versus the depth-grain-size ratio. In addition the distinction between 2-D and 3-D sandwaves appeared to be related to a variability in current direction during periods of appreciable sand transport. There are also differences in sedimentary structures between the two types of sandwaves

INTRODUCTION

In recent years considerable progress has been made in the recognition of tidal deposits in the sedimentary record. However, the reconstruction of palaeoflow conditions is still a difficult task. The main problems are to determine flow velocity, water depth, tidal range and sand transport rate from the sedimentary structures and textures. Such reconstructions can only be based on a detailed analysis of the flow characteristics and bedform behaviour of recent analogues.

Such studies are scarce for subtidal as well as intertidal settings. It is the purpose of this paper to

'Present address: Koninklijke Shell/Exploratie en Pro- duktie Laboratorium, P.O. Box 60, 2280 AB Rijswijk, The Netherlands.

analyse bedform behaviour on an intertidal shoal and to establish any flow thresholds and time lags that may be involved. Furthermore, differences in the behaviour of 2-D and 3-D bedforms are investigated and the implications for palaeoflow analysis are discussed.

BEDFORM TERMINOLOGY

There is a considerable confusion in the terminology of (inter)tidal bedforms that cover the stability field between ripples and upper flat beds. We will adopt here the terminology as proposed by Allen (1980).

Allen (1980, fig. 8) employs the term dunes to describe major bedforms, generated under unidirec-

1

2 J . H . J . Terwindt and M . J . N . Brouwer

tional flow and the term sandwaves for bedforms associated with reversing tidal currents. Sandwaves do not reverse completely during a tidal cycle, although a modification of the asymmetry may occur in a subordinate semi-cycle. Thus sandwaves are form- persistent bedforms. Dunes may be present in a tidal environment but then, by definition, have to show a complete revyrsal during one tidal cycle.

Sandwaves may be 2-D or 3-D (Allen, 1968; Rubin & McCulloch, 1980; Costello & Southard, 1981; Harms, Southard & Walker, 1982). From theseauthors the following definition may be summarized :

2-D sandwaGes have fairly straight, continuous, even crests lacking local scour in the trough.

3-0 sandwaves have sinuous, often discontinuous, uneven crests and local scour pits in the troughs.

PREVIOUS STUDIES O N SANDWAVES

Palaeoflow reconstructions can only be based on recent analogues where the relations between flow parameters and sedimentary features (structures, textures) are known.

Qualitatively, systematic trends have been established in the variation in neap-spring tide cycles of peak current velocities, tidal asymmetry, sand transport rate and bedform migration rate, either by observations on the bedform itself or by the lateral succession of sedimentary structures. The migration of sandwaves was observed by several workers to be greatest around springtide and zero or nearly zero around neaptide, due to the low velocities a t these times (De Raaf & Boersma, 1971; Boothroyd & Hubbard, 1975; Allen & Friend, 1976a; Boersma & Terwindt, 1981a, b; Elliott & Gardiner, 1981; Van den Berg, 1982; Siegenthaler, 1982). Structural features indicative of the neap-spring cycle and of the diurnal inequality of the tides were reported from tidal sediments (the succession of thicker and thinner tidal bundles in the lateral sequence of sedimentary structures : the lateral neap-spring-neap cycle on which superimposed the systematic variations due to the diurnal inequality, Boersma & Terwindt, 198 1 a ; Visser, 1980; Terwindt, 1981; Allen, 1982d, e ; Van den Berg, 1982; Siegenthaler, 1982; Allen & Home- wood, 1984; Yang & Nio, 1985).

Non-systematic variations due to wind effects or related to the topography of the shoal (locality effects) can be expected to affect the time-velocity curves, bedform migration rate and bedform shape. These

non-systematic variations probably are responsible for slight deviations in the internal structures of tidal bedforms.

However, quantitative relationships between flow velocity and bedform characteristics and migration rates, essential for palaeoflow reconstructions, are very scarce. In addition, velocity thresholds and timelags involved are still obscure.

Another question is whether sandwave shape is important in palaeoflow analysis. This may be the case if the bedform shape may be reconstructed from the structures and if the shape characteristics are related to flow velocity parameters.

The adjustments or even transformations of sandwave shape in the course of the neap-spring tide cycle have already been reported by several authors (Allen & Friend, 1976a, b ; Boersma & Terwindt, 1981a; Elliott & Gardiner, 1981; Zarillo, 1982). However, quantitative relationships are still lacking, while data on velocity thresholds and time lags involved in the adaptation of sandwaves are scarce.

This adaptation of bedforms to changing flow characteristics poses a special problem, because in a field of mobile bedforms (ripples, dunes/sandwaves) there is a continuous creation, change and vanishing of individuals (Allen, 1968, 1969, 1973, 1974, 1976a, b, c, d, 1982a, b, c, 1983; Costello & Southard, 1981 ; Wijbenga & Klaassen, 1983). Under steady state conditions the bedform assemblage may become adjusted to the flow conditions, which implies that the mean of the dimensional parameters (height, length) that characterize the population of bedforms becomes constant in time. Under unsteady conditions, as on an intertidal shoal, the adjustment of the bedforms to the changing flow may be imperfect. Relict bedforms and those lagging behind in their adaptation may be expected to influence and complicate the characteristics of the flow and the bedform-flow relationship. As a consequence the rate of bedform adjustment is of particular importance. If there is a quick response a good and simple correlation between bedform and flow parameters is likely to appear. If the adjustment is imperfect and lags behind considerably the correlation graphs may show hysteresis lines (compare Simons & Richardson, 1962; Allen, 1974, 1976b, d). If the adaptation exhibits a considerable relaxation time (Allen, 1976d; Allen & Friend, 1976b) we shall find no correlation at all, which precludes the use in palaeoflow reconstructions.

Allen (1976a, b, c, d) concluded from observations in nature as well as simulation studies that the various morphometrical bedform parameters show different

Intertidal sandwaves 3

time-scales of lag. In his studies, dune length lagged more behind than dune height.

Another problem is to define adequately the term ‘time lag’. Allen (1983) and Wijbenga & Klaassen (1983) discuss this matter, but still there is no satisfactory solution. In this study we choose to define time lag as the number of tides after spring tide that maximum values of sandwave height and length are reached.

AREA AND M E T H O D S OF INVESTIGATION

The Ossenisse shoal lies in the middle of the Westerschelde estuary (Fig. 1). It has a triangular form: the greatest length is about 3 km and the greatest width about 2 km (Fig. 2). Four measurement sites were chosen over the shoal. Only two of them, one covering a 2-D, the other a 3-D sandwave field will be dealt with here. They are indicated by 2-D and 3-D in Fig. 2 . The shoal experiences a semi-diurnal tide, with a diurnal inequality (Fig. 3). The tidal amplitude ranges from 3.30 m at neap tide to 5-50 m at spring tide. During the five weeks of our field studies we covered two normal spring tides (ST 1 and ST 3) and one exceptional high spring tide (ST 2). The latter is due to an infrequent interference of some tidal components.

The 2-D sandwave field has a mean elevation of

0 .4m above MSL. The bed material has a median grain size of about 200 pm. The 3-D sandwave field lies 0.7 m below MSL and the bed material was slightly coarser (Md = 230 pm).

In both fields the average sandwave length is about 6 m . In the course of a neap-spring tide cycle the average sandwave height ranged from 0.14 to 0.20 m for the 2-D field and from 0.20 to 0.40 m for the 3-D field.

In the studied fields measurement platforms were erected from which current velocities, current directions and water levels were recorded. In each field vertical profiles of current velocity were obtained by a set of 6 Ott-Minor current meters, distributed over a height of 1.5 m above the crest of the sandwave. These sets of current meters were replaced every LW to ensure that the measured velocities remained indicative for the crestal zone of the sandwave. For comparison a self-recording ‘Flachsee’ current meter was installed to measure continuously the velocity and direction at a fixed position, about 0.75 m above the bed. The inaccuracies of the measurements were determined by combining instrumental errors and estimated inaccuracies in the observations and the data-processing. Throughout this paper a significance level of 5% is used.

The following parameters were determined from the vertical velocity profiles:

the depth-averaged velocity (n, which is defined as the velocity a t 0.38 h fh = water depth) above the

m 0 0 0 . - N m area above mean sea level

area above mean low tide

+ predominant flow

Fig. 1. Location of the Ossenisse shoal

4

6 north

J . H . J . Terwindt and M . J . N . Brouwer

- - _ _ -2.5 m. ~ M.S.L. - +I m

Q 250 590,

Fig. 2. Morphology of the Ossenisse shoal and location of the measurement sites in the 2-D and 3-D sandwave fields

bed, calculated from a plot of velocity versus log h ; the peak depth-averaged velocity for the flood and the ebb (~,,, ", urn,, ebb) (further called the peak flood/ebb velocity). The inaccuracy of the 0 parameters was about 10%; the shear velocity (U,) from the logarithmic velocity distribution. It appears that about 85% of the measured velocity profiles could be described by a logarithmic velocity profile within the 95% confi- dence limit. The inaccuracy of the U* values was about 20%.

It should be noted that the Prandtl-Von Karman formula, used for the determination of U* applies to steady flow, but that according to Soulsby & Dyer (198 l), in accelerating and decelerating flow the values

of U* may deviate some 20% from the steady state value. In addition the following parameters were computed :

W*3. The moment of occurrence of the maximum value of U* normally does not coincide with the moment of om,,. Although no systematic trend could be established i7*,,, normally fell within a 10 min span around the moment of Urn,,. A mean value of U* from the readings 10 min before, a t and 10 min after U,,, was thought to give a better indication of the magnitude of U* in relation to bedform behaviour than the single U*rnax (see also Dalrymple, Knight & Lambiase, 1978). Therefore the mean of the three values of U* around U,,, for the ebb and the flood tide (U*3 ", U*3 ebb) were used.

An estimate of the roughness length zo. This

-


HIGH TIDE LEVEL -

t

ST1+2 +5 +10 +15 NT1 +5 4-10 ST2 +5 +1ONT2 +5 +1OST3 +5 springtide neap tide springtide neap tide springtide

Fig. 3. Observed tide levels and neap-spring tide sequence during the measurements on the Ossenisse shoal.

parameter may be determined by the Prandtl-Von Karman equation for hydrodynamically rough flow. It appears that the values of zo show considerable scatter. In order to obtain some ‘representative’ values for the moments of peak velocity in the tidal cycle we calculated a value of zo ,, and zo ebb, using Om,,, h,,, and U*3 according to

in which K = Von Karman’s constant = 0.4. The mean of three Chezy’s C roughness values

(C, ,,, C3 &b) occurring 10 rnin before, at and 10 min after the moment of urn,,. The most reliable way to determine the C value is to measure the water slope and the velocities and to solve the equation of (tidal) motion. However, over the shoal the water slope is quite variable in time and place, thus it is virtually impossible to obtain representative values. This drawback forced us to use a much more inaccurate method to calculate C, namely from C = (O/U*)Jg . The inaccuracy of this C value is 20-40%.

The sand transport per flood and ebb tide (Q, ,,, Qs ebb). The Engelund & Hansen (1967) total load formula was used to obtain a relative value of the sand transport per flood and ebb tide. The choice of this particular formula seems arbitrary, but .this formula appears to give satisfactory results in shallow areas with both bed and suspended load as is the case on the Ossenisse shoal (Heathershaw, 1981).

The depth-averaged velocities 0 were correlated

with time-corresponding velocity values of the ‘Flach- see’ current meter. From this high correlation, values were estimated for the periods in which the vertical profiles of current velocities were not determined for practical reasons (nights, technical trouble, etc.).

The migration of the bedforms and the morphometric parameters such as length, height, asymmetry and steepness index were determined from lacquer peels and from detailed bed surface measurements. Differ- ently coloured luminophore tracers were spread over the lee side of selected bedforms exposed at LW, to determine the migration distance between successive observations. The internal structures could be deduced from lacquer peels which were taken after a few tides.

The bed surface recordings were performed in 27 m long transects, lying parallel to the dominant flow direction. Along each transect seven permanent stakes were placed at intervals of 4.5m. At emergence a measuring bar was attached horizontally between the stakes to height-marks corresponding to a datum level. Subsequently the vertical distances between this bar and the bed were measured (Fig. 4). In every transect 65 of such measurements, each 0.4 m apart, were performed and this resulted in a quite accurate outline of the bed topography. The inaccuracy of the bed surface profiles was less than 0.5 cm, as determined from repeated levellings.

The bed form profiles were used to determine several morphometric parameters, indicated in Fig. 5 : length (L) ; height (H); steepness index (LIH); asymmetry (b/


Fixed height -- Fig. 4. Method of bed surface recording

a ) ; the height of the crest (Ha) with respect to a reference line and the depth of the trough (Td) below the same reference line (this reference line is the mean height of the transect above or below Ordnance Datum); the bedform height/water depth ratio (H/h). In the latter case the maximum water depth was not used, but the water depth at the moment of urn,,, since it was felt that bedform adaptation was mainly a function of maximum flow velocity and the water depth that corresponded with it.

By plotting the bed profiles from successive tides in one graph, the migration distance (M) , measured half- way between the crest and trough on the lee-side could be determined as well as the volume of erosion (E) and sedimentation ( S ) (Fig. 5 ) . The migration distance ( M ) was checked afterwards in the lacquer peels. There appeared to be a very good agreement.

Appendix B presents the data obtained.

TIDAL STREAMS AND THE EFFECT ON INTERTIDAL BEDFORMS

Flow conditions on an intertidal shoal are related to the distortion of the tidal wave. Thiz distortion is the result of non-linear phenomena that play an important role in shallow seas and estuaries, viz.: a variable decreasing width of the water surface during emergence of the shoal, a non-linear friction, a non-constant

propagation of the tidal wave, due to the small water depth and non-linear interactions between the several tidal components (Dronkers, 1964). These shallow water effects may create an asymmetrical time- velocity curve for the complete tidal cycle. This normally results in higher peak velocities of relatively short duration during one tide and lower peak velocities with longer duration during the other tide, but with zero net flux of water. The flow over the shoal may be influenced further by the character of the surrounding channels. If there are ebb and flood channels a residual water flux may be present over some areas of the shoal. Occasionally, wind effects may further complicate the flow pattern over the shoal.

All these phenomena may change in the course of time, some more or less systematically (diurnal inequality, neap-spring tide cycle) others randomly (wind effects). As a result, the magnitude of the peaks and the form of the time-velocity curves may change considerably with time in intertidal areas, and the sand transport capacity will therefore also vary substantially. These variations may complicate the bedform-flow analysis because it can be expected that they have a pronounced effect on the migration rate, the shape and the dimensions of the bedforms and on the internal structures.

Thus we are dealing with unsteady and non-uniform flow processes and it is obvious that simple sinusoidal

k M 7 I ‘

1 I

E = Erosion m3ni1tide1 S = Deposition rr?m’tide’

I L

Ripple symmetry index = b/a Steepness index = L/H M = Migration m tide-’

Fig. 5. Definition sketch of the morphometric parameters.

Intertidal sandwaves

velocity functions, derived from merely theoretical oscillatory tidal flow cannot be applied on such intertidal shoals (cf. Siegenthaler, 1982). This is illustrated in Fig. 6, which shows the variation in the time-velocity relationship during the most relevant time interval of the flood-ebb cycle for spring and neap tides in the 2-D and 3-D fields. In both fields there appears to exist a clear velocity asymmetry during spring as well as neap tide with the flood acting as the dominant tide.

In the 2-D field a t spring the velocity curve shows a steep upward limb and a less steep downward limb. This means that during waxing flood there is a rapid increase in flow velocity at a relatively small water depth giving rise to high shear velocities. Peak values of Doccur one to two hours before the water level has reached its highest point. A similar velocity curve is observed for the ebb, although with lower peak values. At this instance shear velocities also remain low and so is sand transport. At neap tide both ebb and flood velocity curves are more symmetric, while the peak valuesof u a r e lower than at spring tide; the difference between ebb and flood, however, is small.

The 3-D field a t spring tide shows a very rapid decrease of the flood velocity (@ after a less rapid increase. The reverse is the case for ebb. From Fig. 6(B) it can be seen that peak velocity, shear velocity and sand transport occurs shortly before H W (flood) and just after H W (ebb) a t relatively great water depths. At neap tide the difference in magnitude between the peak flood and peak ebb velocities is rather small but the ebb tide lasts only 70 min, while the flood currents last about 5 hr.

In both the 2-D and 3-D fields the slack water period between flood and ebb is very short and normally there is not a standstill. This suggests that mud deposition that will escape subsequent erosion can hardly be expected. By contrast, after the other slack water period from ebb to flood, preceding low water with shoal emergence, current velocities remain low for a considerable time and mud deposition may be expected. This goes especially for the neap tide.

From Fig. 6 it can be concluded again, that for a shallow area such as the Ossenisse shoal, which emerges during half of the tidal cycle, at least, a sine- schematization of the time-velocity curve, as proposed by Allen (1 980, 1982a, b, c, d) and Siegenthaler ( I 982), is too crude an approximation. Therefore,.the strength index and velocity asymmetry index, as employed by Allen (1980), cannot be used in the proposed form. Instead we propose the following descriptive alterna- tives :

strength index :

velocity asymmetry index:

in which:

urn,, dom = peak depth-averaged velocity of the dominant tide,

Urn,, subord = peak depth-averaged velocity of the subordinate tide,

UC',,,, = critical mean velocity for the movement of sand. (From Hjulstrom's diagram and from our own observations on the Ossenisse shoal a value for uc',,,, of 0.2 m s- ' could be derived.)

HYDRODYNAMICS OF SANDWAVE FIELDS

Figure 7 presents some results of the flow measurements in the 2-D and 3-D field on the Ossenisse shoal. Below, a summary is given of how the different tidal phenomena such as tidal asymmetry, diurnal inequality and neap-spring tide cycle work out on the many hydrodynamic parameters. The results are of importance to reconstructions of palaeoflow conditions.

In both fields the neap-spring cycle is clearly visible in the peak flood velocity curve, but to a much lesser degree in the peak ebb velocity curve. However, the neap-spring cycle is hardly apparent in the U*3 and C, curves in the 3-D field and is absent in these parameters in the 2-D field. Thus the peak velocity of the dominant tide is most sensitive for the neap- spring variations in velocity.

The diurnal inequality is well established in the peak velocities of the dominant tide in the 3-D field, but hardly in the 2-D field. The subordinate tide shows only a faint diurnal inequality trend. Such a trend is absent in the U*3 and C3 parameters in both fields. Thus diurnal inequality, although manifest in some areas, can be suppressed in other areas of the same tidal basin, even on the same shoal.

Both fields show a marked tidal dominancy in the peak velocities and the Velocity Asymmetry Index. Such dominancy can also be seen in the U*3 values in the 3-D field, but become faint for the same parameter

8

\ \ \ \ I I \ \ l - / / J J J J ~ J J / Neap tide - G ms-’ Current

direction + -


..... .... 0 .... 1 ...... +. ..... 1 ....... h..- , 1 I I , I . I ...... 1” I . ....,...... ..... .... “‘1”. ...,.....*,. J 0 A 8 00 9 00 10 00 11 00 hour

Fig. 6. (A) Measured water depth (h), current directions, depth-averaged current velocities (n, shear velocities (U,) and calculated sand transport rate (Q,), characteristic for spring and neap tide on the 2-D sandwave field.

in the 2-D field and is almost absent in the C , parameters. Thus tidal dominancy is best connected with the om,, and VAI parameters.

Some authors (e.g. Allen & Homewood, 1984) used an estimate of the roughness length in order to predict palaeocurrent velocities. This procedure is very unsat- isfactory because of the great variability of U* and zo in a tidal cycle and the neap-spring cycle. There is a general tendency of increase of zo towards peak current velocities and towards spring tide (Appendix B). Flood values of zo are usually smaller than ebb values. The order of magnitude of our data on zo is similar to those obtained by Carling (1981) for intertidal areas.

MORPHODYNAMICS OF SANDWAVE FIELDS

Several questionsmay be posed, relevant to palaeoflow analysis of tidal sediments:

are there, besides the sandwave height, systematic variations in the other morphometric parameters in the course of the neap-spring-neap cycle?; are morphometric parameters indicative of current velocities, or flow depth. Are there quantitative relationships? ; is there a quantitative relationship between migration of the bedform and flow velocity? Are there thresholds involved?


s,u. , u t

-I

\ A

. _.. .. ......,. ._.' . __...,

19 ( " I L"" " ' I ' " " L ' ' L ' ' ' L 0

16 00 17 00 18 00

Spring tide -I- - 3 0

- 2 5

- 2.0

-15

-. -. -.

h

t \. \. -. \. \. x.

x.

- 0 5 .... .... . . . . . . . . . ....................

10 20 00 21 00 hour

Fig. 6. (B) Ibid. for the 3-D sandwave field.

These questions will be treated below, based on mean values per tide of these morphometric parameters in the sandwave fields (R, 1, ( T H ) , (G), lii, S, a.

NEAP-SPRING TIDE VARIATIONS IN MORPHOMETRIC PARAMETERS

Height

Several authors (e.g. Allen & Friend, 1976a, b ; Boersma & Terwindt, 1981a; Dalrymple, 1984) have reported that intertidal sandwaves increase in height up to ST and decrease towards NT. This increase in H is accomplished more by deepening of the trough than by heightening of the crest. Similar tendencies were observed by the present measurements (Fig. 8)

in 2-D as well as 3-D sandwave fields. However, the absolute value of H and the range of variation is much less in the 2-D field in comparison to the 3-D field.

Length

Neither the 2-D fields nor the 3-D fields show a general tendency for L in the neap-spring cycle. Sandwave length remains virtually the same in the 2-D field. The wide range of the values indicates a high variability. In the 3-D field a small increase in L values takes place, but the highest values are found only three tides after ST.

Steepness index (VH)

Both fields show a tendency of decreasing steepness index (i.e. increasing steepness) towards ST whereaf- ter it increases again toward NT.

10

1-

2-


strength index

'I= Ocrit Omax d o m - h i t

........................ .... ...""""".\_A ..... ........... 2-D sandwaves '.. - 3-Dsandwaves

0-

4 t I I 1 Velocityasymrnetryindex

......... VA, - umaxdom

Umaxsubord

Fig. 7. Variation of flow parameters during the successive spring-neap tide cycles. Parameters are : the peak depth-averaged current velocities for flood and ebb (Urn,,, ", Urn,,, ebb); the mean of three shear velocity and Chezy C values recorded 10 min before, at and 10 min after the moment of Urn,,, (U*3. C3); the velocity asymmetry and the strength index (VAL SI).

Intertidal sandwaves &%wave* -1 immohile mohile mvnobile mobile

rn ms 1 6 0 8 1 2 0 6

0 8 0 4 0 max ebb 0 4 0 2 Fr

0 max fl h max

0 0 m , I 1

11

0 2

0 rn

0 20

-1 0

H

Ha Td

t 2 1 5 -10 415 - 5 -10 . 5 410 1 5 t10 B ST1 NTl. ST2 NT2 ST3

Bedform shape changing

Bedform shape unaltered

Mean of 5-6 Bedforms

Fig. 8. Change of morphometric and current parameters during the successive spring-neap tide cycles for 2-D (A) and 3-D (B) sandwaves. For the definition of the morphometric parameters, see Fig. 5.


+ 4517- +

Fig. 9. Successive profiles showing splitting and coalescing of sandwaves in the 3-D field

Symmetry

3-D sandwaves tend to be more symmetric a t ST than around NT. This is mainly due to the formation of ebb caps which results in more symmetrical rounded crests as they appear during emergence. The 2-D field has quite variable symmetry values not showing specific trends.

In the 3-D field R and L are much more variable during ST3 than ST2. The reason is (Fig. 9) that towards ST3 some sandwaves split up into two smaller ones. After ST3 some sandwaves unite again. Splitting up and merging of sandwaves during ST3 seems to indicate that the shapes left behind after the high spring tide ST2 were not in equilibrium with the more normal conditions of ST3. This is also demonstrated


by the fact that the bed resistance during ST3 was significantly higher than during ST2. Flow conditions during the high ST has a definite effect on the bed morphology, a tendency already noted by Allen & Friend (1976a) and complicating the time-lag adaptation trends and time-lag analysis.

In summary : neap-spring cycles are best reflected in an increase in sandwave height and symmetry and to a lesser extent in the steepness index.

RELATIONSHIP BETWEEN MORPHOMETRIC AND

HYDRODYNAMIC PARAMETERS

Correlation coefficients in linear, semi-log and log-log plots of the peak flood velocity (urnax ") and the morphometric parameters are below 0.40 for the 2-D, as well as in the 3-D fields. The low correlation can also be observed in Fig. 10. This means that for palaeoflow reconstruction the height and length of sandwaves are not indicative of the flow velocities for conditions comparable of those on the Ossenisse intertidal shoal.

However, qualitatively, there is a systematic increase of H and L with amax n in the 3-D field, following hysteresis loops with a time lag of one to three tides (Fig. lo). The same holds for R in the 2-D field. The steepness index, asymmetry and bedform height/water depth ratio do not show trends with urnax fl and appear to have considerable relaxation times. Thus the average sandwave height and to a lesser degree length are the only morphometric parameters exhibiting a qualitative relationship with the current velocity parameter.

Another question in palaeoflow analysis is whether bedform dimensions (height, length) are indicative for the flow depth. Fig. 11 shows that there is only a faint trend of increase of with h,,, for the mobile 3-Dsandwaves. Sucha trendisabsent forthe immobile 3-D sandwaves and for all 2-D sandwaves. Further- more it appears that there is no trend at all in the plot o f t and maximum flow depth. Thus, on the Ossenisse shoal sandwave dimensions do not predict flow depth with an acceptable degree of accuracy.

CURRENT VELOCITY THRESHOLDS FOR SANDWAVE MIGRATION,

EROSION AND DEPOSITION

In the course of the neap-spring cycle two thresholds in the current velocity may be distinguished with

respect to the movement of sandwaves on the Ossenisse shoal.

Thejrst threshold separates the immobile from the mobile period. At the onset of movement the sandwaves do not change in shape: their morphological parameters remain unaltered.

Threshold values of the peak dominant velocity (urn,, fl) are about 0.6 m s-l for the 2-D field and 0.5 m s-' for the 3-D field (Fig. 8 and Appendix B). It may be noted, that below this first threshold velocity, there may be some sand transport (e.g. moving small ripples).

Important modifications in shape occur when a second threshold is surpassed, separating the unaltered from the altering sandwaves. Threshold values of peak dominant velocities (a,,, ") are now 0.75 m s - ' for the 2-D fields and 0.8 m s- ' for the 3-D fields.

Another threshold is found where the formation of ebb (or flood) 'caps' by the subordinate tide is con- cerned. These are formed when, towards spring tide, not only the velocities of the dominant but also those of the subordinate tide increase. At a certain stage of the neap-spring cycle the upper steepest side flank of the sandwaves left behind by the dominant tide, becomes eroded during the subordinate tide. The eroded material in part is deposited in the crestal zone of the sandwave where it forms an ebb cap (Boersma & Terwindt, 1981a), superimposed upon the main crest. At the Ossenisse shoal this phenom- enon starts when Urn,, ebb exceeds the threshold value of 0.45 m s - ' . The more pronounced caps are formed when the peak subordinate velocity exceeds 0 .6ms- ' .

A complete reversal of the flood oriented bedform into an ebb directed one was observed when Urn,, ebb > 0.85 m s- ' (a similar value was reported by Boersma & Terwindt, 1981a). These threshold values hold for 2-0 as well as for 3-D fields.

SANDWAVE MIGRATION VERSUS PEAK DOMINANT VELOCITY

In the 2-D sandwave field the correlation coefficient between urnax and I@ is rather low (r = 0.63), which indicates that the migration of this type of sandwaves, although generally showing an increase and decrease in the course of a neap-spring-neap cycle, still lags behind the changes in urn,, (Fig. 12). In the 3-D field, however, the correlation is quite good (r = 0.88). This points to a direct response between ~,,, and A.

14 J. H . J . Terwindt and M. J. N . Brouwer

I , I I ,

i , I

r ,c , i . i i \

572-112 J

i 5

j

i ~- '_- -

3 - n ~ a n d w a ~ e s

om : :> 1 2 ms urnaif l

Fig. 10. Time lags and hysteresis trends in the relationships between the peak depth-averaged flood velocity (Dmax ") and the mean heights and lengths of sandwaves in 2-D and 3-D fields during neap-spring tide cycles (see Fig. 3 for further information).

m

04

0 3

02


- H

A

. . . ' ' . ..

0 0 0 . .

0 0 . * O Q

0 0 0

0 0

't " = . . . 0 .. 0 .

0 0 0 . 00 oo 0 0 ..

- 0

0 0 .* . * 0 0 0 0 0 0 t A A

I

08 1 2 16 20 24 28 32 51 hmaxfl

A immobile 2-D sandwave A mobile 2-Dsandwave o immobile 3-D sandwave

mobile 3-D sandwave

Fig. 11. Relationship between the flow depth at flood tide at the moment that D = om,,, (h,,, ") and the mean height length of the sandwaves in the 2-D and 3-D fields

SEDIMENTATION AND EROSION VERSUS PEAK DOMINANT VELOCITY

In the 2-D field there appears to be no correlation between urn,, , and or E (Fig. 12). This is in contrast to the 3-D field where s a n d Eshow a good correlation with urn,, , (Fig. 12). Closer inspection of our data reveal that in the rising phase of the high spring tide (ST2) erosion exceeds the total volume of sedimentation mainly because of a higher degree of erosion in the troughs. When the peak dominant velocity exceeds 1 m s - ' then s almost equals E, but after the high spring tide sedimentation is greater than erosion and infilling of the troughs occurs. Such tendency was not found at the lower spring tide ST3. This supports the earlier finding that the high spring tide has a definite

15

6m

and

effect on the modelling of the 3-D sandwaves; the lower spring being of minor importance.

SANDWAVE MIGRATION, SEDIMENTATION AND EROSION

VERSUS CALCULATED DOMINANT SAND TRANSPORT

The calculated total flood transport (Qs ,)_shows no correlation with the migration distance ( M ) and the bedform erosion (E) or sedimentation (3 in the 2-D field (Fig. 13). This is at variance with the 3-D field where the computed sand transport reasonably pre- dicts the migration distance and the volume of deposited and eroded material during migration. It

m=rn tide-’ 1 s=m3,-ltiddl.

E = m3rrT’tide’-

0 5 -

01- I -

m=rn tide-’ s= rn3m’tide E= rn3m’tide

5

2-Dsandwaves

E 03 Urnaxfi

r=0.59 ’ 1 mmomax f l c .* 3 VJ ‘max fl

r=0.44

.. * %

*. r=0.63 . . . . . A* . * . . .. 2 *I. 5 - a .

..

10

0 5

01

3-D sandwaves

M ~ 1 3 W n a x fl

r=0.88

-

log rnax fl =0.194 log M+0.018

r=0.75

/ r=0.83 - log Urnax f,=0.265 log r-0.09E

-

log fl =0.251 log 3-0.094

- ms- Urnaxf

0054 , , , I , 05 10 05 10 05

Fig. 12. Relationship between the peak depth-averaged current velocity of the dominant tide (urn,,, ,,) and the mean migration rate (m, the mean net sedimentation ( S ) and erosion (0 per tide in the 2-D and 3-D sandwave fields.


-

.. -

17

02

01

2-D sandwaves

. .. ..

i O4

lr=0.38) I

1 0 01 0 2 - 0 3 0 4 mtidel

Q S f l rn3m-l

3 D sandwaves tide-'

20

1 t i

1 0

/ /

/ /

/

14

1 2

1 0

0 8

O h

0 1

0 2

0

.. (r=0.44) . .

.-.

1 - 2 m3m-ltid S

0 3 I ' .*

(r=O 2 2 )

0 0 1 - 1 m3rn-' tide-'

L

I . Q s f l I m3m i , tide-'

2 0

18

16 -

1 1

1 2 -

10

08 -

O h -

0 4 -

0 2 -

0 L 0

-

-

-

Fig. 13. Relationship between the calculated sand transport during flood (Q, ") and the mean migration rate (iii), the mean net sedimentation ( S ) and erosion (a per tide in the 2-D and 3-D sandwave fields.

may be that for the low current velocities, as occurring in the 2-D field, the calculated sand transport by Engelund-Hansen's formula is not very reliable.

DISTINCTION BETWEEN 2 - D AND 3 - D SANDWAVES

Stability fields for distinct types of bedforms may be used for palaeoflow reconstructions to establish the range in current velocities and flow depth. during formation of these bedforms. Several authors pre-

sented such stability fields, relating bedform size to flow velocity, water depth and grain size (Allen, 1968, 1982e, 1983; Southard, 1971, 1975; Middleton & Southard, 1977; Rubin & McCulloch, 1980; Davies, 1982; Zarillo, 1982). Often a distinction is made between 2-D and 3-D bedforms, each with their own stability field. Such distinction is based on: an apparently different morphological form (Allen, 1968, 1982e; Boothroydtk Hubbard, 1975; Dalrympleerul., 1978; Harms et al., 1982); a possible difference in generating mechanism (Costello, 1974; Costello & Southard, 1981) or a difference in the lateral sequence

18 J. H . J . Terwindt and M . J . N . Brouwer

of internal structures (Nio et al., 1980; Boersma & Terwindt, 1981a; Terwindt, 1981).

It was further observed that with increasing velocity 2-D bedforms may change into 3-D forms. This tendency was established for ripples (Guy, Simons & Richardson, 1966; Harms, 1969; Allen, 1968, 1969, 1977; Banks & Collinson, 1975; Mantz, 1978) as well as for large-scale bedforms (Rubin & McCulloch, 1980; Costello & Southard, 1981; Harms et al., 1982; Dalrymple, 1984). Tidal bedforms fit very well in the bed-phase diagrams. Most authors take the peak depth-averaged current velocity of the dominant tide as the representative parameter for the current velocity.

Dealing with tidal bedforms, Costello & Southard (1981) located 2-D and 3-D sandwaves in different fields in their velocity-depth diagram. In this diagram a vertical line can be drawn separating 2-D and 3-D sandwaves for flow depths greater than 1 m (Fig. 14); 2-D sandwaves occur below flow velocities of 0.75 m s- ' and 3-D sandwaves above this value. This limiting flow velocity is in good agreement with the findings of the Ossenisse shoal, where we found the maximum value of Urn,, to be 0.80 m s ' for the 2-D field. Boersma & Terwindt (1981a) reported a limiting flow velocity for 2-D sandwaves of 0.70 m s - ' . Thus for grain sizes between 200 and 500pm, as occurred in the above mentioned studies a velocity of 0.8 m s- ' is appropriate for the boundary between 2-D and 3-D sandwaves.

If we plot the Ossenisse 2-D and 3-D sandwave data in Vanoni's (1974) bedform stability diagram, which relates Froude number to the water depth-grain-size ratio (Fig. 15) another boundary can be encountered lying at h,,, , /d,, = 8 x lo3.

Besides the boundaries, which refer to velocity, water depth and grain size, the variability in current direction may be an additional property determining 2-D and 3-0 sandwaves. From a theoretical point of view current direction can be expected to exert influence on the sandwave as long as it is in its mobile period. If during the dominant tide the current direction during one part of the tide differs from the remaining part, two sand transport vectors may be present. Another possibility is that during a single dominant tide the direction of the sand transport is almost constant, but that during consecutive tides these directions change. Such changes can be held responsible for cross-patterns of bedforms as is frequently observed in 3-D sandwaves on intertidal shoals. As demonstrated by Allen (1968) such cross- patterns initiate the winding of the crest lines of

I A A IA A'

A I f A A b'

I I I 1 I I

t I

0 0 0 0 0 0 I 0 5 I I 1 , / , 1 , 1 1 I

01 02 04 06 08 1 2 3 flowvelocity (ms-1)

sandwaves 2-D(3-D

Dalrympleet. al. (1978) A Boothroyd &Hubbard (1974)

0 Pratt (1971)

Fig. 14. Distinction between 2-D and 3-D sandwaves in a velocity-depth graph including data from several authors (after Costello & Southard, 1981).

individual bedforms. The possible effect of current direction as an additional factor (besides velocity) to distinguish between 2-D and 3-D sandwaves is illustrated in Fig. 16. In the 2-D field the current directions during the mobile period are rather uni- formly 120", which is normal to the crest lines. Only around spring tide there is an additional direction of sand transport, but as it is related to velocities less than 0.5 m s - ' it can be expected not to have much effect. In the 3-D field, however, the direction of sand transport shifts over about 40"; not only during the high velocity part of a single tide but also in the course of the whole mobile period. Furthermore it may be noted that the main directions around spring tide deviate about 25" from those towards neap. As stated earlier, 3-D sandwaves are normally present at lower levels of the shoal, surrounding the banks of the tidal channels. Velocity but also direction of the currents here may be influenced by the conditions in these channels, which are more variable than on the higher parts of the shoal, where the 2-D sandwaves occur.


II t

1 :j 01

I I I I 1 1 1 1 I I I I I I I I I

1 o4 3 lo2 lo hmax fl

d 50

A Mobile 2-D sandwaves Mobile 3-D sandwaves

- Bedforrn boundariers, Vanoni, 1974

Fig. 15. Plot of our data in Vanoni’s (1984) graph of Froude number versus depth-grain-size ratio showing a separation of 2-D and 3-D sandwaves.

This greater variability could be demonstrated by the numerous current measurements made in Dutch tidal channels which surround shoals.

Another distinction of 2-D and 3-D sandwaves, not relevant for palaeoflow analysis, is the difference in height-length ratio. Some authors mentioned (Booth- royd & Hubbard, 1974; Dalrymple et al., 1978) that there are boundaries in L / H ratios. Figure 17 shows a plot of H and L values of individual 2-D and 3-D sandwaves from the Ossenisse shoal. Above L / H = 35 only 2-D sandwaves are found and below L / H = 23 only 3-D sandwaves. For 23 < L / H < 35 both 2-D and 3-D sandwaves occur. The boundary L / H = 35 agrees with the findings of Dalrymple et al. In our study area average L / H values range from 15 at ST to 32 a t NT in the 3-D field and from 32 at ST to 46 at N T in the 2-D field.

From a sedimentological point of view the most conspicuous difference between 2-D and 3-D sandwaves is that the former produce angular and tangential sets of tabular nature and the latter festoon cross-bedding with concave and sigmoydal foresets and even topsets (Kohsiek & Terwindt, 1981; Van den Berg, 1982). These topsets can be attributed to high current velocities, occurring in the transition af the dune to the upper flat bed part of the stability field, as demonstrated by the flume experiments of Saunder- son & Lockett (1983).

Another difference refers to the bundle thickness. As a result of the relatively short migration distance, 2-D sandwaves have in general thinner tidal bundles than 3-D ones. The 2-D sandwave bundles mostly exhibit nice neap-spring-neap lateral sequences of increasing bundle thickness and lowering of the lower set boundary toward spring tide and the reverse towards neap (Boersma & Terwindt, 1981a, b; Visser, 1980; Siegenthaler, 1982). Examples of 2-D sandwave deposits, fitting in the above characteristics may in our opinion be found in Nio et al. (1980, fig. 9); Visser (1980, figs 2 and 5 ) ; Boersma & Terwindt (1981a, figs 6 and 8); Terwindt (1981, figs 4, 5, 11, 12 and 13); Allen (1982d, plates 1.2, 1.4, 5.5, 6.1, 7.1 and 7.2); Siegenthaler (1982, figs 3, 4A, 5A, B); Van den Berg (1982, fig. lo); Teyssen (1984, fig. 7); Yang & Nio (1985, figs 5 and 6) . By contrast 3-D sandwaves build much thicker bundles, because of their greater migration distance, up to a few metres per tide. The single tidal bundles have erosive concave lower set boundaries : the deeper incised part is formed during the highest current velocities. Diurnal inequality of the tide is usually better reflected in the successive bundles than in 2-D sandwaves. This is due to the rapid response of sediment movement and migration to changes in peak dominant current velocities. By the combined effect of a strong migration and the subsequent thick bundles, the strong erosion in the

2 Dsandwaves

NT2+5

NT2

ST2+10

ST2 +5

ST2

NTl+10

NTl f5

NT1

0 !10 100 150 LOO 2'50 300 350 current direction y

Fig. 16. Variation during successive tides of current directions and related current velocities. The vertical axis gives per tide the length in time in minutes that a certain current direction is observed, with in black a current velocity above 0.5 m s - and in white a current velocity below 0.5 m s - ' . Thus the figure illustrates the sand transport capacity per current direction per tide.


H

.... m /... '. .. ...'. ....'

I; L/@ /

0.20 ,

/ /

2 - D sandw 3-D sandw

Fig. 17. Plot of our data on sandwave height versus sandwave length in a graph with envelopes of 2-D and 3-D sandwaves found by Dalrymple ef al. (1978).

trough and the relative narrow spacing of the 3-D sandwaves the complete neap-spring-neap sequence often escapes preservation (Boersma & Terwindt, 1981a). Examples of 3-D sandwaves, in our opinion, based on comparison of the structural characteristics of known intertidalexamples and subtidal equivalents, may be found in Nio et al. (1980, fig. 8), Terwindt (1981, figs 6 , 7 and 9) and Van den Berg (1982, fig. 7 ) .

Mud draping constitutes another difference between 2-D and 3-D sandwaves as well as between sub- and intertidal settings. In our experience mud draping occurs but is relatively rare in 2-D subtidal sandwave deposits although recently some remarkable well- preserved examples have been described (Nio et al., 1980; Visser, 1980; Allen, 1982d; Siegenthaler, 1982; Allen & Homewood, 1984; Teyssen, 1984). In 3-D sandwaves mud draping is even less frequent. In intertidal settings mud drapes are normally absent at

spring tide, due to the short slack water period. During neap tide, however, mud draping occurs in 2-D as well as 3-D sandwaves.

C O N C L U S I O N S

From our study on the Ossenisse intertidal shoal, it appears that only a few hydrodynamic and bedform shape parameters are relevant for palaeoflow analyses. The peak depth-average flow velocity of the dominant tide is the only usable hydrodynamic parameter. urn,, represents quite well the neap-spring variation, the diurnal inequality, the tidal dominance and is well correlated with the sandwave migration, especially for 3-D sandwaves. As sandwave migration is easily measureable in exposures, Urn,, may be estimated from &f; this is more precise for 3-D than for 2-D


sandwaves (Fig. 12). Other flow parameters as U*3, C,, zo are so scattered in the neap-spring cycle and are uncorrelated with the mean migration distance that they cannot be used in palaeoflow reconstructions in settings similar to the Ossenisse shoal.

From the morphometric parameters, the mean sandwave height in the field has the best response to the peak dominant velocity in the course of the neap- spring cycle, although time lags in the development of one to three tides occur. The mean sandwave length shows a similar tendency although to a lesser degree. All other morphometric parameters show such scatter that they are useless for palaeoflow analysis. As there are no quantitative relations between the peak dominant velocity and Is, nor 1, but only qualitative relations, the predictive value of A and 1 for om,, is very low. However, qualitatively the neap-spring variation in increase in may be reflected in the set height of the lateral sequence in (inter)tidal deposits, provided that no crestal erosion has taken place. The 3-D sandwaves show an additional feature: lowering of the lower set boundary towards spring tide.

As there appears to be no relationship between A and 1 and the maximum flow depth (hmaX) these parameters cannot be used for palaeoflow depth determinations in intertidal settings at least (Fig. 11). The same holds for the set height in intertidal deposits.

Several velocity thresholds could be established for sandwavemigration and alteration. The first threshold separates the immobile from the mobile sandwaves: u,,, : 0.5-0.6 m s - ' . The second threshold separates moving sandwaves, not showing changes in shape, from moving sandwaves with altering shapes : urn,, ,, : 0.75-0.80m s -I . Ebb caps occurred if urn,, ebb > 0.45 m s - ' . Complete reversal of sandwaves took place if both peak depth-averaged velocities for the dominant and subordinate tide exceeded 0.85 m s - ' . Such reversal can only be expected at a few locations on the shoal in 3-D fields where such high subordinate velocities occur. In 2-D fields the threshold of 0.85 m s - ' will not be reached.

Two-dimensional sandwaves occur in areas where a distinct velocity asymmetry exists with peak values of depth-averaged current velocity below 0.8 m s- and a unidirectional, but low sand transport rate. The changes in form and dimensions during the mobile period of these sandwaves in the neap-spring tide cycle are limited. The relaxation time is comparatively long.

Three-dimensional sandwaves are found in areas with, or without velocity asymmetry where peak values of the depth-averaged current velocity exceeds

0.8 m s - and a bidirectional sand transport exists. Towards spring tide these sandwaves become higher, mainly by deepening of the troughs; they also become more symmetrical. The relaxation time is comparatively short.

It was possible to makeafurtherdistinction between 2-D and 3-D sandwaves based on several properties. Incorporating the results of other authors we conclude that a boundary velocity of 0.8 m s - I separates 2-D from 3-D sandwave stability fields for grain sizes between 200 and 500pm in the velocity-depth diagram.

Another boundary between the 2-D and 3-D sandwaves of the Ossenisse shoal appears on the Vanoni bedform stability diagram relating Froude number to the water depth-grain-size ratio. This boundary was found to be h,,, " /dSo = 8 x lo3. Variability in current direction during periods of appreciable sand transport may be another distinctive feature for 2-D and 3-D sandwaves. In the 3-D sandwave fields much more variability in current direction was observed than in 2-D fields.

Another distinction, not relevant for palaeoflow analysis, for 2-D and 3-D sandwaves is the difference in height-length ratio. Only 2-D sandwaves were found if LIH > 35 and only 3-D sandwaves if LIH < 23. For 23 < L/H < 35 both 2-D and 3-D sandwaves occur.

Finally there are differences in sedimentary structures in 2-D and 3-D sandwaves. The 2-D sandwaves are made up of angular or tangential sets of a tabular nature. Topsets are absent; the tidal bundles are relatively thin, the bundles are arranged in neap- spring-neap lateral sequences, which are often re- markably well preserved. The 3-D sandwaves consist of festoon concave or sigmoidal sets and occasionally topsets. The bundles are thicker and the neap-spring- neap lateral sequences are often not preserved because of the high migration rate.

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TERWINDT, J.H.J. (198l)Originand sequenceofsedimentary structures in inshore mesotidal deposits of the North Sea. In Holocene Marine Sedimentation in the North Sea Basin (Ed. by S.-D. Nio, R. T. E. Schuttenhelm and Tj. C. E. van Weering). Spec. Publs int. Ass. Sediment. 5, 4-26. Blackwell Scientific Publications, Oxford.

TEYSSEN, T.A.L. (1984) Sedimentology of the Minette oolitic ironstones of Luxembourg and Lorraine: a Jurassic subtidal sandwave complex. Sedimentology, 31, 195-21 1.

VANONI, V.A. (1974) Factors determining bedforms of alluvial streams. J . Hydraul. Diu. Am. SOC. cin. Engrs, 100,

VANDEN BERG, J.H. (1982) Migrationoflargescale bedforms and preservation of cross-bedded sets in highly accretional parts of tidal channels in the Oosterschelde, SW Nether- lands. Geologie Mijnb. 61,253-263.

VISSER, M. J. (1980) Neap-spring cycles reflected in Holocene sub-tidal large scale bedform deposits : a preliminary note. Geology, 8, 543-546.

WIJBENGA, J.A.H. & KLAASSEN, G.J. (1983) Changes in bedform dimensions under unsteady flow conditions in a straight flume. In: Modern and Ancient Fluvial Systems (Ed. by J. D. Collinson and J. Lewin). Spec. Publs inf. Ass. Sediment. 6 , 35-48. Blackwell Scientific Publications, Oxford.

YANG, C.S. & Nio, S.-D. (1985) The estimation of palaeo- hydrodynamic processes from subtidal deposits using time series analysis methods. Sedimentology, 32,41-57.

ZARILLO, G.A. (1982) Stability of bedforms in a tidal environment. Mar. Geol. 48,337-351.

HY 3,363-377.


APPENDIX A

25

List of symbols U i7 o m a x

U* u* 3

Z O

C C3

L E

H R

h hnl,, fl

U

b

bla

A

E

s

- dom

- subord

SI VAI

= current velocity (m s-') = depth-averaged current velocity (m s- ') = maximum value of depth-averaged current

velocity in tidal semi-cycle (m s- ') = shear velocity (m s-I)

= m e a n of three maximum values of U*

= bed roughness (m) = Chezy roughness coefficient (mli2 s- I )

= m e a n of three maximum values of C

= maximum water discharge (h3 m - ' s- I )

= calculated sand transport per tidal semi cycle (m3 m ' tide - I )

= sandwave length (m) = mean sandwave length in sandwave field

= sandwave height (m) = mean sandwave height in sandwave field

= steepness index of sandwaves in sandwave

= height of crest above reference level (m) = depth of trough below reference level = water depth (m) = local water depth at moment that 0 = om,, = descriptive length of the lee side face of

bedform (m) =descriptive length of stoss side face of

bedform (m) = asymmetry index of sandwaves in sand-

wave field = mean migration distance over tidal cycle

(m tide- I )

= mean volume of eroded material due to migration of sandwaves in a tidal cycle (m3 m - tide I )

= mean volume of deposited material due to migration of sandwave in a tidal cycle (m3 m - ' tide-')

= peak depth-averaged velocity of the dominant tide (m s- ')

= critical mean velocity for the movement of sand (m s - ' )

= peak depth-averaged velocity of subordinate tide (m s- I )

= strength index = (urn,, = velocity asymmetry index = urn,,

(m s-')

1 (ml/2 s- 1

(m)

(m)

field

(m)

- i7cr,t)/i7crlt -

subord


Tides ummaxfl u m d x e b b u*3 fl ‘*3 ebb ‘3 0 ‘3 ebb m l i 2 s - I m l / 2 - 1 m s - ’ m s-’ m s - ’ m s-’

(a) 2-D sandwaves STI + 2 STl + 3 ST1 + 4 ST1 + 5 ST1 + 6 STI +7 STI + 8 STI + 9 ST1 + 10 ST1+11 STI + 12 STI + 13 ST1 + I4 STI + I5 ST1 + 16

DT I DTI + I DTI t 2 DTI + 3 DTI + 4 DTI + 5 DTI + 6 DTI +7 DTI t 8 DT1+9 DTI + 10 D T I t l I DTl + 12 DTI + I3 DTI + 14 DTI + 15

ST2 ST2+ 1 ST2 + 2 ST2+3 ST2 + 4 ST2 + 5 ST2 + 6 ST2 + 7 ST2 + 8 ST2 + 9 ST2+ 10 ST2+11 ST2+ 12

DT2+ 1 DT2 + 2 DT2 + 3 DT2+4 DT2 + 5 DT2 + 6 DT2+7 DT2 + 8 DT2 + 9

DT2+ I I

DT2

DT2+ 10

0.76

0.82

0.69

0.60 0.55

0.46

0.50 0.40 0.35

0.34 0.32 0.36 0.41 0.47 0.51 0.58 0.54 0.62 0.64 0.68 0.77 0.79 0.68 0.75 0.61

0.70 0.78 0.86 0.71 0.80 0.76 0.75 0.70 0.62 0.59 0.55 0.54 0.48

0.48 0.52 0.5 1 0.63 0.74 0.69

0.76

0.69

0.42

0.45

0.40

0.42 0.38

0.25

0.28 0.30 0.29

0.29 0.30 0.32 0.30 0.32 0.41 0.39 0.37 0.42 0.37 0.43 0.41 0.42 0.44 0.42 0.41

0.44 0.45 0.50 0.47 0.50 0.4 1 0.42 0.39 0.37 0.36 0.35 0.33 0.32

0.39 0-40 0.42 0.38

0.43

0.41

0.046

0.038

0.044

0.039 0.041

0.038

0.048

0.023

0.023

0.045

0.036

0.051

0.049

0.034

0.037

0.041

0.039

0-037 0.041

0.038

0.029

0.034

0.053

0.047

0.053

0.057

0.030

0.031

0.038 0.030

0.025

0.043

0.032

0.03 I

0.035

0.028

0.036

0.033

0.032

0.030

0.028

0.028

0.024 0.024

0.024

0.033

0.027

0.050

0.028

0.034

47

58

44

41 38

39

31

45

43

35

42

37

43

57

54

46

53

54 45

41

46

53

34

42

36

21

46

39

32 35

29

19

27

27

32

38

35

41

40

45

51

43

46 46

36

29

43

20

44

37

APPEN

z o n zo ebb Qmax n 10-3m 1 0 - ~ m m3s-’

6.7

0.1

0.9

0.9 1.7

3.8

7.2

1 .o

I .4

0.0043

0.0004

0.00 I 1

0.0023

0.0003

0.000 1

0.0004

0~0001

0.0002 0~0011

0.00 10

0,0004

0.0002

0.0020

0.0006

0.0024

0.0272

0.00 12

0.0027

0.0049 0.0023

0.0088

0.0343

0.0120

0.0069

0.0077

0.0022

0.0049

0.0028

0.0024

0~0001

0.0005

0~0010

0.0007 0.00 10

0.001 1

0.0067

0~0000

0.0176

0.0008

0.0035

0.95

1.03

0.80

0.6 1 0.5 1

0.55

0.58 0.42 0.40

0.3 1 0.26 0.29 0.34 0.49 0.59 0.72 0.71 0.74 0.68

0.9 I 1.12 0.99 0.93 0.62

0.90 1.08 1 .oo 0.70 0.74 0.65 0.90 0.8 1 0.69 0.60 0.5 1 0.52 0.39

0.40 0.5 I 6.42 0.69 0.6 1 0.74 0.63

0.69

0.76

Intertidal sandwaces 27

DIX B

m3m-1 tide ' ~ ' m m m m t i d e - ' m 3 m 7 ' tide-' ' m3m- ' tide-' Q, n SI VAI h,',,, A 1 m h m d x n (3% (2, 5 E

0.35

0.26

0.2 I

0.1 I 0.09

0.06

0.15

0.1 5

0.1 3

0.25

0.31

0.15

0.14

0.16

0- I 5

0.1 1 0.10

0.06 0.03

0.07

0.21

0.21

0.25

1.27 2.80 1.83 1.25

1.25 3.10 1.82 1.25

1.04 2.95 1.73 1.16

1.08 2.00 1.43 1.02 1.75 1.45 0.92

1.04 1.30 1.84 1.20

1.18 1.50 1.79 1.16 1.00 1.33 1.05 0.75 1.21 1.13

1.20 1.17 0.92 1.58 1.05 0.83 0.80 1.13 1.05 1.37 1.35 1.47 1.55 1.24 1.90 1.49 1.24 1.70 1-46 1.32 2.10 1.48 1.20 2.20 1.73 1.07 2.40 1.58 1.20 2.85 1.88 1.17 2.95 1.88 1.42 2.40 1.55 1.46 2.75 1.79 1.24 2.05 1.49 1.01

2.50 1.59 1.28 2.90 1.73 1.38 3.30 1.72 1.06 2.55 1.51 0.98 3.00 1.60 0.92 2-80 1.79 0.85 2.75 1.79 1.20 2.50 1.79 1.16 2.10 1.68 1.12 1.95 1.64 1.02 1.75 1.57 0.92 1.70 1.64 0.96 1-20 1.50 0.81

0.155

0.155

0.150 0.140

0.145

0.145

0.140

0.135

0.140

0.140

0.170

0.180

0. I75

0.175

0.175

0.160 0.175

0.150

0.150

6.85 6.99

6.97 6.40 6.26 6.25 6.29 6.25 6.15 6.22 6.26 6.19

6.16 6.10

6.02 6.10 6.05 6.09 6.09 6.09 6.35 6.35 6.05 6.17

6.15 6.23 6.10 6.03 6.05 5.99 6.05 5.97 5.91 6.09 6.03 5.93 6.05

2.45 2.03 0.96 5.85 2.15 1.58 0.97 0.114 6.06 2.68 1.75 1.00 5.94 2.45 1.82 0.92 0.148 6.07

1.12 5.90 2.80 1.77 0.91 0.135 5.96

1.12 6.03 2.45 1.68 1.10 0.160 6.28

0.124

0.134

0.147 0. I52

0.121

0.125

0. I24

0-102

0.131

0.120

0.1 16

0.178

0.127

0- I79

0.206

0.140 0-160

0-160

0- 190

0.12

0.16

0.15

0.15

40.3 2-33 39.6 1-70

0-98 1.86 2.06

40.0 1.91 36.6 2-73 39.8 3.21 42.3 3-24 40.0 2-83 39.8 2-81 40.3 4.80 41.0 5-29 41.5 2.64 42.3 3-02

43.0 2-72 41.0 2.63

32.5 2.88 40.2 2.47 43.0 2.31 41.5 3.03 40.7 3.57 41.0 3.33 37.8 2.43 38.0 3.46 34.0 3.24 33.0 3.71

34.0 2.36 34.0 2.26 33.6 1.90 34.0 1.93 40.0 1.41 35.0 1.36 40.2 2.14 40.8 2.59 45.3 3.25 45.0 4.70 46.5 2.71 44.8 3.66 40.0 3.23

46.5 1.63 42.0 2.34 47.5 2.93 46.0 2.14 46.0 3.82 47.6 3.24 40.7 2.56 40.2 3.18

0.01 0.06

0.07

0.10 0.09 0.17 0.10 0.27 0.17 0.26 0.37 0.28

0.36 0.42 0.28 0.19 0.28 0.30 0.10 0.26 0.08 0.09 0.02

0.01

0.02 0.12 0.13 0.20 0.15

0.20

0.55 0.60 0.15

0.33 0.1 1

0.33 0.45 0.26 0.35 0.48 0.49 0.32 0.52 0.66

0.71 0.67 0.42 0.33 0.65 0.49 0.48 0.56 0.27 0.48 0.28 0.04 0.16

0.20 0.28 0.18 0.39 0.61 0.5 1 0.40

0.22

0.08

0.22 0.28

0.2 1 0.20 0.39 0.35 0.53 0.51 0.50 0.83 1.08

0.87 0.86 1.20 0.60 0.48 0.39 0.37 0.36 0.47 0.1 1 0.15 0.40 0.2 1

0.29 0.19 0.53 0.25 0.27 0.57 0.85


Tides ummaxfl urnaxebb u*3 fl u*3 ebb c3 fl c3 ebb z o fl zo ebb Qmax fl m s - ' m s- ' m s - l m s - l m l / Z - I m l / Z S - l 10-3m 10-3m m3s-l

ST3 ST3+ 1 0.74 0.42 0,048 0,083 42 15 0.0008 0.0486 0.68 ST3 + 2 ST3 + 3 0.77 0.46 0,041 0,027 52 49 0.0003 0.0006 0.98 ST3 + 4 ST3 + 5 0.68 0.41 0,049 0.026 42 43 0.0015 0.0007 0.65

(b) 3-D sandwaves

ST1+2 STI + 3 ST1 + 4 ST1+5 ST1 + 6 ST1+7 ST1 + 8 ST1 + 9 ST1 + 10 ST1+11 ST1 + 12 ST1 + 13 ST1 + I4 ST1 + 15 ST1 + I6

NT1 NT1+ 1 NT1+2 NTI + 3 NT1+4 NT1+5 NT1 +6 NT1+7 NT1+8 NT1+9 NT1+ 10 N T l f l l NT1+ 12 NT1+ I3 NT1+ 14 NT1+ 15

ST2 ST2+ 1 ST2 + 2 ST2 + 3 ST2 + 4 ST2 + 5 ST2 + 6 ST2 + 7 ST2 + 8 ST2 + 9 ST2+ 10 ST2+11 ST2+ 12

NT2 NT2+ 1 NT2 + 2

1.02 0.85 0.9 1 0.75 0.74 0.82 0.88 0.62 0.59 0.50 0.44 0.54 0.58 0.40 0.37

0.42 0.41

0.6 1 0.69 0.83 0.85 1 .oo 0.87 1.14 0.9 1 1.27 0.88

I .20 I .oo 1.07 0.83 0.96 0.75 0.89 0.84 0.76 0.63 0.50 0.53 0.46

0.55 0.50 0.50 031 0.48 0.46 0.45 0.45 0.45 0.47 0.40 0.38 0.43 0.38 0.30

0.34 0.28

0.40 0.34 0.47 0.44 0.51 0.46 0.54 0.50 0.53 0.53

0.62 0.58 0.62 0.52 0.52 0.55 0.50 0.55 0.50 0.48 0.46 0.42 0.40

0.47 0.56 0.50

0-027

0.018

0.041

0.037

0.043

0.064

0.046

0.043

0.066

0.048

0.033

0.036 0.028

0.025

0.0 18

0.030

0.021

0.027

0.020

0,031

0.046

0.026

0.280

0.380

0.035

0.030

0,040 0.017

0.022

0.016

60

56

29

53

56

39

58

61

44

52

70

65 82

63

70

39

44

27

30

40

29

55

60

38

35

45

48 82

54

65

0.2

0.2

11.1

0.6

0.4

4.7

0.4

0.3

0.3

1.2

0.1

0.1 0.0

0.2

0.0

2.9

2.8

9.6

1.1

3.6

19.7

0.5

510.3

690.8

3.0

0.6

4.0 0.0

0.2

0.0

2.40 1.96 2.07 1.64 1.51 1.81 1.92 1.33 0.96 0.79 0.68 1.02 1.30 0.83 0.78

0.76 0.62

1.32 1.64 2.06 2.22 2.68 2.34 3.19 2.50 3.28 2.39

3.65 3.18 3.25 2.41 2.57 1.81 2.23 2.04 1.66 1.25 0.91 1 .oo 0.83

0.83 1.06 0.92


1 .oo 6.07 38.3 3.56 0.62 0.57 0.30 2.70 1.76 0.92 0.160 6.20 0.17 36.3 3.54 0.20 0.72 0.28

1.08 5.57 31.8 3.20 0.46 1.66 0.22 2.85 1.67 1.28 0,165 5.76 0.13 35.3 2.52 0.15 0.41 0.57

1 .oo 5.5 1 48.3 1.28 0.93 0.14 2.40 1.66 0.96 0.08 0.13 0.68

0.58

0.12

0.36

0.13 0.05

0.01

0.04

0.0 1

0.06

0.14

0.38

0.98

0.83

0.46

2.82

0.60

0.12

0.16 0.15

0.06 0.07

4.10 3.25 3.55 2.75 2.70 3.08 3.40 2.10 1.93 I .48 1.18 1.70 1.90 1 .oo 0.85

1.85 1.70 1.82 1.47 1.54 1.77 1.96 1.38 1.30 1.05 1.09 1.42 1.90 0.197 5.26 1.35 2.25 0.212 5.26 1.05 2.07 0.210 5.30 1.23 2.10 0.203 5.32

1.10 1.24 1.82 0.200 5.32 1.05 1.46 1.52 0.210 5.32

2.05 2.45 3.15 3.25 4.00 3.35 4.70 3.55 5.35 3.40

5.00 4.00 4.35 3.15 3.80 2.75 3.45 3.20 2.80 2.15 1.50 1.65 1.30

1.53 2.03 1.77 1.93 1.96 1.89 2.1 1 1.82 2.40 1.66

1.94 1.72 1.73 1.60 1.85 1.36 1.78 1.53 1.52 1.32 1.09 1.26 1.15

2.16 2.33 2.48 2.61 2.68 2.69 2.80 2.75 2.80 2.72

3.04 3.18 3.04 2.90 2.68 2.41 2.50 2.43 2.18 1.98 1.82 1.88 1.80

1.76 1.90 1.84

0.206 0.194 0.197 0.201 0,190 0.189 0.277 0.329 0.370 0.375

0.400 0.414 0,387 0,381 0.325 0.335 0.275 0.260 0.288 0.277 0.285 0.269 0.261

5.31 5.28 5.22 5.32 5.73 5.86 5.94 5.98 5.90 5.86

5.90 6.06 6.27 6.35 6.06 5.93 6.06 6.03 5.65 5.63 5.55 5.48 5.55

0.104 0.094 0,101 0.097

0.1 10 0.138

0.095 0.082 0.079 0,077 0.07 1 0.070 0,099 0.120 0.132 0.138

0.132 0.130 0.127 0.131 0.121 0.139 0.1 10 0.107 0.132 0.140 0.157 0.143 0,145

31 2.83 30 3.24 32 2.69 30 3.27

32 3.14 31 3.14

32 3.60 32 4.87 31 3.26 29 3.59 46 2.34 39 2.85 21 1.14 21 1.82 15 1.99 15 2.05

16 1.93 15 1.53 17 1.77 18 1.80 20 2.15 19 2.69 23 1.84 24 2.34 19 2.25 19 2.57 18 2.55 19 2.41 19 1.85

0.25 0.01

0.04

0.17 0.26 0.42 0.94 0.35 1.67 0.35 1.24 0.38

1.69 0.79 1.08 0.30 0.78 0.19 0.50 0.30 0.22 0.12

0.06

0.25

0.59 0.12

0.43 0.29 0.92 1.55 0.66 4.55 1.16 3.66 1.16

5.34 2.66 4.40 1 .oo 2.56 0.55 1.74 0.56 0.82 0.32 0.18 0.52 0.52

0.50

0.6 I

0.28

0.5 I 0.52 1.31 1.15 0.92 3.67 1.56 3.56 I .63

4.92 3.28 3.68 0.99 1.45 1.10 0.77 0.72 0.68 0.60 0.33 0.52 0.25


NT2+3 NT2+4 NT2+5 NT2 + 6 NT2+7 NT2+8 NT2+9 NT2+ 10

ST3 ST3+ 1 ST3+2 ST3 + 3 ST3+4 ST3 + 5

0.65 0.66 0.8 1 0.77 1.12 0.83 1.14 0.83

0.99 0.75 0.99 0.9 1 0.88 0.67

0.43 0.45 050 0.48 0.5 1 0.42 0.48 0.48

0.52 0.49 0.49 0.47 0.42 0.47

1.30 0.034 0,026 55 47 0.4 0.9 1.42

1.88 0.047 0.024 48 48 1.3 0.3 1.73

2.93 0.060 0.034 40 37 4.1 7.3 2.13

3.15 0.052 0.046 45 30 I .9 16.9 2.27

2.73 0.074 0.390 30 35 19.3 673.0 2.09

2.80 2.75 2,43

0,060 0.040 34 33 12.3 9.8 1.80


Qs o SI VAI hmaxn A 1 m m m m 3 m - 1 ' tide- I

2.25 1.51 2.00 0.09 2.30 1.47 2-15

3.05 1.62 2.32 0.31 2.85 1.60 2-25

4.60 2.20 2.62 0.90 3.15 1.98 2.57

5.70 2.38 2.76 0.69 3.15 1.73 2-74

~ ~~~

0.238 0.229 0.247 0.252 0.229 0.180 0.191 0.219

5.59 5.59 5.61 5.63 5.63 5.63 5.34 5.29

0.1 19 0.107 0.106 0.112 0.087 0.070 0.069 0.080

(LIH) ($1 s E m tide-' m'm-' tide-' m'm-' tide-'

21 2-80 22 2.92 0.02 0.66 0.08 21 2-96 0.26 0.45 0.75 20 2.25 0.27 0.68 0.97 23 2.20 1.12 3.50 1.29 23 1-94 0.22 0.92 0.83 26 1.94 0.93 3.50 1.70 20 2-09 0.33 0.71 1.75

3.95 1.90 2-76 0.249 4.24 0.090 17 1.81 1.00 3.08 I .65 1.47 2.75 1.53 2.78 0.212 4.16 0,091 18 2.23 0.26 1.20 0.68

3.95 2.02 2.83 0.255 5.26 0.090 22 2.31 0.76 2.00 1.78 1.10 3.55 1.94 3.02 0.235 5.29 0.078 33 2.34 0.26 0.82 1.06

3.40 2.10 2.76 0.238 5.24 0.086 33 2-18 0.37 1.20 1.21 0.65 2.35 1.43 2.68 0.02 0.81 1.70

the behaviour of intertidal sandwaves during neap-spring tide cycles and the relevance for...

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