the lunar semi-diurnal tide in cook strait, new zealand

The Lunar Semi-Diurnal Tide in Cook Strait, N e w Zealand

By 1%. A. Heath

UDC 551.466.72 ;M462

Summary. The lunar semi-diurnal tide in Cook Strait responds to two tidal systems one on each end of the S~rait, these systems being about 1400 out of phase. The tide in Cook Strait and that in the adjacent Tasman ,Bay are examined by numerical integration of the momentum and continuity equations with tidal forcing from both the open boundaries. This model simulates the tide very closely. The region of rapid phase change in the narrowest part of Cook Strait is found to be consistent with two overlapping standing waves. Elsewhere the tidal wave has a dominant standing wave component.

Die halbtiigige Mondtide in der Cook-StrMle, Neuseeland (Zusammenfassung). I n der Cook- Stral3e wi rd die ha lb tgg ige M o n d t i d e yon den E n d e n der Stral3e her d u r c h zwei Schwingungs- sys t eme angeregt , de ren Phasend i f fe renz 1400 betr/~gt, lV[it t I i l fe eines n u m e r i s c h e n Mode]ls wet- den die regionale Ver te i lung yon P h a s e u n d A m p l i t u d e dieser Tide sowie die S t romverh / i l tn i s se sowohl ffir die Cook-Stral3e als a u c h for die b e n a c h b a r t e T a s m a n - B u c h t u n t e r s u c h t . Ff i r die l%echnung werden die h y d r o d y n a m i s c h e n Bewegungsg le i chungen u n d die Kon t inu i t i i t sg l e i chung in ve r t i ka l in tegr ie r t e r F o r m b e n u t z t ; a n den offenen ~ g n d e r n wi rd die Tide vorgegeben . ]:)as Modell g ib t die na t i i r l i chen Verh/~ltnisse r ech t g u t wieder . Es zeigt sich, daI~ der P h a s e n s p r u n g a n der engs t en Ste]le der Cook-Stral3e d u r c h Ube r ] age rung zweier s t ehende r Wel len en t s t eh t . I n den i ib r igen Geb ie ten h a t die Tide f iberwiegend den C h a r a k t e r einer s t e h e n d e n Welle.

La marde lunaire semi-diurne dans le ddtroit de Cook, Nouvelle-Z61ande (Rdsumd). L a marde luna i re semi-d iurne dans le d4%roit de Cook rdpond /~ deux sys tbmes de marde, u n g chacune des extrdmitds du ddtroit, ees syst~mes dtant ddphas~s d'environ 140 ~ La marde dans le ddtroit de Cook et clans la baie adjacente de Tasman sont examindes par intdgration numdrique des 4quations de moment et de eontinuit4 avee la marde imposde aux deux extrSmitds ouvertes. Ce module simule de tr6s pr6s ]a marde. On a trouv4 que la rdgion de ehangement rapide de phase dans la partie ]a plus 4troite du ddtroit de Cook est compatible avec deux ondes stationnaires se recou- vrant. Ailleurs, ]'onde de marde a une eomposante d'onde stationnaire dominante.

Introduction

The New Zealand tide regime is unique in that the phase of the major components, the principal lunar and solar semi-diurnal constituents (M2, $2) embrace the complete range from 0 to 360 degrees (J. A. T. B y e and 1%. A. H e a t h [in press]). Among the interesting effects this produces is a large phase and amplitude difference in the principal lunar semi- diurnal tide on either side of Cook Strait, the Strait separating the North and South Islands of New Zealand (Fig. 1). Cook Strait at its narrowest point is about 22 km wide but from there it opens out rapidly to the north and south (Fig. 1). Of the 1400 difference in phase of the M 2 tide between New Plymouth and Wellington (Hydrographic Department [1963]) a distance of about 270 km, 118 o takes place between Wellington and Makara, a distance of only 28 km through the Cook Strait Narrows. Four closely-spaced tidal elevation gauges have been operated in this region of rapid change in phase by A. E. G i l m o u r [in press], two each on either side of Cook Strait. This rapid change produces large tidal flows, with speeds of up to 3.5 m s: I having been reported (Hydrographic Department [1958]). B. 1%. Olsson [1955] and A. E. G i l m o u r [1960] both studied the tidal flow in'Cook Strait and found that the flow was highly variable. This variability superimposed on the tidal flow presumably results from the influence of the winds for in Cook Strait orographic influences make gales common.

H e a t h , Lunar Semi-Diurnal Tide in Cook Strait 215

Although there have been measurements of specific aspects of the tides in Cook Strait to date there has been no account given of the overall dynamics involved. In ~his paper the details of the tidal waves in Cook Strait Narrows, where the phase changes rapidly with distance, are examined firstly by fitting analytical Solutions to the wave equation to the observed phases (Fig. 1). Then a numerical model, with open boundary forcing is used to try to simulate the broad features of the tide on a larger scale (Fig. 1) - the grid size of the numerical model is too coarse to allow the details of the region of rapid phase change in the Cook Strait Narrows to be studied and therefore it was necessary to examine the possible simple analytical solution.

IT,~ 172 ~ 173 ~ 174 ~ ,75 ~ 176 ~

Farewell

Inlet 300 . . . . . . .

275

41 ~

We / u~.9,7/. Cape Palliser

ape Campbell

I I I I

Fig. 1. Isolines of the phase of the principal lunar semi-diurnal tide in and near Cook Strait. The rectangular outline gives the outer bounds of the numerical model

The lunar semi-diurnal tide in the Cook Strait Narrows

We first consider simple one-dimensional analytical solutions to the wave equation which fit the observed phase and amplitude changes in the Cook Strait Narrows. Rotational effects on tidal waves are strong with possible analytical solutions existing in the form of Kelvin and Poinear6 W~ves. However, because Cook Strait is narrow compared with the cross- stream scale of a Kelvin Wave the barotropic tidal wave can be considered as one-dimensional.

The rapid phase change cannot be accounted for by either a single progressive wave (the phase speed being too large) or by a single standing wave. A further possibility is to r<atch two separate standing waves each with a node at the same point in the centre of the Straits. However in this ease the large phase change would only take place at this node. Also there would be a discontinuity in the slope of the sea surface at the node. The most likely simple solution for the tidal elevation which fits the observed tides is two overlapping standing waves (Fig. 2) of the form,

= A cos ~t sin #1 x + B cos (wt-- ~0) sin/co ( L - x), (i)

216 Deutsche }Iydrographisehe Zeitschrifg, Jahrgang 27, 1974, } I e f ~ 5/6

where A, B are constants, (o the lunar semi-diurnal tidal period, /%/~2 the wave numbers associated with the standing wave with a node in the northern (x = 0) and southern (x = L) parts of the Narrows, x being positive towards the south. In that part of the Strait south of x = L and north of x -- 0 where the phase change is small, other waves can be matched

-.4 E < "2

- 300

r - 25(

~ - 2 0 (

-15C

x observed

-1ooL~, i i I I p l i i Wellington 50 40 Oteranga 30 20 Makara 10 km 0

Bay Titan Bay

Fig. 2. The phase (in degrees, lower curves) a n d a m p l i t u d e (in mete rs ) in Cook S t r a i t Na r rows g iven b y two s t a n d i n g waves. T he x 's give t h e obse rved va lues a t Wel l ing ton , O t e r a n g a Bay , M a k a r a a n d T i t ah i Bay . The solid curves are for x = 0 a t Makara , t he d a s h e d eurves for x = 0 a t T i t ah i B a y

to those given by Equation 1. Over the distance L the phase changes rapidly by ~0. The fact that amplitude of the principal solar semi-diurnal tidal component ($2) , with a period of 12 h, decreases rapidly east of Makara (Table 1) indicates that the reflection of the S 2 wave advancing from the west must take place in Cook Strait Narrows. This agrees with the solution presented here, the characteristics of the tide in northern Cook Strait being determined by the tidal wave on the west coast of New Zealand while the characteristics of the tide east of Cook Strait Narrows are determined by the wave on the east coast of New Zealand.

Taking the observed phases at Wellington, Oteranga Bay, XKakara and Titahi Bay (Table 1, Fig. 2) as representing the area of rapid phase change gives L = 54 km, g0 = 140 ~ At x = 0 we have B sin k 2 L = a, where a is the M 2 amplitude at Titahi Bay (Table 1). Similarly at x = L we have A sin /c 1 L = b where b is the tidal amplitude at Wellington (Table 1). The tidal phase and amplitude given by Equation 1 are plotted-in Fig. 2 for a representative depth of 300 m with /q = # z. Between Makara and Titahi Bay the phase change is less rapid than between Wellington and Makara which could indicate that most of the reflection of the wave from the soutt] takes place nearer Makara than Titahi Bay. The phase and amplitude given by Equation 1 has also been plotted for this reduced value of L = 35 km. Considering the simplicity of the solution with total reflection from one point for each wave (x = 0, x = L) tile fit to the observation is good, being better for the smaller than for the larger value of L. Clearly more closely-spaced tidal observations are needed to determine the exact form of the phase change with distance.

The speed averaged across the Strait associated With the wave given by Equation 1 is

U = U 0 [ - A sin (or cos/c~ x + B sin ((ot - ~o) cos #1 (L - x)], (2)

where U o = ~ , h the depth, g the acceleration of gravity. The maximum speed at, say,

x = 0 occurs when ~t = 52 o and is 1.3 m s -1. This compares favourably with current observations in the Strait and the values given by the numerical model (Fig. 6). Further, using Equation 2 as a first approximation to the flow in Cook Strait Narrows it can easily be shown that the non-linear field accelerations are small compared with the other forces. They will not therefore be included in the numerical model.


A numerical model of the semi-diurnal tide in Cook Strait

For the purposes of numerical simulation the bounds of Cook Strait were taken to extend naturally from latitude 40~ to 41~ (Fig. 1) and thereby including all of the northern coast of the South Island. This then allows the boundary elevations to be specified in positions away from the region of immediate interest, the Cook Strait Narrows and Tasman Bay.

The numerical model used was tha t developed by Dr J. A. T. Bye of the Flinders Uni- versity of South Australia, as a tool for evaluating the response of the ocean to different types of forcing (J. A. T. B y e [1974]). The vertically integrated continuity and momentum equations for a homogeneous ocean in spherical polar cordinates are taken as

a t /+ 1 I a U aV ] ~/ ~ - ~ + ~ c o s 0 =0, (3)

au gH R U, (4) at I V = a c o s 0 a~

aV4-IU_ gH a~l at a a0 Rlv]V, (5)

where 2, 0 are the longitude and latitude respectively, a is the radial distance from the centre of the earth, ~ is the elevation of the sea surface taken as positive upwards, U, V are the volume transports positive to the east and north respectively, v the mean velocity, / the Coriolis Parameter 2 co sin 0, co the earth 's angular velocity, H the depth of the water, g the c~ceeleration of gravity, R the quadratic frictional coefficient (taken as R = 0.0025) i.e., differing from Laplace's Tidal Equation in that the direct forcing through the equilibrium tidal terms

a cos 0 a~. etc.

is not included. Now we transform the earth's surface on to the x, g plane by the use of the Mercator projection where

x=a , t. 1 a 1 a

The operators - - a cos 0 a~' a a0 expressed in the new coordinates are

1 a a 1 a c~ a c o s 0 a]~--Max ' a aO -M~y '

where M = sec 0.

The area under study is bounded by latitudes 40~ to 41~ and longitudes 172040'E to 175~ which is approximated by a Mercator projection with M = M 0 = sec 00, where 00 is the latitude of the centre of the model - the grid points then have equal geometrical spacing on the Mercator map. Transforming (3-5) to the x, y coordinates gives

an / a u " a V \ a +Mo =0,

a u an at - I v = - g H i o R U,

(6)

(7)

~V+l an U = - g H Mo R V. (s)

218 Deutsche ttydrographische Zeitsehrift, Jahrgang 27, 1974, I-Iefg 5/6

The system of Equations (6-8) is solved numerically using a space and time staggered finite- difference scheme. The difference equations corresponding to the system are

n n n At U" -- U" + " Vi j_~) , ~ij = ~ i j - - ~ 8 8 ( i + l j i - l j V i i + l - - (9)

U" +1= n Atg -x . . ~ . R 2 _ iS U i j -- ~ 8 8 H i j ( ~ i + 1 j - ~ i _ l j ) ~F /a t , j -- l~x.~ " (V i j -17 V: ; ) I /2U~j ,

tj (lO)

where

V n + l = V n - ~ H Y j ( ~ j + l - - ~ ] n j _ l ) - /A t ~7 n + l - 2 ([7"+12 + vn2)l/2vn.. ' ij ij --ij ~ Y x--ij tj tj

ij

Bi~ = lff2(Hi j+l + H/j_1),

(11)

and

HYii = l~2(Hi+l j + H i - 1 j) '

H/j ~ (/fl x- 1 j --x = + H i + l j ) =

--y

= 1/4(Hi+l j+l + H i - l j+l + H i + i j - 1 + H i - i j - i ) "

The Coriolis Parameter is approximated by the value on a/~ plane i.e., / =/0 +/~ AS (j _ N ~ )

where y)" = j AS is the y coordinate of the ?" th horizontal line, N is the total number of horizontal lines, [0 is the value of [ at the centre of the model 0 = 00, 2 ~o sin 00, 00 = 40~ and

1 ~1 o=o0" fl a ~ At solid boundaries the velocity component normal to the boundary is specified

to be zero. The finite difference network consists of a network of 32 x 24 lines and the depths

(Fig. 3) which are specified at each grid point were obtained from J . W . B r o d i e [1965, 1966]. The line spacing AS was chosen as 5 minutes of longitude which at the latitude of the centre of the model is 6.94 kin. The time step At was chosen to satisfy the stability criterion for long waves.

2 AS At < - -

(g Hmax) �89

where//max is the maximum depth. The value of At used was 1.33 min.

B o u n d a r y E l e v a t i o n s The amplitude and phase of the M~ tidal wave was specified at four land boundaries,

two on the southern side of Cook Strait (near Cape Campbell and Cape Palliser, Fig. 1) and two on the northern side of Cook Strait (near Cape Farewell and near the mouth of the Rangi- tikei River). Of these four land boundaries, harmonic constants have been published only for Cape Campbell (Table 1). The constants for Cape Palliser were found by subtracting the amplitude and phase differences between the tide at Cape Palliser and Wellington, given in the Admiralty Tide Tables, (e.g. Hydrographic Depa~ment [1963]). The values for the Rangitikei River mouth were found by averaging the amplitude and times of high water at the adjacent Wanganui and Manawatu Rivers (Fig. 1) relative to the harmonic constants


Fig. 3. The bathymetry (in meters) of the area contoured from the depths at the grid points in the numerical model. Original depths taken from J. W. Brodie [1965, 1966]. The numbers in circles 1-5 give the positions at which the observed and computed current velocities are shown

(Figs, 6-7)

for Westport given in the Admiralty Tide Tables, (e.g. Hydrographic Department [1963]). Similarly for Cape Farewell the values were found by averaging between Collingwood and Whanganui Inlet (Fig. 1). The harmonic constants used were

Place Amplitude Phase

m

Near Cape Campbell 0.64 1510 Cape Palliser 0.60 1420

Near Rangitikei River 1 2810 Cape Farewell 1.6 2740

The tidal elevations at these four points were specified at 22.50 intervals of the tidal cycle (i.e., once every 46.6 min). On the grid points along the open boundaries the tidal elevations were specified by linear interpolation between the appropriate two land boundaries. This can be expected to give a good approximation to the actual tide elevations, for there is little change in the phase of the tide along either the southern or northern open boundaries.

Numerical model results

The model was run for 2300 time steps of 1.33 min giving four complete tidal cycles. Tidal elevations and velocities were printed every lunar hour. The tidal characteristics over the last tidal period will be used for comparison with the observations.

220 Deutsche Hydrographisehe Zeitschrift, Jahrgang 27, 1974, Heft 5/6

255--285

Tasman Bay

272

195-225

135-165

~'~-~I151

Fig. 4. Phase (in degrees) of the principal lunar semi-diurnal tidal component from the numerical model at 300 intervals. The nmnbers ~round the coast give the observed values

C o m p a r i s o n of P h a s e The phase of the M~ tide within 300 (1 lunar hour) intervals is shown in Fig. 4. The

phase in the model agrees very closely with those observed with a region of slow phase change in the Cook Strait Narrows and Htt]e change elsewhere. As was previously explained, the M~ tide in this region is consistent with overlapping standing waves.

C o m p a r i s o n of A m p l i t u d e Contours of the M~ tidal amplitude are shown in Fig. 5. The agreement with the observed

amplitude is generally good with large amplitudes in the north, small amplitudes in the Cook Strait Narrows, and larger amplitudes again in southern Cook Strait. The one excep- tion is at Nelson, in the head of Tasman Bay, where the model amplitude is larger than that calculated by harmonic analysis. However, using the observed range of spring and neap tides at other locations in Tasman Bay as well at Nelson gives the estimates of the M 2 amplitudes shown below.

Location Latitude Longitude M2 Amplitude from Tidal Range

m

Nelson 410 16'S 1730 16'E 1.3 Astrolabe 400 58' 1730 03' 1.8 Co]lingwood 400 40' 172 ~ 40' 1.6

The fact that the amplitude for Nelson estimated from the tidal range at spring and neap tides is about the same as tha t given by harmonic analysis gives us some confidence in these

[ H e a t h , Lunar Semi-Diurnal Tide in Cook Strait

./ 221

\ 0.2~

Fig. 5. Amplitude (in meters) of the principal lunar semi-diurnal tidal component from the numerical model. The numbers around the coast give the observed amplitudes

estimates. The amplitudes at the other two locations (these values are shown inside squares in Fig. 5) are larger than at Nelson and of the same size as shown in the model. The smaller amplitude at Nelson probably reflects the effeet of tidal dissipation on the extensive mudflats in Nelson Harbour.

C o m p a r i s o n of T i d a l C u r r e n t s The tidal velocity components in the model near five positions (Fig. 3) where current

observations over a tidal cycle have been made (Hydrographic Branch [1960]) are shown along with the observed components in Figs. 6 and 7. The tidal streams and representative current velocities at seven locations are shown at quarter cycle intervals in Fig. 8.

Tidal ellipses in this region have essentially degenerated into straight lines. There is good agreement between the model and observed phase of the velocities and between the speeds in the areas of large flow. This close correlation emphasises the fact that the M 2 tidal components must dominate the flow in Cook Strait for the observed flow values also include other tidal constituents and the mean flow. The model velocities in Tasman Bay (Fig. 7) did not correlate as well as those in Cook Strait. This probably reflects the influence of the other significant tidal constituents in this area (Table i) notably the larger S~ tide.

Except in Cook Strait Narrows the minimum tidal speed occurs near mid-tidal condL tions indicating that in these regions the tides have a dominant standing wave component. In the centre of the region of rapid phase change in Cook Strait Narrows (i.e., g2 -- 215) the ~]e~ximum tidal speed occurs also at mid tide. However the analytical solution (Equations 1 and 2) for the two overlapping standing waves indicates that although the phase of the tidal elevations changes rapidly in Cook Strait Narrows the phase of the tidal velocities is nearly constant. The numerical model agrees with this situation (Fig. 8). There is good agreement of the maximum speed in Cook Strait for the analytical solution, the numerical model, and that observed, the speed being near 1.2 m s -I.

222 D e u t s c h e H y d r o g r a p h i s c h e Zeitschrift , J a h r g a n g 27, 1974, H e f t 5/6

North STATION 3 North STATION 5 t High Tide

0 41 "-C~pe Campbell ms [, / t High Tide 0.8

0-2L t ~ " ~ 0.6 ,

I ~ o. T - o . :

-0.41- C East

0.2 r .- ........ -0., ms , , , : / " , ~" . ._.~ . . . . 12_0.z ~ / 1 2.~._~___.~,.. -~- 5 6 7 8 9 10 11

Mean 0-06 at 177~ _0.21.- ,~ .... .-" East

. North STATION 4 0.6[-- , I

i f 0"4p /

~/H igh Tide uz l - C~.pe Campbell 0 2 F

m~-'O/ ] . . . ~ _ _ 3 . j ~ 1,1 I? o.I

East t o 4 L 1 High Tide . . . . . . . - " /

0-2l.- s "'~ "" -0"6L- ms~/ I ? .3 4 ~ i

0"2~ " ~ / " Mean 0.01 at 158~T

6 7 8 9 10 1 .1"12. " . ' " ~ ~ ' ' ~...L Lunar

I 2 3 4 5 " ~ .,,.,,I/ Hours

High Tide t

kN. Lunar ! i ! i

1 2 3 4 / i 6 7 8 9 10 l l \12Hours \

s s s 4'

Mean 0.02 at 310 ~ T

F ig . 6. T ida l ve loc i ty c o m p o n e n t s at S ta t ions 1 (40~ 175~ a n d 2 (41~ 1740 29 .6 'E ) in Cook Strait . The s ta t ion pos i t ions are shown in Fig . 3. The sol id curve g ives the c o m - p o n e n t s from the numerical model , the dashed curves g ive the observed c o m p o n e n t s from Chart IxTZ46 (Hydrographic Branch [1960]). The m e a n of the observed ve loc i t ies is also g iven

Between the times of high and low tides near Cape Campbell the tidal flow is directed northwards through Cook Strait and into Tasman Bay where high tide occurs about 4 h after that at Cape Campbell (Fig. 8). Between low and high tide at Cape Campbell the flow is directed out of Tasman Bay and south through Cook Strait. The maximum tidal excursion occurs in Cook Strait Narrows and is about 17 km.

Conclusion

The tidal wave in both Cook Strait and Tasman Bay away from Cook Strait Narrows has a predominant standing wave component, the wave on either side of the Narrows being driven by the separate out of phase offshore tidal systems. Further long term tidal elevation measurements will be needed to determine the extent of the progressive wave component or to determine if any phase differences not due to experimental limitations are caused by enhanced tidal dissipation.

There is a marked increase of the tidal amplitude in Tasman Bay both in the observations and the model. Strong interaction between the tidal systems on either side of Cook Strait produce a region of rapid phase change'and large flow in the narrowest section of Cook Strait with little tidal energy passing through from one coast to the other. The good agreement between the observed flow in Cook Strait Narrows and that given by the barotropic numerical model would suggest that if baroclinic tides are present, the modal structure is such that the horizontal velocity component near the sea surface is small.


North STATION 2 STATION 1

m s -1 s

1"0

0"8 - \ \ High Tide 0-6 "~,~ phase 215~

-t "\ 0'4 High Tide . .. ', \ ,v 0"~ -Cape Campbell \ ~ /

-0"2

- 0.4 " , \

0"~

-1"0

I' / \ t i

1 ~ 6 7 8 9 10 11 12 ,_ _r . , ~ , ~='~'~-~ . . . . . .

-0 .4L Mean 0"09 ms-' at 203~ \

High Tide t

6 7 8 9 1o 11...~2 r " �89 3 '4 b - ' ~ ' ~ ' ' - ' ' - - - : . . . - ' " " ~ , f Lunar Hours

1 ? ~ ,} ? 6 . " " . . . . . . . . . . , , | s ~ . I r l |

- - ~ 7 8 ~ 10, 1 1 " ' q 2 " - . . . . . , . - ' ' ' - . . . . Lunar Houm

Mean 0.005 ms-' at 338~

Fig. 7. Tidal velocity components at Stations 3 (41~ 173~ 4 (40~ 173~ and 5 (40~ 174~ in western Cook Strait and Tasman Bay. The station positions are shown in Figure 3. The solid curve gives the components from the numerical model, the dashed curves give the observed components from Chart NZ46 (ttydrographie Branch [1960]) and Chart

NZ 61 (Hydrographic Branch [1960]). The mean of the observed velocities is also given

T a b l e 1 Phase g (in degrees, referred to Greenwich Mean Time) and amplitude A (in meters) of the principal

lunar (Ms) and solar ($2) semi-diurnal constituents in and near Cook Strait taken mainly from the Admiralty Tide Tables 1964 (Hydrographic Department [1963]). The constants for Oteranga Bay, Titahi Bay, Whekenui (Tory Channel) and Lake Grassmere are from

A.E. G i l m o u r [in press]

Place Lati tude Longitude gM~ AM~ gS2 A S 2

New Plymouth 390 04'S 1740 03'E 277 1.22 318 0.34 Westport 410 44' 1710 36' 309 1.13 349 0.30 Nelson 410 16' 1730 16' 280 1.31 335 0.40 Greville Harbour 40~ ' 1730 48' 272 1.16 324 0.46 Havelock 410 !7' 1730 46' 285 0.88 050 0.34 Pieton 410 17' 1740 00' 249 0.49 331 0.21 Tory Channel 410 12' 1740 18' 230 0.33 325 0.15 Titahi Bay 410 06' 1740 50' 277 0.37 340 0,21 Makara 410 13' 1740 37' 255 0.34 346 0.21 0teranga Bay 410 18' 1740 37' 192 0.18 328 0.12 Wellington 410 17' 174 ~ 47' 137 0.49 340 0.03 Lake Grassmere 410 42' 1740 11' 155 0.61 269 0.06 Cape Campbell 410 44' 1740 15' 151 0.64 288 0.03 Castlepoint 400 55' 1760 13' 143 0.58 153 0.03 Kaikoura 420 24' 1730 42' 140 0.67 038 0

224 Deutsche Hydrographisehe Zeitsehrift, Jahrgang 27, 1974, Heft 516

H

( \ l

Fig. 8. Tidal streams (curved arrows) taken from the numerical model at quarter cycle intervals; t = 0 gives the streams at high tide at Cape Campbell. The straight arrows give the current velocity

at seven locations

172040 ' 175~15,E

References

Brodie, J.W., 1965: Tasman bathymetry. N.Z. oceanogr. Inst. Chart coast. Ser. 1 : 200,000.

B r o d i e , J. W,, 1966: Cook Strai~ bathymetry. ~.Z. oceanogr. Inst. Chart coast. Ser. 1 : 200,000.

B y e , J . A . T . , 1974: The " F L O W " series of numerical models. Computing Rep. Flinders Inst. atmos, mar. Sci. Flinders Univ. S. Aust.

Bye, J.A.T., 1~. A. Heath [in press]: The New Zealand semi-diurnal tide. J. mar. Res.

Gilmour, A.E., 1960: Currents in Cook Strait, New Zealand. N.Z.J. Geol. Geophys. 3, 410.

O i l m o u r , A. E., [in press]: Cook Strait tides. N . Z . J . Geol. Geophys.

Hydrographic Branch, Navy Department, Wellington, 1960 : Chart, Wellington to Pates including Cook Strait. 1:200,000. NZ 46.

Hydrographic Branch, Navy Department, Wellington, 1960: Chart, I4aramea River to Stephens Island. 1:200,000. NZ61.

Hydrographic Department, London, 1958: The New Zealand Pilot. 12th Edition. London, 500 pp.

Hydrographic Department, London, 1963: The Admiralty Tide Tables. Volume 3. 1964. Pacific Ocean and adjacent Seas. London.

Olsson, B. ]~., 1955: The electrical effects of tidal streams in Cook Strait, New Zealand. Deep-Sea IRes. 2, 204.

Eingegangen im September 1974

Anschrift des Vcrfassers: R. A. Heath, New Zealand Oceanographic Institute, Department of Scientific and Industrial Research, P. O. Box 8009, Wellington, New Zealand

the lunar semi-diurnal tide in cook strait, new zealand

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