Sedimentology (1980) 27, 225-229

SHORT COMMUNICATION

Flows above oscillatory ripples

H. HONJT, A. K A N E K O & N. M A T S U N A G A

Research Institute for Applied Mechanics, Kyushu University, Fukuoka 8 12, Japan

ABSTRACT

The flows above ripples of glass beads and ripple models have been visualized in an oscillatory water tunnel. Some ripples were observed to form without flow separation. Two types of vortices, the standing vortices without flow separation and the separation vortices have been observed, and their similarity is discussed.

INTRODUCTION

The study of sand ripples has a long history (Darwin, 1883 ; Bagnold, 1946). Various aspects of the ripples in waves and oscillatory flow are covered i n recent treatizes (Davis & Ethington, 1976; Komar, 1976; Raudkivi, 1976; Stanley & Swift, 1976; Allen, 1977). Flows above the ripples have also been studied by Lyne (1971), Sleath (1975, 1976) and others. How- ever, direct visualizations of the oscillatory flows (with which this paper is concerned) seem rather scarce.

displacement in stroke (do) and frequency (f) for water oscillation were less than 13 cm and 1.7 Hz, respectively. A diagram of this tunnel is shown in Kaneko & Honji (1979a).

Glass beads with specific gravity of 2.43 and mean diameters (D) between 0.01 and 0-50 cm were used as a bed material. Flows were visualized by means of the methods of direct shadow, dye generation, and suspension of aluminium flakes. Flow patterns were photographed with a 35 mm camera at rest with respect to the tunnel.

RESULTS AND DISC 1.1 S SI 0 N S EXPERIMENTAL METHODS

The experiments were carried out using a closed- type 3 m water tunnel, of which a horizontal test section was 120 cm in length, and 15 cm in width and in height. Water in the tunnel was oscillated by a motor-driven piston. The kinematic viscosity of water was between 0.0095 and 0.014 cm2s-l. The test section was made of glass plates, except for a tunnel floor equipped with a sand pit of 10 cm depth. The

0037-0746/80/0400-0225 $02.00 0 1980 International Association of Sedirnentologists

Above ripples, steady streaming is induced in the primary oscillatory flow when do is much smaller than the ripple wavelength L (Lyne, 1971; Sleath, 1976; Kaneko & Honji, 1979b). Figure 1 shows streaming above the ripples made up from an initially flat bed of glass beads by the same stream- ing. Figures 1 and 3 were photographed by using another smaller tunnel filled with a working solution of glycerine and water. The streaming in this solution was visualized by means of the direct shadow method. The primary flow is toward the right in Figure 1. This picture shows that ripples can form

226 H . Honji, A. Knneho & N . Mutsunugu

Fig. 1. Steady streaming above ripples of glass beads in a viscous fluid with the kinematic viscosity of 1.20 cm’s ’ (Scale bar: 2 cm). D, 0.028 cm, do, 5.5 cm,.f, 1.52 Hz.

without flow separation. When the fluid viscosity was large, ripple crests did not become steep.

This streaming also shows up a double structure consisting of upper and lower pairs of counter- rotating vortices. Such a structure is described in Lyne (1971), Sleath (1976) and Kaneko & Honji (1979b). The upper streaming forms a pair of ‘standing vortices’ above the trough, and the lower streaming a similar pair above the crest. For stationary ripples a relationship L = 2s holds approximately, s being the horizontal length of a single vortex.

In water the lower vortex layer thickness is so

small owing to the low viscosity that only an upper layer is seen as in Fig. 2, where streak-lines of a white dye educed electrochemically from the surface of a ripple model made of metal are shown. The flow direction in the vortices is identical with that of the upper vortices in Fig. I .

When individual particles make rolling motions, their displacements relative to a surrounding fluid remain small and do not give rise to flow separation. This leads to the formation of standing vortices above the particle-wave ripples discussed in Kaneko & Honji (1979a), as shown in Fig. 3 wherc the lower vortex layer is dominant. Similar

Fig. 2. Streaming in water above a ripple model at do ~ 1 2 cm much smaller than L (Scale bar: 1 cm). f ; 1.65 Hz.

Flows above oscillatory ripples 221

Fig. 3. Standing vortices above the particle-wave ripples of rolling glass beads in a viscous fluid with the kinematic viscosity of 0.979 cmrs-l (Scale unit in cm). D, 0.50 cm, do, 2.2 cm, f , 1.52 Hz.

standing vortices may also form above the rolling- grain ripples of Bagnold (1946), if the piling-up of grains is not conspicuous and the primary flow remains free from separation. Otherwise, separation vortices (discussed below) may form above these ripples, although the vortices may be of small scale.

Above common stationary ripples or vortex ripples as in Bagnold (1946), the primary flow is separated and ‘separation vortices’ form as shown in Fig. 4, since do is not much smaller than L. Visual observations indicated that s did not depend on f appreciably in this experiment. Therefore, in order to obtain a clear flow pattern visualized with aluminium flakes, it was photographed at f’= 0.1 1 Hz, reduced from 0.75 Hz at which this ripple had formed. When a vortex-ripple system is in a stationary state, a dividing streamline separated from a crest reattaches to the centre of a trough, and a relationship L = 2s holds similarly as in the case of the standing vortices.

This does not hold for non-stationary ripples because s is too long or too short for the vortices t o be well accommodated in troughs. Figure 5 shows a separation vortex too long to be well accommodated. This picture was taken immediately after do was increased from 9.6 cm at which the

ripple had formed. Continuous oscillations a t increased do led to the formation of larger ripples. Thus, mainly do determines s, and s determines L of the stationary ripples.

An instantaneous streamline pattern such as Fig. 4 shows a single separation vortex for every half period of water oscillation. However, as displayed in Fig. 6, dye streaks show up separation vortices pairing above the trough, owing to a residual effect in the diffusion of dye. Based on Fig. 6 one can imagine, for one complete cycle of oscillation, the formation of a pair of separation vortices as illus- trated in Fig. 7. The rotation of these vortices is identical with that of the lower standing vortices in Fig. 1 , and the flow close to the ripple surface mounts up the crest. This indicates that the imaginary pair of separation vortices should be an analogue of a pair of lower standing vortices, not of upper ones in Fig. 1, the vortices being considered to pair above the trough in this case. These geometrically similar standing and separation vortex pairs, both satisfying the relationship L = 2s, play the same role in transporting sand particles from the trough to the crest.

The flows above stationary oscillatory ripples are thus composed of a primary oscillatory flow and an induced characteristic flow forming ripple

228 H . Honji, A . Kuneko & N . Mutsunagu

Fig. 4. Separation vortex fully developed behind a crest of glass bead ripple (Scale bar: 1 cm). D, 0.028 cm, do, 9.6 cm, A 0.1 1 Hz.

Fig. 5. Separation vortex formed immediately after do has been increased from 9.6 to 12 cm. Other data are the same as those for Fig. 4.

Ffows above oscillatory ripples 229

Fig. 6. Streak pattern of separation vortices above a ripple model (Scale bar: 1 cm). do, 6.6 crn, 0.2 Hz.

. . . * . . . . . . . . . . . . . . . . . . - . . Fig. 7. Imaginary separation-vortex pair; arrows indicate the flow direction.

profiles. The characteristic flow may be of a standing- vortex pair or of a n imaginary separation-vortex pair, depending upon the occurrence of flow separation.

Most flows above ripples observed in nature are not free from separation. However, mathematical analysis of fully separated flows is so difficult that most non-empirical analyses have been concerned with standing vortical flows, without reference to the reasonable correspondence between the standing and separation vortices. The correspondence seems clear on the basis of the two types of vortex pairs so far discussed.

ACKNOWLEDGMENT

The authors thank Y . Shiraishi for technical help.

REFERENCES

ALLEN, J.R.L. ( I 977) Physical Processes of Sedimentation, 4th imprn. Allen & Unwin Ltd, London.

BAGNOLD, R.A. (1946) Motion of waves in shallow water. Interaction between waves and sand bottoms. Proc. R. Soc. Lond. 187, 1-18.

DARWIN, G.H. (1883) On the formation of ripple marks in sand. Proc. R. Soc. Lond. 36, 18-43.

DAVIS, R.A., JR & ETHINGTON, H. (1976) Beach and Nearshore Sedimentation, pp. 187, Spec. Publ. Sor. econ. Paleont. Miner. Tulsa, 24.

KANEKO, A. & HONJI, H. (1979a) Initiation of ripple marks under oscillating water. Sedimentology,

KANEKO, A. & HONJI, H. (1979b) Double structures of steady streaming in the oscillatory viscous flow over a wavy wall. J. Fluid Mecli. 93, 727-736.

KOMAR, P.D. (1 976) Beach Processes and Sedimentation. Prentice Hall, Engtewood Cliffs, N.J.

LYNE, W.H. (1971) Unsteady viscous flow over a wavy

RAUDKIVI, A.J. (1976) Loose Boundary Hydraulics,

SLEATH, J.F.A. (1975) A contribution to the study of

SLEATH, J.F.A. (1976) On rolling-grain ripples. J. Hydraul. ' Res. 14, 69-81.

STANLEY, D.J. & SWIFT, D.J.P. (1976) Marine Sediment Transport and Environmental Management. Wiley & Sons, New York.

26, 101-113.

wall. J. Fluid Mech. 50, 3348.

2nd edn. Pergamon Press, Oxford.

vortex ripples. J. Hydraul. Res. 13, 315-328.

(Manuscript received 30 November 1978; revision received 18 October 1979)