This text introduces and draws together pertinent aspects of fluid dynamics, physical oceanography, solid mechanics, and organismal biology to provide a much-needed set of tools for quantitatively examining the biological effects of ocean waves. "Nowhere on earth does water move as violently as on wave-swept coasts, " writes the author, "and every breaker that comes pounding on the shore places large hydrodynamic forces on the organisms resident there." Yet wave-swept coral reefs and rocky shores are home to some of the world's most diverse assemblages of plants and animals, and scientists have chosen these environments to carry out much of the recent experimental work in community structure and population dynamics. Until now these studies have been hampered because biologists often lack a working understanding of the mechanics of the wave-swept shore. Mark Denny here supplies that understanding in clear and vivid language.Included are an introduction to wave-induced water motions and the standard theories for describing them, a broad introduction to the hydrodynamic forces these water movements place on plants and animals, and an explanation of how organisms respond to these forces. These tools are put to use in the final chapters in an examination of the mechanisms of "wave exposure" and an exploration of the mechanical determinants of size and shape in wave-swept environments.

Biology and the Mechanics of the Wave-Swept Environment

Attention is given to the properties of sediment beds over the full range of conditions (silts to gravel), in particular the effect of fine silt on the bed composition and on initiation of motion (critical conditions) is discussed. High-quality bed-load transport data sets are identified and analyzed, showing that the bed-load transport in the sand range is related to velocity to power 2.5. The bed-load transport is not much affected by particle size. The prediction of bed roughness is addressed and the prediction of bed-load transport in steady river flow is extended to coastal flow applying an intrawave approach. Simplified bed-load transport formulas are presented, which can be used to obtain a quick estimate of bed-load transport in river and coastal flows. It is shown that the sediment transport of fine silts to coarse sand can be described in a unified model framework using fairly simple expressions. The proposed model is fully predictive in the sense that only the basic hydrodynamic parameters (dep...

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Unified view of sediment transport by currents and waves. I: Initiation of motion, bed roughness, and bed-load transport

The problem of the response of a porous elastic bed to water waves is treated analytically on the basis of the three-dimensional consolidation theory of Biot (1941). Exact solutions for the pore-water pressure and the displacements of the porous medium are obtained in closed form for the case of waves propagating over the poro-elastic bed. The theoretical results indicate that the bed response to waves is strongly dependent on the permeability k and the stiffness ratio G/K’, where G is the shear modulus of the porous medium and K’ is the apparent bulk modulus of elasticity of the pore fluid. The earlier solutions for pore-water pressure by various authors are given as the limiting cases of the present solution. For the limits G/K′ → 0 or k→ ∞, the present solution for pressure approaches the solution of the Laplace equation by Putnam (1949). For the limit G/K′→ ∞, the present solution approaches the solution of the heat conduction equation by Nakamura et al. (1973) and Moshagen & Torum (1975).The theoretical results are compared with wave tank experimental data on pore-water pressure in coarse and fine sand beds which contain small amounts of air. Good agreement between theory and experiment is obtained.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112078003006

On the response of a poro-elastic bed to water waves

This study deals with turbulent oscillatory boundary-layer flows over both smooth and rough beds. The free-stream flow is a purely oscillating flow with sinusoidal velocity variation. Mean and turbulence properties were measured mainly in two directions, namely in the streamwise direction and in the direction perpendicular to the bed. Some measurements were made also in the transverse direction. The measurements were carried out up to Re = 6 × 106 over a mirror-shine smooth bed and over rough beds with various values of the parameter a/ks covering the range from approximately 400 to 3700, a being the amplitude of the oscillatory free-stream flow and ks the Nikuradse's equivalent sand roughness. For smooth-bed boundary-layer flows, the effect of Re is discussed in greater detail. It is demonstrated that the boundary-layer properties change markedly with Re. For rough-bed boundary-layer flows, the effect of the parameter a/ks is examined, at large values (O(103)) in combination with large Re.

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Turbulent oscillatory boundary layers at high Reynolds numbers

https://cirp.usace.army.mil/products/files/doc/Hallermeier1981-ProfileZonation.pdf

A profile zonation for seasonal sand beaches from wave climate

Velocity measurements are presented for turbulent oscillatory flow over rough beds. Two components of velocity were measured with a laser-Doppler anemometer and the rough beds consisted of a single layer of sand, gravel or pebbles on a flat surface. Turbulence intensities showed significant variation during the course of the cycle. Maximum turbulence intensity propagated out from the bed at a more or less constant velocity for all beds. Variation of time-mean turbulence intensity with height was qualitatively similar to that observed in steady flows. Reynolds stress showed several interesting features. Near the bed, maximum Reynolds stress was in phase with one of the two peaks of turbulence intensity but further out it was in phase with the other, i.e. the phase of maximum Reynolds stress showed a 180° phase shift at a certain height above the bed. A related effect was seen in the time-mean eddy viscosity which was negative near the bed but positive further out. It is suggested that these effects are caused by the jets of fluid associated with vortex formation and ejection in oscillatory flow over rough beds. Maximum Reynolds stress was also significantly less than the horizontal force per unit area of bed obtained from the momentum integral. Eddy viscosity and mixing length were found to vary significantly during the course of the cycle. Variation with height of time-mean values of these variables showed similar trends, except in the near-bed region, to those observed in steady flow but derived values of the Karman constant were significantly lower. Non-dimensional defect velocity appeared to show dependence on a/ks as well as on y/δ in the outer layer away from the bed, even at high Reynolds numbers.

Turbulent oscillatory flow over rough beds

Sea bed mechanics

A bed-load model, based on a generalization of Bagnold's (1954) constitutive equations together with the assumption of similarity profiles for velocity and concentration, was proposed for sediment transport by waves by Sleath (1994). This model is now extended to wave/current flows and applied to three different situations: (a) oscillatory flows with superimposed currents, (b) net transport produced by progressive waves over a flat horizontal bed, and (c) longshore transport induced by waves approaching a beach. In all three cases the model gives reasonable agreement with experiment. In the case of longshore transport the model produces almost the same formula as that of the Coastal Engineering Research Center (1977), apart from additional terms for density and grain size.

Sediment transport by waves and currents

Measurements of the variation of the fluctuating component of pressure have been made in two different beds of sand in a wave channel. The sand was laid from an overhead hopper, and it is shown that the stratification of the bed produced by this method causes the permeability to be different in the vertical and horizontal directions. It is suggested that a similar situation exists in the sea bed. Analytical relationships for the pressure and velocity distributions in such a situation are developed, and the agreement between theory and experiment is found to be quite good. As far as is known, this is the first time that the applicability of traditional porous-media analytical methods to wave-induced flow in beds of sand has been verified experimentally.

Wave-Induced Pressures in Beds of Sand

The conditions under which plug formation may occur in oscillatory flow over beds of sediment are examined. The term plug formation is used to describe the situation where sediment starts to move as a solid block when the flow reverses. It is shown analytically that there is a lower bound on the value of the parameter S = ρU 0 ω /( ρ s − ρ ) g for plug formation. For values of S above this limit plug formation is determined by the degree of compaction of the sediment. It is suggested that the degree of compaction depends on the parameter W 0 / ωδ s where W 0 is the fall velocity of the sediment and δ s is the maximum thickness of the mobile layer. Re-examination of the measurements of Dick and Sleath (1991) and Zala Flores and Sleath (1998) showed that for their acrylic sediment plugs formed when W 0 / ωδ s was less than about 0.12. All of the tests which showed plug formation were in Bagnold’s (1954) ‘viscous’ regime. For these conditions there is good agreement between the measured velocity distribution in the shear layer below the plug and the velocity distribution calculated from Bagnold’s constitutive equations provided an appropriate value of effective viscosity is selected. Comparison of tests in which plug formation occurred with those in which it did not suggests that plug formation leads to much larger values of the effective viscosity in the shear layer close to the bed. For plug flows the measured values of effective viscosity were more than 1000 times those suggested by Bagnold (1956) .

John F. A. Sleath

Papers

Turbulent oscillatory flow over rough beds

Sea bed mechanics

Sediment transport by waves and currents

Wave-Induced Pressures in Beds of Sand

Conditions for plug formation in oscillatory flow