Laurent Thais

Turbulent structure beneath surface gravity waves sheared by the wind

New experiments have been carried out in a large laboratory channel to explore the structure of turbulent motion in the water layer beneath surface gravity waves. These experiments involve pure wind waves as well as wind-ruffled mechanically generated waves. A submersible two-component LDV system has been used to obtain the three components of the instantaneous velocity field along the vertical direction at a single fetch of 26 m. The displacement of the free surface has been determined simultaneously at the same downstream location by means of wave gauges. For both types of waves, suitable separation techniques have been used to split the total fluctuating motion into an orbital contribution (i.e. a motion induced by the displacement of the surface) and a turbulent contribution. Based on these experimental results, the present paper focuses on the structure of the water turbulence. The most prominent feature revealed by the two sets of experiments is the enhancement of both the turbulent kinetic energy and its dissipation rate with respect to values found near solid walls. Spectral analysis provides clear indications that wave-turbulence interactions greatly affect energy transfers over a significant frequency range by imposing a constant timescale related to the wave-induced strain. For mechanical waves we discuss several turbulent statistics and their modulation with respect to the wave phase, showing that the turbulence we observed was deeply affected at both large and small scales by the wave motion. An analysis of the phase variability of the bursting suggests that there is a direct interaction between the waves and the underlying turbulence, mainly at the wave crests. Turbulence budgets show that production essentially takes place in the wavy region of the flow, i.e. above the wave troughs. These results are finally used to address the nature of the basic mechanisms governing wave-turbulence interactions.

Laboratory observations of mean flows under surface gravity waves

In this paper we present mean velocity distributions measured in several different wave flumes. The flows shown involve different types of mechanical wavemakers, channels of differing sizes, and two different end conditions. In all cases, when surface waves, nominally deep-water Stokes waves, are generated, counterflowing Eulerian flows appear that act to cancel locally, i.e. not in an integral sense, the mass transport associated with the Stokes drift. No existing theory of wave–current interactions explains this behaviour, although it is symptomatic of Gerstner waves, rotational waves that are exact solutions to the Euler equations. In shallow water (kH ≈ 1), this cancellation of the Stokes drift does not hold, suggesting that interactions between wave motions and the bottom boundary layer may also come into play.

Experimental investigation and numerical modelling of steep forced water waves

Steep forced water waves generated by moving a rectangular tank are investigated both experimentally and numerically. Our main focus is on energetic events generated by two different types of external forcing. Horizontal motions are arranged to give wave impact on the sidewall. Steep standing waves forced by vertical acceleration can result in spectacular breaking modes similar to, and more energetic than, those reported by Jiang, Perlin & Schultz (1998, hereinafter J98). Among them we find thin sheets derived from sharp-crested waves, (‘mode A’ of J98) and the ‘flat-topped’ crest or ‘table-top’ breaker (‘mode B’ of J98). We report here on experimental observations of ‘table-top’ breakers showing remarkably long periods of free fall motion. Previously such breakers have only been observed in numerical computations. Both types of breakers often thin as they fall to give thin vertical sheets of water whose downward motion ends in either a small depression and a continuing smooth surface, or air entrainment to appreciable depths. Experimental results are compared graphically with numerical results of two theoretical models. One is an extended set of Boussinesq equations following Wei et al. (1995), which are successful up to wave slopes of O (1). The other numerical comparison is with a fully nonlinear irrotational flow solver (Dold 1992) which can follow the waves to breaking.

A triple decomposition of the fluctuating motion below laboratory wind water waves

Understanding of the dynamics of the top meters of the ocean requires an improvement of present knowledge about interactions between wind waves, mean sheared current, and turbulence. To achieve this goal, a key point lies in relevant definitions and evaluations of orbital and turbulent motions. The aim of this paper is to build and validate a separation technique allowing one to distinguish all three crucial contributions of the fluctuating motion, namely the potential and rotational parts of the orbital motion, as well as turbulent fluctuations. The whole method is first developed and tested for periodic rotational waves. The first step of this technique consists of a determination of the instantaneous stream function associated with the potential motion induced by the waves in presence of a linear sheared current. The second step consists of a linear filtration of the remaining motion from which the orbital rotational motion is extracted. The strong hypotheses involved in the technique are then carefully checked and shown to be relevant in the case of laboratory wind waves. The method is finally applied to experimental data obtained by laser Doppler velocimetry measurements in a wind-water laboratory facility. Influence of the mean sheared current on the prediction of orbital velocities is pointed out, and the orbital rotational contribution is found to have a significant magnitude.

Tide, turbulence and suspended sediment modelling in the eastern English Channel

Abstract The present paper is concerned with modelling fluid and suspended sediment dynamics in a tide-dominated environment. The procedure consists of a one-dimensional vertical model driven by an oscillatory horizontal pressure gradient derived from a two-dimensional vertically integrated tidal model. The vertical model includes two linearised momentum equations for the horizontal velocity components and a series of advection–diffusion equations for concentrations of suspended sediment of specific size. Turbulence generated at the seabed is computed with the aid of a two-equation closure describing the time–space evolution of the turbulent kinetic energy k and of the dissipation rate of the turbulent kinetic energy e (standard k−e model). A mixed type bottom boundary condition for the sediment concentration equations is adopted to take into account downward fluxes at times of decelerating flow and slack waters. The model is applied to the eastern part of the English Channel. The tidal currents, turbulent kinetic energy and the total suspended sediment load predicted by the model are compared with field data collected in two sites. The vertical structure of these flow properties is fairly well predicted by the present model. Better results are found at the measuring point located farther from the coastline where advective terms can be reasonably neglected.

Orbital rotational motion and turbulence below laboratory wind water waves

New experimental results describing the structure of both orbital and turbulent motions below laboratory wind water waves are presented. The data obtained by means of a submersible laser probe are processed through the triple decomposition method developed by the authors. This method allows one to distinguish three contributions in the fluctuating motion, namely the potential and rotational parts of the orbital motion, as well as the turbulent fluctuation. The results show that the orbital rotational motion has spectral properties very similar to those of its potential counterpart and represents a contribution of significant magnitude. The behavior of all three components of the turbulent motion is discussed. Their near-surface level is comparable with that found near a wall, but their vertical decay is quite different The dissipation rate estimate confirms that under present conditions the turbulence is essentially unaffected by the orbital motion. In contrast, a study of the cross correlations between orbital rotational and potential motions shows that the rotational contribution plays a key role in energy transfers between the wave motion and the mean shear flow. Finally, the origin of the orbital rotational motion is addressed. Several theoretical mechanisms capable of contributing to the generation of a wave-related component of the vorticity are examined. Comparison between theory and experiments supports the idea that in laboratory experiments an important part of the orbital rotational motion results from wave-current interactions linked to the vertical variations of the mean shear.

Reynolds number variation in oscillatory boundary layers. Part I. Purely oscillatory motion

A numerical model based upon a low Reynolds number turbulence closure is proposed to study Reynolds number variation in reciprocating oscillatory boundary layers. The model is used to compute the boundary layer for flow regimes ranging from smooth laminar to rough turbulent. Criteria for fully developed turbulence are derived for walls of the smooth and rough types. In particular, a new criterion to identify the rough turbulent regime is determined based on the time-averaged turbulence intensity. The reliability of the present model is assessed through comparisons with detailed experimental data collected by other investigators. The model globally improves upon standard high Reynolds number closures. Variation through the wave cycle of the main flow variables (ensemble-averaged velocity, shear stress, turbulent kinetic energy) is remarkably well-predicted for smooth walls. Predictions are satisfactory for rough walls as well. Yet, the turbulence level in the rough turbulent regime is overpredicted in the vicinity of the bed.

Estimates of wave decay rates in the presence of turbulent currents

A full-depth numerical model solving the free surface flow induced by linear water waves propagating with collinear vertically sheared turbulent currents is presented. The model is used to estimate the wave amplitude decay rate in combined wave current flows. The decay rates are compared with data collected in wave flumes by Kemp and Simons [J Fluid Mech, 116 (1982) 227; 130 (1983) 73] and Mathisen and Madsen [J Geophys Res, 101 (C7) (1996) 16,533]. We confirm the main experimental finding of Kemp and Simons that waves propagating downstream are less damped, and waves propagating upstream significantly more damped than waves on fluid at rest. A satisfactory quantitative agreement is found for the decay rates of waves propagating upstream, whereas not more than a qualitative agreement has been observed for waves propagating downstream. Finally, some wave decay rates in the presence of favourable and adverse currents are provided in typical field conditions.

Bed Friction in Combined Wave-Current Flows

The accurate prediction of shear stresses at the seabed forms an essential element in modelling of the coastal environment. Flows which induce bed friction generally include a mean component (from wind-induced currents or tides) and an oscillatory component (from waves), and this paper describes an investigation into seabed friction under such combined wave-current flow. In particular, it presents new laboratory measurements of the shear stress exerted by waves or wave-like flows on a rough boundary and how that oscillatory component is modified by the addition of a current. The effect of the waves on the current is reported, and the results compared with predictions from wave-current models, including some being developed as part of the present project.