C. Brouzet

Internal wave attractors examined using laboratory experiments and 3D numerical simulations

In the present paper, we combine numerical and experimental approaches to study the dynamics of stable and unstable internal wave attractors. The problem is considered in a classic trapezoidal setup filled with a uniformly stratified fluid. Energy is injected into the system at global scale by the small-amplitude motion of a vertical wall. Wave motion in the test tank is measured with the help of conventional synthetic schlieren and PIV techniques. The numerical setup closely reproduces the experimental one in terms of geometry and the operational range of the Reynolds and Schmidt numbers. The spectral element method is used as a numerical tool to simulate the nonlinear dynamics of a viscous salt-stratified fluid. We show that the results of three-dimensional calculations are in excellent qualitative and quantitative agreement with the experimental data, including the spatial and temporal parameters of the secondary waves produced by triadic resonance instability. Further, we explore experimentally and numerically the effect of lateral walls on secondary currents and spanwise distribution of velocity amplitudes in the wave beams. Finally, we test the assumption of a bidimensional flow and estimate the error made in synthetic schlieren measurements due to this assumption.

Energy cascade in internal wave attractors

One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal-wave attractors in the large-amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochromatic input to multi-scale internal-wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how, beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing.

Scale effects in internal wave attractors

As a necessary preliminary step toward geophysically significant extrapolations, we study the scale effects in internal wave attractors in the linear and nonlinear regimes. We use two geometrically similar experimental set-ups, scaled to factor 3, and numerical simulations (a spectral element method, based on the Nek5000 open solver) for a range of parameters that is typically accessible in laboratory. In the linear regime, we recover the classical viscous scaling for the beam width, which is not affected by variations of the amplitude of the input perturbation. In the nonlinear regime, we show that the scaling of the width-to-length ratio of the attractor branches is intimately related with the energy cascade from large-scale energy input to dissipation. We present results for the wavelength, amplitude and width of the beam as a function of time and as a function of the amplitude of the forcing.

Abyssal Mixing in the Laboratory

One of the important questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose a unique self-consistent experimental and numerical set up that models a cascade of triadic interactions transferring energy from large-scale monochromatic input to multi-scale internal wave motion. We show how this set-up can be used to tackle the open question of studying internal wave turbulence in a laboratory, by providing, for the first time, explicit evidence of a wave turbulence framework for internal waves. Finally, beyond this regime, we highlight a clear transition to a cascade of small-scale overturning events which induce mixing.

Added mass: a complex facet of tidal conversion at finite depth

This paper revisits the problem of tidal conversion at a ridge in a uniformly stratified fluid of limited depth using measurements of complex-valued added mass. When the height of a sub-marine ridge is non negligible with respect to the depth of the water, the tidal conversion can be enhanced in the supercritical regime or reduced in the subcritical regime with respect to the large depth situation. Tidal conversion can even be null for some specific cases. Here, we study experimentally the influence of finite depth on the added mass coefficients for three diffierent ridge shapes. We first show that at low forcing frequency the tidal conversion is weakly enhanced by shallow depth for a semi-circular ridge. In addition, added mass coefficients measured for a vertical ridge show strong similarities with the ones obtained for the semi-circular ridge. Nevertheless, the enhancement of the tidal conversion at low forcing frequency for the vertical ridge has not been observed, in contrast with its supercritical shape. Finally, we provide the experimental evidence of a lack of tidal conversion due to the specific shape of a ridge for certain depth and frequency tuning.