Hélène Scolan

Nonlinear Fate of Internal Wave Attractors

We present a laboratory study on the instability of internal wave attractors in a trapezoidal fluid domain filled with uniformly stratified fluid. Energy is injected into the system via standing-wave-type motion of a vertical wall. Attractors are found to be destroyed by parametric subharmonic instability via a triadic resonance which is shown to provide a very efficient energy pathway from long to short length scales. This Letter provides an explanation of why attractors may be difficult or impossible to observe in natural systems subject to large amplitude forcing.

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.

Finite-size effects in parametric subharmonic instability

The parametric subharmonic instability in stratified fluids depends on the frequency and the amplitude of the primary plane wave. In this paper, we present experimental and numerical results emphasizing that the finite width of the beam also plays an important role on this triadic instability. A new theoretical approach based on a simple energy balance is developed and compared to numerical and experimental results. Because of the finite width of the primary wave beam, the secondary pair of waves can leave the interaction zone which affects the transfer of energy. Experimental and numerical results are in good agreement with the prediction of this theory, which brings new insights on energy transfers in the ocean where internal waves with finite-width beams are dominant.