Scale effects in internal wave attractors

TL;DR

This study investigates how scale influences internal wave attractors in both linear and nonlinear regimes using experiments and numerical simulations, revealing classical viscous scaling and energy cascade effects.

Contribution

It provides the first detailed analysis of scale effects in internal wave attractors, combining experimental and numerical methods across regimes.

Findings

Linear regime shows classical viscous scaling for beam width.

Nonlinear regime links width-to-length ratio scaling with energy cascade.

Results include wavelength, amplitude, and width variations over time and forcing amplitude.

Abstract

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.