Wave turbulence in a two-layer fluid: coupling between free surface and interface waves

TL;DR

This study experimentally investigates how the coupling between free surface and interface waves affects wave turbulence in a two-layer fluid, revealing how increased upper fluid depth extends the inertial range and alters wave dissipation.

Contribution

It provides new insights into the coupling effects in two-layer fluid wave turbulence using precise measurements and dispersion relation analysis.

Findings

Extended inertial range with increased upper fluid depth

Decreased crossover frequency between gravity and capillary regimes

Increased dissipative cut-off frequency due to wave decoupling

Abstract

We experimentally study gravity-capillary wave turbulence on the interface between two immiscible fluids of close density with free upper surface. We locally measure the wave height at the interface between both fluids by means of a highly sensitive laser Doppler vibrometer. We show that the inertial range of the capillary wave turbulence regime is significantly extended when the upper fluid depth is increased: The crossover frequency between the gravity and capillary wave turbulence regimes is found to decrease whereas the dissipative cut-off frequency of the spectrum is found to increase. We explain these observations by the progressive decoupling between waves propagating at the interface and the ones at the free surface, using the full dispersion relation of gravity-capillary waves in a two-layer fluid of finite depths. The cut-off evolution is due to the disappearance of parasitic capillaries responsible for the main wave dissipation for a single fluid.