Frozen waves in the inertial regime

Interfaces subjected to strong time-periodic horizontal accelerations exhibit striking patterns known as frozen waves. In this study, we experimentally and numerically investigate the formation of such structures in immiscible fluids under high-frequency forcing. In the inertial regime – characterised by large Reynolds and Weber numbers, where viscous and surface tension effects become negligible – we demonstrate that the amplitude of frozen waves scales proportionally with the square of the forcing velocity. These results are consistent with vibro-equilibria theory and extend the theoretical framework proposed by Gréa & Briard (2019 Phys. Rev. Fluids 4 , 064608) to immiscible fluids with large density contrasts. Furthermore, we examine the influence of both Reynolds and Weber numbers, not only in the onset of secondary Faraday instabilities – which drive the transition of frozen wave patterns toward a homogenised turbulent state – but also in selecting the dominant wavelength in the final saturated regime.