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Frozen waves in the inertial regime
Published online by Cambridge University Press: 14 October 2025
Abstract
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.
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Gréa et al. supplementary movie 1
Visualization movie of experimental frozen interfacial waves under varying forcing frequencies and accelerations.
File
13.4 MB
Gréa et al. supplementary movie 2
Movie of a frozen-wave simulation illustrating the development of secondary Faraday instabilities.
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23.7 MB