Harmonic to subharmonic transition of the Faraday instability in miscible fluids

Abstract

When a stable stratification between two miscible fluids is excited by a vertical and periodic forcing, a turbulent mixing zone can develop, triggered by the Faraday instability. The mixing zone grows and saturates to a recently predicted final value L sat [Grea and Ebo Adou, J. Fluid Mech. 837, 293 (2018)] when resonance conditions are no longer fulfilled. Notably, it is expected from the Mathieu stability diagram that the instability may evolve from a harmonic to a subharmonic regime for particular initial conditions. This transition is evidenced here in the full inhomogeneous system using direct numerical simulations with 1024 3 points: the analysis of one-point statistics and spectra reveals that turbulence is greatly enhanced after the transition, while the global anisotropy of both the velocity and concentration fields is significantly reduced. Furthermore, using the concept of sorted density field, we compute the background potential energy e b p of the flow, which increases only after the transition as a signature of irreversible mixing. While the gain in e b p strongly depends on the control parameters of the instability, the cumulative mixing efficiency is more robust. At saturation of the instability, available potential energy is partially released in the flow as background potential energy. Finally, it is shown numerically that for fixed parameters, a multiple-frequency forcing can modify the duration of the harmonic regime without significantly altering the asymptotic state.