Mixing induced by Faraday surface waves

TL;DR

This study explores how Faraday surface waves induce mixing between two miscible fluids with slight density differences, revealing complex dynamics and proposing a model to predict mixing behavior.

Contribution

It combines experimental, numerical, and modeling approaches to understand Faraday wave-driven mixing and introduces a depth-dependent turbulent diffusivity model.

Findings

Mixing rate is non-monotonic with respect to energy input.

Large crests collapse to form bubbles, aiding mixing.

A one-dimensional model captures the qualitative evolution.

Abstract

We investigate how surface waves enhance mixing across the interface between two miscible fluids with a small density contrast. Imposing a vertical, time-periodic acceleration, we excite Faraday waves both experimentally and numerically. In systems with a shallow density gradient, these standing waves advect the interface and can trigger secondary instabilities. When driven beyond the linear regime, large Faraday crests collapse to form cavities, injecting bubbles and lighter fluid deep into the heavier layer. Together, these mechanisms gradually homogenize the upper layer, diminish the interfacial density jump, and drive the interface downward until it decouples from surface forcing. We report a non-monotonic mixing rate -- first increasing as the interfacial energy barrier lowers, then decreasing as less energy is injected into the weakened surface -- revealing a balance between barrier reduction and energy input. Based on these observations, we introduce a one-dimensional model incorporating a turbulent diffusivity coefficient that depends on depth and the internal Richardson number, which captures the qualitative evolution of the system.