The role of fluctuations across a density interface

TL;DR

This paper develops a statistical mechanics framework to describe the equilibrium states of a stratified fluid, validated through laboratory experiments measuring density fluctuations across a density interface.

Contribution

It introduces a model linking the evolution of the density profile to a sequence of statistical equilibrium states and distinguishes between wave and turbulent density fluctuations.

Findings

Statistical mechanics accurately predicts turbulent density fluctuations near the interface.

Density fluctuations in the mixed layer exhibit exponential tails in their probability distribution.

The wave part of the density field aligns with Phillips' theory.

Abstract

A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is related to the presence of irreversible mixing, which alters the global distribution of density levels. We propose a model in which the vertical density profile evolves through a sequence of statistical equilibrium states. The theory is then tested with laboratory experiments in a two-layer stably stratified fluid forced from below by an oscillating grid. Quantitative measurements of density fluctuations across the interface are made by planar laser induced fluorescence. These fluctuations are splitted in a "wave" part and a "turbulent" part. The wave part of the density field is well described by a previous theory due to Phillips. We argue that statistical mechanics predictions apply for the turbulent part of the density field sufficiently close to the interface. However inside the mixed layer density fluctuations are instead controlled by a balance between eddy flux downward and dissipation by cascade to small scales. We report exponential tails for the density pdf in this region.