Turbulent Fluxes in Stably Stratified Boundary Layers

TL;DR

This paper develops an advanced statistical approach to describe stably stratified turbulent boundary layers, successfully predicting mean profiles and correlations without unphysical turbulence suppression, applicable up to moderate Richardson numbers.

Contribution

It introduces a comprehensive method accounting for all second-order statistics, ensuring energy conservation and improving predictions of turbulence in stable boundary layers.

Findings

Analytic solutions for mean quantities and correlations are derived.

The approach avoids unphysical turbulence suppression at moderate Richardson numbers.

It is applicable to the lower atmospheric boundary layer up to Richardson numbers of order unity.

Abstract

We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the stable atmospheric boundary layer in mind is addressed. Traditional approaches to this problem, based on the profiles of mean quantities, velocity second-order correlations, and dimensional estimates of the turbulent thermal flux run into a well known difficulty, predicting the suppression of turbulence at a small critical value of the Richardson number, in contradiction with observations. Phenomenological attempts to overcome this problem suffer from various theoretical inconsistencies. Here we present an approach taking into full account all the second-order statistics, which allows us to respect the conservation of total mechanical energy. The analysis culminates in an analytic solution of the profiles of all mean quantities and all second-order correlations removing the unphysical predictions of previous theories. We propose that the approach taken here is sufficient to describe the lower parts of the atmospheric boundary layer, as long as the Richardson number does not exceed an order of unity. For much higher Richardson numbers the physics may change qualitatively, requiring careful consideration of the potential Kelvin-Helmoholtz waves and their interaction with the vortical turbulence.