A Theoretical Analysis of Mixing Length for Atmospheric Models From Micro to Large Scales

Rachel Honnert,Christine Lac,Tim Nagel,Valéry Masson

doi:10.3389/feart.2020.582056

Abstract

A new mixing length adapted to the constraints of the hectometric-scale gray zone of turbulence for neutral and convective boundary layers is proposed. It combines a mixing length for mesoscale simulations, where the turbulence is fully subgrid and a mixing length for Large-Eddy Simulations, where the coarsest turbulent eddies are explicitly resolved. The mixing length is built for isotropic turbulence schemes, as well as schemes using the horizontal homogeneity assumption. This mixing length is tested over three boundary layer cases: a free convective case, a neutral case and a cold air outbreak case. The later combines turbulence from thermal and dynamical origins as well as presence of clouds. With this new mixing length, the turbulence scheme produces the right proportion between subgrid and resolved turbulent exchanges in Large Eddy Simulations, in the gray zone and at the mesoscale. This opens the way of using a single mixing length whatever the grid mesh of the atmospheric model, the evolution stage or the depth of the boundary layer.

Highlights

The atmospheric boundary layer (ABL) is the part of the atmosphere directly in contact with and rapidly influenced by the surface (Stull, 1988)
The growth of the convective boundary layer (CBL) slows in the LES, which is not the case in high resolution simulations using LRM17 and LDEAR
This article describes a new mixing length, L, built on a previously proposed approach to blend a LES and a mesoscale mixing length in order to produce the right amount of subgrid turbulence at hectometric scales: (9)

Summary

Introduction

The atmospheric boundary layer (ABL) is the part of the atmosphere directly in contact with and rapidly influenced by the surface (Stull, 1988). Honnert et al (2011) studied the resolved and subgrid parts of dry and cumulus-topped convective ABL (denoted hereafter CBL) simulations between 62.5 m grid spacing (i.e., large-eddy simulations or LES) and 8 km grid spacing (i.e., mesoscale regime) They found that the gray zone of turbulence ranges between 0.2 and 2 times the ABL height in convective cases (or the top of the cloud layer in cumulus-topped cases). Beare (2014) has defined an effective length scale for numerical models, ld,eff , accounting for the modeled energy dissipation emerging from the subgrid and the advection scheme He showed that the transition between the gray zone and the mesoscale occurs at h/ld,eff 0.7 in a convective case (where h is the boundary-layer height). The gray zone of turbulence concerns the hectometric scales

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