Wave propagation through a stationary field of clouds: A homogenisation approach

Abstract

The effect of a sub‐grid scale cloud field on the propagation of long atmospheric waves is investigated using a new scale‐consistent formulation based upon the asymptotic theory of homogenisation. A key aim is to quantify potential model errors in wave propagation speeds, introduced by using averaged fields in place of the fully resolved circulation, in the setting of a simple stratified Boussinesq mid‐latitude β‐channel model. The effect of the cloud field, represented here by a random array of strongly nonlinear axisymmetric circulations, is found to appear in the large‐scale governing equations through new terms which redistribute the large‐scale buoyancy and horizontal momentum fields in the vertical. These new terms, which have the form of non‐local integral operators, are linear in the cloud number density, and are fully determined by the solution of a linear elliptic equation known as a cell problem. The cell problem in turn depends upon the details of the nonlinear cloud circulations. The integral operators are calculated explicitly for example cloud fields and then dispersion relations are compared for different waves in the presence of clouds at realistic densities. The main finding is that baroclinic Rossby waves are significantly slowed and damped by the clouds, whilst inertia‐gravity waves are affected almost exclusively by damping, most strongly at the lowest frequencies. In contrast, all waves with a barotropic structure are found to be almost unaffected by the presence of clouds, even at the highest realistic cloud densities.An important consequence of this study is a new approach to the closure of sub‐grid scale cloud fields in the parameterisation of convection in large‐scale atmospheric models.This article is protected by copyright. All rights reserved.

The sandpaper theory of flow–topography interaction for multilayer shallow-water systems

“…For instance, Vanneste (2003) considered quasi-geostrophic flows over a one-dimensional small-scale bathymetry and formulated large-scale evolutionary equations representing flow–topography interaction for a continuously stratified fluid. A homogenization approach was also recently used by Goldsmith and Esler (2023) to describe the propagation of large-scale internal waves through a stationary field of small-scale clouds. The scattering of tidally generated waves by a rough seafloor (Li and Mei 2014) is yet another example of the analytical treatment of stratified systems by multiscale methods.…”