Effects of clouds and phase changes on fast-wave averaging: A numerical assessment

Abstract

A remarkable property of geophysical fluids is that, even for nonlinear flows, a slow component can sometimes evolve independently of the fast-wave components. The dry Boussinesq equations, for instance, are known to exhibit this property for small Froude and Rossby numbers (i.e. strong stratification and rapid rotation). Here, we ask: Do the moist Boussinesq equations also exhibit this property, even if clouds are included as changes of water between different phases (vapour and liquid)? To investigate, the authors recently performed an asymptotic analysis and identified several ways in which phase changes could possibly induce coupling between the slow component and fast waves; however, these possibilities were not clearly settled from theoretical considerations alone. Here, to investigate further, a suite of numerical simulations is conducted, using a sequence of small values. For, the influence of waves on the slow component is relatively small, but does not decrease proportional to and, as and are decreased to and. As an explanation and physical interpretation, it is shown that, while linear waves have a time average of zero, the piecewise-linear waves that arise due to phase changes actually have a non-zero time-averaged component.