Computation of mountain wave clouds in a moist Boussinesq fluid model

This thesis presents computations of time-steady 2D clouds forming over mountain topography, with an interest in resolving the fine-scale physics at the cloud edge. The underlying model takes the incompressible Euler equations as its basis, and couples the atmospheric fluid flows to the physics of phase change in order to compute cloud-edge boundary locations in a vertically-stratified atmosphere. This coupling gives rise to a free-boundary problem for the cloud edge. This model has been employed here to successfully recover mountain cloud behaviour for a variety of atmospheric conditions, including computations of the well-known lens shape of the lenticular cloud. The problem of time-steady, density-stratified flow over ground topography can be reduced to a 2D Helmholtz problem for the streamfunction due to Long's theory. The domain of this PDE is a perturbed 2D half-space, and the streamfunction is specified by a bottom boundary that follows a localized mountain terrain. This thesis presents a new extension of Long's theory to include cloudy air, where the derived Helmholtz equation now includes localized forcing associated with small regions of cloud. The nature of the PDE domain makes the problem well-suited for a boundary method application. The scheme used in this work utilizes the method of fundamental solutions (MFS), a numerical approach related to the boundary integral equation method, which approximates the solutions to elliptic problems by finite sums of fundamental solutions of the PDE operator. The MFS is coupled with an iterative solver to resolve the free-boundary problem for the cloud geometry, and the numerical performance of this scheme is analyzed.