Numerical issues in the simulation of orographic gravity waves

Abstract

Orographic gravity waves have been the subject of active research for several decades. Their effects have been parametrized in global numerical weather prediction models since the 1980s, but our understanding of trapped lee waves remains incomplete. Other phenomena such as rotors are linked to trapped lee waves, and these represent a significant aviation hazard, as well as an aspect of the flow which is not well understood or well represented in numerical models. Most previous investigations into flow over topography have included the boundary layer over small scale hills, but neglected it for larger scale mountain-induced gravity wave flows. These two situations have traditionally been treated separately, but the boundary layer cannot be ignored in gravity wave cases, because it can significantly change the flow over complex terrain. The simulations presented in this thesis use a high resolution, non-hydrostatic numerical model, which was originally designed to simulate boundary layer flows over small scale hills. The work presented here consists of two-dimensional simulations, with no boundary layer, in order to test the model's ability to predict adequately both upwardly and horizontally propagating waves. The model is used to simulate several two-dimensional idealised cases of orographic gravity waves, without a boundary layer, using a larger mountain and a larger numerical domain than in previous work, and these have shown good agreement with published analytical results. These simulations are carried out with a view to providing a sound base for turbulent boundary layer simulations, including turbulent flow phenomena observed around mountains, such as rotors, in order to better understand the flow patterns involved and the conditions conducive to their formation. This will lead to improvements in parametrizations and NWP performance. In the long term, the work may lead to a more sophisticated local lee wave/rotor forecasting tool for aviation use, to reduce the hazard posed by these phenomena, which are currently very difficult to predict. The work described in this thesis lays further ground work for future studies of this nature. Various tests are carried out in order to obtain a robust numerical configuration for the model. Grid independence is investigated in both the horizontal and the vertical, using both uniform and stretched grids, and the boundary condition at the top of the model domain is tested. An option was introduced shortly before the start of this work to use inflow/outflow boundary conditions upstream and downstream of the mountain, and the formulation of these boundary conditions, particularly the radiative outflow boundary condition at the downstream edge, is tested. Other sensitivity tests were carried out into the model timestep, the surface boundary condition, the mountain shape, and the initial transience caused by growing the mountain into the model domain at the start of a simulation.

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