Nonlinear mountain waves in two and three spatial dimensions

Abstract

AbstractA three‐dimensional, time‐dependent, anelastic model is employed to simulate the evolution of nonlinear internal waves which are forced by stratified flow over isolated topography. Both two‐dimensional and three‐dimensional flows are considered. In the former case the discussion focusses upon the development of the wave field induced by a uniform mean flow with constant stability. The full three‐dimensional model is employed to study the nonlinear development of atmospheric ‘ship‐waves’ which have recently been observed in satellite photographs to the lee of oceanic islands in the Norwegian and Barents seas. The model is able to reproduce the characteristics of the observed wave patterns rather nicely when it is initialized with vertical profiles of wind and stability obtained through upper air ascents from stations located on the islands themselves. Detailed comparisons of the output of the nonlinear model with the results of three‐dimensional linear steady state theory are also provided. As is found to be the case in two‐dimensional analyses, linear theory may considerably underestimate the forced wave amplitude for symmetric topographic excitation.