Flow of nonuniformly stratified fluid of large depth over topography

Abstract

This thesis extends Long's model (Long 1953) for steady flow of a hydrostatic, Boussinesq, uniformly stratified fluid of large depth over topography, to accommodate two latters of uniform stratification and subsequently variable stratification. The two-layer solution follows the work by Durran ( J. 992) and is obtained in a piecewise fashion with the appropriate matching conditions at the stratification interface. The variable stratification solution is obtained by resolving the vertical dependence of the stratification with a numerical 'shooting' or integration technique. Consequently, this solution is in general not fully analytical. These techniques are applied to small and finite-amplitude two-dimensional problems as well as small-amplitude three-dimensional problems. The two-layer solution, when implemented, encounters many of the same numerical problems seen by Durran. However, the variable stratification allows for the close approximation of the two-layer situation and does not suffer from the same convergence problems. Further, variable stratification allows for general stratification profiles. The effect known as tropopause tuning is diminished as the stratification interface continuously varies over a transition region. Similar results are also obtained for the small-amplitude three-dimensional case.