On the Structural Characteristics of Steady Finite-Amplitude Mountain Waves over Bell-Shaped Topography

Abstract

The characteristics of the two-dimensional steady state flow of unbounded stratified Boussinesq fluid over an isolated obstacle of finite height are analyzed for the simplqst case in which the incident flow speed, UO, and Brunt-Vaisala frequency, NO, are constant. The Helmholtz equation which describes this flow (Long 1953) issolved numerically subject to the exact nonlinear lower boundary condition, and the maximum steepness of the streamlines is determined as a function of the height, b, and half-width, a, of a bell-shaped obstacle. The celebrated value of Noh/ Uo = 0.85 for the critical steepening of hydIostatic waves obtained by Miles aqd Huppert(1969) is recovered in the limit of very broad obstacles such that Noh/Uo, 9 1. Salient features'of the full nonhydrostatic Long's solution which are relevant to the study of the stability of such large amplitude mountain waves-a topic which is the focus of two companion papers in this issue of the journal (Laprise and Peltier)- are fully enumerated.