Thermally Forced Low Froude Number Flow past Three-Dimensional Obstacles

Abstract

The present study extends the discussion of the flow of a density-stratified fluid past three-dimensional obstacles for Froude number O(1) to flows past an isolated obstacle with heated/cooled surface. The study focuses on a response of thermally forced stratified flows representative of mesoscale flows past mountainous islands such as Hawaii or Taiwan. In order to minimize the span of the parameter space, uniform ambient wind and stratification, axially symmetric bell-shaped hills with moderate slopes representative of mesoscale mountains, and a simple thermal forcing function that mimics natural effects over mountainous islands are assumed. The earth's rotation, surface friction, viscosity, dissipation, and moisture are neglected. With these simplifications flows can be characterized with two parameters: the Froude number and a characteristic scale of thermal forcing (defined later in this paper). The principal question addressed in this study is under what circumstances will a transition occur from the low Froude number flow regime, characterized by the stagnation and splitting of the lower upwind flow, to the regime in which flow passes over rather than around the obstacle. It is shown that the linear theory captures adequately a tendency for such a transition. To provide quantitative measures of flow variability with the Froude number and scale of thermal forcing, a numerical model is employed and the results of numerous simulations are summarized in the form of a regime diagram. The principal result obtained is a simple criterion for the transition of a heated flow from the blocked to unblocked flow regime. The relevance of the theoretical considerations and idealized numerical simulations to natural flows is illustrated with an example of an application to a flow past the Hawaiian Archipelago. Comparison with held observations collected during the Hawaiian Rainband Project supports these theoretical findings.