A Note on Gravity Waves Associated with a Density Current

Abstract

Gravity waves associated with the density current in a stably stratified environmental flow are considered employing a 2-dimensional steady adiabatic Boussinesq system, confined to a region between 2 horizontal planes separated by a height H. The consideration is restricted to gravity waves which are stationary relative to the density current. The system consists of warm and cold air masses, the buoyancy frequency of the former is N, and the propagation speed of the latter is U. The following results are obtained. If the stratification within the warm air mass is sufficiently weak compared with that between the warm and cold air masses, then far upstream or downstream gravity waves do not emerge. On the other hand, if the stratification is so strong that NH/π>U, then far upstream and/or downstream gravity waves do necessarily emerge.