The Effects of a Periodic Upstream Flow on Nonlinear Hydrostatic Mountain Waves

Abstract

Steady, two-dimensional, hydrostatic, nonlinear mountain waves are examined within the context of Long's model. Both uniform and periodic upstream flows are considered. The well-known condition for a hydrostatic wave to break (convective instability), under uniform upstream conditions, is reviewed and a reinterpretation provided. Long's wave solution appropriate for periodic upstream conditions is introduced, and shown to satisfy the same wave-breaking condition that is appropriate for uniform upstream flow: overturning is associated with convective instability. Moreover, there is no obvious relationship between wave overturning and the upstream distribution of either the static stability or the Richardson number. In essence, the physical process of wave breaking, associated with this particular solution, is decoupled from details of the upstream profiles. However, the levels at which breaking occurs, and profiles of streamline displacements, are both affected by upstream conditions.