Transcritical flow over a step

Abstract

In both the ocean and the atmosphere, the interaction of a density stratified flow with topography can generate large-amplitude, horizontally propagating internal solitary waves. Often these waves appear as a wave-train, or undular bore. In this talk we focus on the situation when the flow is critical, that is, the flow speed is close to that of a linear long wave mode. In the weakly nonlinear regime, this is modeled by the forced Korteweg de Vries equation. We will review how Whitham's modulation theory has been applied to obtain an analytical description of undular bores for flow over isolated obstacles, and then show how the same approach can be used for flow over a step.