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
article 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 demonstrate how
Whitham’s modulation theory may be applied to obtain an analytical description
of undular bores, for flow over isolated obstacles and for flow over a step.