Flow patterns and drag in near-critical flow over isolated orography

Since early manned space flight orographically forced cloud patterns have been described in terms of the single isolated shock structure of shallow-water flow or, equivalently, compressible fluid flow. Some of these observations show, behind an initial 'bow wave,' a series of almost parallel wave crests. This paper considers the simplest extension of shallow-water theory that retains not only nonlinear steepening of waves but includes departures from hydrostatic balance, and thus wave dispersion, showing that the single shocks of shallow-water theory are transformed into multiple parallel finite-amplitude wave crests. The context of the discussion is the forced Kadomtsev--Petviashvili equation from classical ship wave dynamics, which plays the same role in two-dimensional near-critical fluid flow as the more familiar Korteweg-de Vries equation in one-dimensional flow. The drag and flow regimes in near-critical flow over isolated orography are described in terms of the three governing parameters of the flow: the deviation of the flow speed from critical, the strength of nonhydrostatic effects, and the strength of orographic forcing.