Mountain-induced stagnation points in hydrostatic flow

The Bernoulli and hydrostatic relations are used to derive an exact diagnostic equation relating wind speed to the integral of vertical displacement aloft. The form of this equation does not support the “kinetic energy” concept of flow stagnation proposed by Sheppard (1956). Linear theory estimates of the displacement integral are used to predict the occurrence of stagnation points as a function of hill shape and ambient shear. For a long ridge perpendicular to a weakly sheared flow, stagnation begins aloft, thus allowing wave breaking and transition to a severe state. For a ridge aligned with the flow, waves dispersively weaken aloft and stagnation occurs first on the surface. This allows density surfaces to intersect the ground and the low-level flow to split around the hill.