Hydrostatic adjustment: Lamb's problem

The prototype problem of hydrostatic adjustment for large-scale atmospheric motions is presented. When a horizontally infinite layer of compressible fluid, initially at rest, is instantaneously heated, the fluid is no longer in hydrostatic balance since its temperature and pressure in the layer have increased while its density remains unchanged. The subsequent adjustment of the fluid is described in detail for an isothermal base-state atmosphere. The initial imbalance generates acoustic wave fronts with trailing wakes of dispersive acoustic gravity waves. Use of the one-dimensional analogue of the conservation of Ertel's potential vorticity removes hydrostatic degeneracy and determines the final equilibrium state directly. As a result of the adjustment process, the heated layer has expanded vertically. Since the region below the layer is unaltered, the region aloft is displaced upward uniformly. The energetics of the adjustment are documented. -from Author