Numerical simulations of orographic gravity waves in flows which back with height

Numerical simulations are carried out to determine the steady-state gravity-wave structure above a circularly-symmetric, bell-shaped hill when the wind backs with height. Two types of idealized basic state flow are considered; one representing the advection of a uniform baroclinic shear flow, and the other being a flow of constant speed but with a wind vector that rotates uniformly in height. of particular interest is the nature of the critical level processes that must appear at all heights due to the three-dimensionality of the wave field and the rotation of the wind vector. As suggested by linear theory, a critical level or asymptotic wake is found downwind of the hill at any height, where ‘downwind’ refers to the wind at that level only. For small hills (where the nondimensional mountain height << unity), the simulated vertical momentum flux profiles are in very good agreement with linear hydrostatic wave theory if it is assumed that wave-component critical-level absorption is total (i.e. no wave transmission or reflections are permitted). the vertical momentum fluxes generated by a 1 km high hill show nonlinear enhancement by a factor of about 1.5. an interesting feature of the gravity-wave field generated by this 1 km mountain is an asymptotic wake that is dominated by a single intense shear layer in which the Richardson number is order unity.