Numerical simulations of orographic gravity waves in flows which back withheight

Numerical simulations are carried out to determine the steady-state gravity -wave structure above a circularly-symmetric, bell-shaped hill when the win d backs with height. Two types of idealized basic state flow are considered ; one representing the advection of a uniform baroclinic shear flow, and th e 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 l evel processes that must appear at all heights due to the three-dimensional ity 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 l inear hydrostatic wave theory if it is assumed that wave-component critical -level absorption is total (i.e. no wave transmission or reflections are pe rmitted). The vertical momentum fluxes generated by a 1 km high hill show n onlinear enhancement by a factor of about 1.5. An interesting feature of th e 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 n umber is order unity.