Flow separation and rotor formation beneath two-dimensional trapped lee waves

Numerical simulations of trapped lee waves generated in flow over a two-dimensional ridge are presented. It is shown that for sufficiently large amplitude waves flow separation occurs beneath the wave crests when a no-slip lower boundary condition is applied. The occurrence of separation corresponds to rotor motion, or recirculation, under the wave crests. The dependence of the wave-induced horizontal flow perturbations near the ground on the wave amplitude, wavelength and surface roughness is examined. It is shown that the normalized critical wave amplitude, above which rotors form, is a function of the ratio of the lee-wave horizontal wavelength to the surface roughness length. This normalized wave amplitude is defined as the ratio of the lee-wave pressure amplitude within the boundary layer, to the square of the friction velocity. Linearized turbulent equations for motion beneath the wave crests are considered and numerical solutions to the linear problem are compared with results from the simulations. When the waves are of sufficiently small amplitude that flow separation does not occur, the linear flow perturbations are shown to agree closely with the results from the simulations. It is also shown that linear theory provides a useful prediction of the occurrence of rotor formation.