Flow separation and rotor formation beneath 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 near-surface horizontal flow perturbations on the wave amplitude, wavelength and surface roughness is examined. It is shown that a normalized critical wave amplitude can be defined, above which rotors form. This normalized amplitude is a function of the ratio of the lee-wave horizontal wavelength to the roughness length.

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. Providing an accurate estimate of the lee-wave amplitude can be obtained, it is shown that the linear theory for the flow beneath the wave crests can be used to predict the occurrence of rotor formation.