Trapped lee waves: a special analytical solution

A special analytical solution is derived for the classical orographic configuration of two-dimensional, stratified, linear, non-hydrostatic and dry model (without friction and Coriolis force). The well-known differential equation for the vertical velocity involves the vertical distribution of the Scorer parameter l super(2) (z) and in this case l super(2) is specified such that the lower atmosphere has a stable duct near the surface and is capped by a layer which acts as a good reflector. Examination of the solution for the vertical amplitude in the vicinity of singularities indicates the dominant lee wave-length and observations confirm that in comparable settings resonant trapped gravity waves develop in the lee of mountains. Comparison with a real atmospheric lee-wave event gives good predictions for the wavelength and wave drag, but, as in other linear models, the amplitude is underestimated.