Tropospheric and Stratospheric Ducting of Stationary Mountain Lee Waves

Abstract

The mountain lee-wave problem is solved for a steady-state linearized model yielding both real and complex resonance modes. Filters applied to the wind and potential temperature determine the mean conditions and the number of layers required. Continuity of the wavenumber at the layer interfaces excludes spurious resonance modes. For multilayer models the solutions usually include six to nine waves ducted in the stratosphere and one wave ducted in the troposphere. Changing the tropospheric duct changes the tropospheric resonant wavelength and modulates the amplitude of the stratospheric waves. Progressive lowering of the top of the stratospheric duct from infinity changes the horizontal wavenumber of the longest waves from real to complex. These radiating waves dampen downstream from the mountain. Rotor pairs and steps in the stratospheric streamlines, generated when the ducting is strong, suggest sources of clear air turbulence. Large-amplitude tropospheric waves, thought to produce shock waves and strong surface winds, are shown to be caused by a strong shear of the mean wind in the lower troposphere and by horizontal wavelengths approaching 2π times the half-width of the mountain barrier.