Wave Ducting in a Stratified Shear Flow over a Two-Dimensional Mountain. Part I: General Linear Criteria

Abstract

A linear theory for wave ducting is developed by solving a three-layer, steady-state nonrotating flow over a two-dimensional mountain analytically. The reflection coefficient (Ref), transmission coefficient, and the strongest horizontal wind speed at the surface are calculated based on the linear theory as functions of the Richardson number (Ri) and the depth of the lowest layer, with uniform wind speed. The relationship between the low-level response and reflectivity is also investigated. Based on this linear theory, a more general linear criteria is proposed for wave ducting, with the case considered by R. Lindzen and K.-K. Tung being only its subset. The linear theory is then applied to investigate the wave-ducting mechanism for long-lasting propagating waves in the atmosphere through a series of nonlinear numerical simulations. In the presence of a critical level, wave ducting may occur over a relatively wider range of Ri, once Ref is close to 1. That is, it is not necessary to have Ri < 0.25 in the shear layer for wave ducting to occur. The effects of varying N2/N1, N3/N1, and ?U3/U1 on the low-level response in a three-layer atmosphere have also been investigated. When a stable lower layer of thickness 0.25 + n/2 times the vertical wavelength is capped by a nearly neutral layer with 0.01 < Ri < 100, it may act as a wave duct due to the reflection from the interface of sharp gradients in static stability. This wave duct exists even if there exists no vertical shear in the wind profile. The wave-ducting criteria derived from the present linear theory could be applicable even to a nonlinear flow regime, although the ducted wave may be strengthened by nonlinearity and new ducted wave modes may be induced.