Wave Ducting in a Stratified Shear Flow over a Two-Dimensional Mountain. Part II: Implications for the Development of High-Drag States for Severe Downslope Windstorms

Abstract

In this study, it is found that the discrepancies among earlier studies of severe downslope windstorms are caused by the use of the critical level height (zc), instead of the low-level uniform flow?layer depth (z1), as an indicator to determine the optimal conditions for the occurrence of high-drag states. It is determined that once the wave breaking occurs, it induces a critical level and establishes a flow configuration favorable for wave ducting in the lower uniform wind layer, which determines the phase of reflected waves. Flow regimes of high- and low-drag states for a two-dimensional, nonrotating flow with uniform static stability and a basic-state critical level over a mountain were also determined as functions of nondimensional mountain height (h?), Richardson number (Ri), and nondimensional z1 in the terrain-following coordinates (σ?1). The authors found that 1) the critical h? for high-drag state increases as Ri increases when σ?1 is fixed, 2) the critical h? for high-drag state increases as σ?1 increases from 0.175 + n to 1.175 + n when Ri is fixed, and 3) the low-level response repeats periodically at one vertical wavelength. It was found that the nonlinear and critical level effects make the selection of high-drag states (σ?1 = 0.175 + n) from the linear wave duct modes (σ?1 = 0.175 + n/2). If a very stable layer is induced above σ?1, then the linear wave duct mode tends to be suppressed and the flow cannot develop into a high-drag state because the wave-ducting structure is destroyed. On the other hand, if a strong unstable layer is induced above σ1, then the linear wave duct mode may further develop into a high-drag state. Therefore, it is proposed that the development of a high-drag or severe wind state is supported by the nonlinear wave-ducting mechanism, whereas the high-drag state at the mature stage is maintained by the hydraulic mechanism as proposed by some earlier studies. It was found that nonlinearity plays an essential role in the downward and downstream expansion of the turbulent mixing region during the development stage of a severe downslope windstorm, which forces the fluid below this region to accelerate and propagate downstream as a hydraulic jump.