Drag associated with 3D trapped lee waves over an axisymmetric obstacle in two‐layer atmospheres

Abstract

Mountain‐wave drag is evaluated explicitly using linear theory and verified against numerical simulations for the flow of idealized two‐layer atmospheres with piecewise‐constant stratification over an axisymmetric mountain. Static stability is either higher in the bottom layer and lower in the top layer (Scorer's atmosphere) or neutral in the bottom layer and positive in the top layer, separated by a sharp temperature inversion (Vosper's atmosphere). The drag receives contributions from long mountain waves propagating vertically in the upper layer and from short trapped lee waves propagating downstream, either in the lower layer or at the inversion. This trapped lee‐wave drag, which is typically not represented in parametrizations, acts on the atmosphere at low levels. As in flow over a 2D ridge, this drag has several maxima as a function of the height of the interface between the two layers for Scorer's atmosphere and is maximized by a marked Scorer parameter contrast between those layers. In Vosper's atmosphere, there is a single trapped lee‐wave drag maximum for Froude numbers near one, when the wind speed matches the phase speed of the dominant interfacial waves, and this drag is maximized for relatively low interface elevations, for which waves at the inversion have higher amplitude. The 3D flow geometry allows resonant wave modes to have various horizontal orientations and a continuous spectrum, forming a dispersive ‘Kelvin ship wave’ pattern, and expanding the regions in parameter space where the drag is non‐zero relative to 2D flow, but it also decreases the drag magnitude dispersively. Nevertheless, the trapped lee‐wave drag on an axisymmetric obstacle can still equal or exceed the drag associated with vertically propagating waves and the reference hydrostatic drag valid for a uniformly stratified atmosphere.