Drag produced by trapped lee waves and propagating mountain waves in a two‐layer atmosphere

The surface drag force produced by trapped lee waves and upward propagating waves in non‐hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for a two‐layer atmosphere with piecewise‐constant static stability and wind speed profiles. The behaviour of the drag normalized by its hydrostatic single‐layer reference value is investigated as a function of the ratio of the Scorer parameters in the two layers l 2 /l 1 and of the corresponding dimensionless interface height l 1 H , for selected values of the dimensionless ridge width l 1 a and ratio of wind speeds in the two layers. When l 2 /l 1 → 1, the propagating wave drag approaches 1 in approximately hydrostatic conditions, and the trapped lee wave drag vanishes. As l 2 /l 1 decreases, the propagating wave drag progressively displays an oscillatory behaviour with l 1 H , with maxima of increasing magnitude due to constructive interference of reflected waves in the lower layer. The trapped lee wave drag shows localized maxima associated with each resonant trapped lee wave mode, occurring for small l 2 /l 1 and slightly higher values of l 1 H than the propagating wave drag maxima. As l 1 a decreases, i.e. the flow becomes more non‐hydrostatic, the propagating wave drag decreases and the regions of non‐zero trapped lee wave drag extend to higher l 2 /l 1 . These results are confirmed by numerical simulations for l 2 /l 1 = 0.2. In parameter ranges of meteorological relevance, the trapped lee wave drag may have a magnitude comparable to that of propagating wave drag, and be larger than the reference single‐layer drag. This may have implications for drag parametrization in global climate and weather‐prediction models. Copyright © 2012 Royal Meteorological Society