Drag produced by trapped lee waves and propagating mountain waves in a two-layer atmosphere under nonlinear conditions

The behaviour of the pressure drag generated by trapped lee waves and upward-propagating internal waves in non-hydrostatic, stratified flow over a mountain ridge is investigated as a function of nonlinearity. A two-layer atmosphere is adopted, with piecewise-constant static stability and a uniform wind profile. The lower layer, between the surface and z = H , has stability N 1 , and the upper layer extends indefinitely above with stability N 2 , where N 2 < N 1 . Simulations are performed with a numerical model suitable for flows ranging from the microscale to the mesoscale, and nonlinearity is varied solely by increasing the mountain height. Linear reference values are obtained from the theoretical results reported by Teixeira et al., (2013). Two configurations are considered: (i) one in which trapped-lee-wave drag dominates over the drag due to propagating waves, and (ii) another in which the two components are of comparable magnitude. A set of diagnostics is introduced to clarify the physical processes associated with increasing nonlinearity. The results show that, as nonlinearity increases, the evolution of the total drag and its components is governed not only by the amplitude of the trapped lee waves, but primarily by the waveguide efficiency, which depends on the upstream Scorer parameter profile and the stable layer depth. This efficiency dictates whether the energy extracted from the incident flow through its interaction with the orography is largely retained and recycled within the trapped mode, or is instead transferred to propagating components and to processes associated with detuning and saturation. These findings may have implications for drag parametrisation in global climate and weather-prediction models.