Pressure drag produced by trapped lee waves and propagating mountain waves under nonlinear conditions

Abstract. 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 N₁, and the upper layer extends indefinitely above with stability N₂, where N₂ < N₁. 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 a previously established linear framework for two-layer trapped and propagating mountain-wave drag. 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 controlled not only by the amplitude of the trapped lee waves, but above all by the waveguide guiding efficiency. This efficiency determines whether the energy extracted from the incident flow through its interaction with the orography is largely retained and recycled within the trapped mode, or instead is transferred earlier 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.