A comprehensive empirical model for non-linear pressure drag across non-hydrostatic flow regimes with trapped lee waves

Abstract. This study introduces a novel and computationally efficient empirical model to estimate the total pressure drag generated by trapped lee waves and upward-propagating internal waves in moderate to severe non-hydrostatic, stratified flow over a mountain ridge, as a function of flow nonlinearity. The model's core framework is based on a two-layer atmosphere characterised by a piecewise-constant Scorer parameter, l. In this configuration, a lower layer extending from the surface to a height z=H is defined by a constant value l1, while an upper layer, extending indefinitely aloft, is characterised by l2, where l2 < l1. Several features are incorporated into this idealised framework to enable the representation of a wide range of flow regimes over mountainous terrain, including those with realistic vertical profiles of the Scorer parameter. To develop the empirical formulation, a numerical model operating at the micro- to mesoscale is employed. This model is well-suited for simulating realistic, nonlinear flows over high mountains with steep slopes. From idealised cases with simple l(z) profiles to more realistic configurations with complex structures, the empirical model yields results that compare favourably with numerical simulations for flow regimes characterised by moderately to strong nonlinearity. This empirical model serves as a valuable foundation for developing parameterisations within weather prediction models to represent the effects of pressure drag generated in nonlinear flow conditions where trapped lee waves form, alleviating the requirement for high-resolution numerical models to downscale over steep terrain.