Drag Produced by Waves Trapped at a Density Interface in Nonhydrostatic Flow over an Axisymmetric Hill

Abstract

Abstract Linear nonhydrostatic theory is used to evaluate the drag produced by 3D trapped lee waves forced by an axisymmetric hill at a density interface. These waves occur at atmospheric temperature inversions, for example, at the top of the boundary layer, and contribute to low-level drag possibly misrepresented as turbulent form drag in large-scale numerical models. Unlike in 2D waves, the drag has contributions from a continuous range of wavenumbers forced by the topography, because the waves can vary their angle of incidence to match the resonance condition. This leads to nonzero drag for Froude numbers (Fr) both <1 and >1 and a drag maximum typically for Fr slightly below 1, with lower magnitude than in hydrostatic conditions owing to wave dispersion. These features are in good agreement with laboratory experiments using two axisymmetric obstacles, particularly for the lower obstacle, if the effects of a rigid lid above the upper layer and friction are taken into account. Quantitative agreement is less satisfactory for the higher obstacle, as flow nonlinearity increases. However, even in that case the model still largely outperforms both 3D hydrostatic and 2D nonhydrostatic theories, emphasizing the importance of both 3D and nonhydrostatic effects. The associated wave signatures are dominated by transverse waves for Fr lower than at the drag maximum, a dispersive “Kelvin ship-wave” pattern near the maximum, and divergent waves for Fr beyond the maximum. The minimum elevation at the density-interface depression existing immediately downstream of the obstacle is significantly correlated with the drag magnitude.