Abstract
The drag and momentum fluxes produced by gravity waves generated in flow over orography are reviewed, focusing on adiabatic conditions without phase transitions or radiation effects, and steady mean incoming flow. The orographic gravity wave drag is first introduced in its simplest possible form, for inviscid, linearized, non-rotating flow with the Boussinesq and hydrostatic approximations, and constant wind and static stability. Subsequently, the contributions made by previous authors (primarily using theory and numerical simulations) to elucidate how the drag is affected by additional physical processes are surveyed. These include the effect of orography anisotropy, vertical wind shear, total and partial critical levels, vertical wave reflection and resonance, non-hydrostatic effects and trapped lee waves, rotation and nonlinearity. Frictional and boundary layer effects are also briefly mentioned. A better understanding of all of these aspects is important for guiding the improvement of drag parametrization schemes.
Highlights
The atmosphere above the boundary layer is almost invariably characterized by positive static stability, supporting the propagation of internal gravity waves, where buoyancy is the main restoring force
While drag on the orography must obviously be exerted at the surface, the reaction force on the atmosphere may be distributed in space, and often acts at high altitudes
They aimed to explain why in flow with constant shear over a 3D mountain the drag decreases with Ri, whereas for a directional shear flow where the wind turns with height at a constant rate keeping a constant magnitude, expressed as: U = U0 cos, V = U0 sin
Summary
The atmosphere above the boundary layer is almost invariably characterized by positive static stability, supporting the propagation of internal gravity waves, where buoyancy is the main restoring force. These campaigns were generally carried out by large consortia, an exception being the smaller-scale campaign in the island of Madeira reported by Miranda et al [36] While they contributed decisively to advance our knowledge about orographic flows, and included pressure measurements that allowed obtaining rough estimates of mountain wave drag, their success in this respect was limited, because of the limited available data sampling and complexity of real-world conditions (see [37]). This hampered a more detailed comparison with theory, numerical simulations and lab experiments, which tend to assume much more idealized conditions. Differentiating (1) with respect to x and (2) with respect to y, adding the two equations and using (5) to eliminate u and v, an equation for p expressed in terms of w is obtained:
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