The drag exerted by weakly dissipative trapped lee waves on the atmosphere: application to Scorer's two-layer model

TL;DR

This paper develops a framework to calculate the momentum flux profiles of trapped lee waves with weak dissipation, clarifying their atmospheric drag effects and enabling better parametrizations in climate models.

Contribution

It introduces a method to unambiguously compute momentum flux profiles for trapped lee waves with dissipation, resolving previous oscillation issues and linking inviscid drag to surface flux.

Findings

Momentum flux profiles converge with weak dissipation.

Inviscid drag is recovered at the surface.

Framework applies to various trapped lee waves.

Abstract

While it is known that trapped lee waves propagating at low levels in a stratified atmosphere exert a drag on the mountains that generate them, the distribution of the corresponding reaction force exerted on the atmospheric mean circulation, defined by the wave momentum flux profiles, has not been established, because for inviscid trapped lee waves these profiles oscillate indefinitely downstream. A framework is developed here for the unambiguous calculation of momentum flux profiles produced by trapped lee waves, which circumvents the difficulties plaguing the inviscid trapped lee wave theory. Using linear theory, and taking Scorer's two-layer atmosphere as an example, the waves are assumed to be subject to a small dissipation, expressed as a Rayleigh damping. The resulting wave pattern decays downstream, so the momentum flux profile integrated over the area occupied by the waves converges to a well-defined form. Remarkably, for weak dissipation, this form is independent of the value of Rayleigh damping coefficient, and the inviscid drag, determined in previous studies, is recovered as the momentum flux at the surface. The divergence of this momentum flux profile accounts for the areally-integrated drag exerted by the waves on the atmosphere. The application of this framework to this and other types of trapped lee waves potentially enables the development of physically-based parametrizations of the effects of trapped lee waves on the atmosphere.