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

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 148; no. 748; pp. 3211 - 3230
• Main Authors: Teixeira, Miguel A. C., Argaín, José L.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.10.2022; Wiley Subscription Services, Inc
• Subjects: Atmosphere; Atmospheric circulation; Damping; Decay; Drag; Fluctuations; gravity wave drag; Lee waves; linear wave theory; Momentum flux; Momentum transfer; mountain waves; Mountains; wave momentum flux; wave trapping; weak dissipation; Wind shear
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.4355

Although 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. Normalized vertical flux of horizontal wave momentum (left panel) and its divergence (right panel) from linear theory, for the two‐layer atmosphere of Scorer, from the perfectly inviscid formula of Broad (Q. J. R. Meteorol. Soc., 2002, 128, 2167–2173) (black dotted line) and from the new quasi‐inviscid formula proposed in this study (red solid line). The ratio between the Scorer parameters in the upper and lower layer is l2/l1=0.2$$ {l}_2/{l}_1=0.2 $$, the dimensionless height of the interface between the two layers is l1H/π=0.6$$ {l}_1H/\pi =0.6 $$, and the dimensionless mountain width is l1a=2$$ {l}_1a=2 $$.