Are finite‐amplitude effects important in non‐breaking mountain waves?

Abstract

AbstractLinear theory has long been used to study mountain waves and has been successful in describing much of their behaviour. In the simplest theoretical context, that of two‐dimensional steady‐state flow with constant Brunt–Väisälä frequency (N) and horizontal wind speed (U), finite‐amplitude effects are relatively minor until wave breaking occurs. However, in more complex environmental profiles, significant finite‐amplitude effects occur below the wave‐breaking threshold. We constructed a linearized version of a fully nonlinear time‐dependent model, thereby facilitating direct comparisons between linear and finite‐amplitude solutions in cases with upstream profiles representative of typical real‐world events. Beginning with the simplest profile that includes a tropopause, namely an environment with constant upstream wind speed and two layers of constant static stability, we progressively investigate more complex profiles that include vertical wind shear typical of the midlatitude westerlies. Our results demonstrate that, even without wave breaking, finite‐amplitude effects can play an important role in modulating the mountain‐wave amplitude and gravity‐wave drag. The modulation is a function of the tropopause height and is most pronounced when the cross‐ridge flow increases strongly with height.