Recently, a new wave-mean interaction effect has been discovered that indicates that conventional gravity-wave parametrization schemes may contain significant errors in the computation of the wave-induced mean forces in magnitude, direction, and location. This changes the theoretical situation, with potentially significant implications for the design of next-generation gravity-wave parametrization schemes.

A theoretical study is presented of this fundamentally new wave-mean interaction effect able to force cumulative change in mean flows in the absence of wave breaking or other kinds of wave dissipation. It is associated with the refraction of nondissipating waves by inhomogeneous mean (vortical) flows. The effect is studied in detail in the simplest relevant model, the two-dimensional shallow-water equations. The refraction of a slowly varying wavetrain of small-amplitude gravity waves by a single weak (low Froude number) vortex is studied in detail. It is shown that, concomitant with the changes in the wave's pseudomomentum due to the refraction, there is an equal and opposite back-reaction force that is felt by the vortex core. This force is called a ``remote recoil'' here to stress that there is no need for the vortex core and wavetrain to overlap in physical space.

The effect is studied perturbatively using the wave amplitude and the vortex weakness as small parameters. The nature of the remote recoil is demonstrated clearly in various setups with wavetrains of finite or infinite length. The recoil force on the vortex core is shown to be described by an expression resembling the classical Magnus force felt by moving cylinders with circulation. Furthermore, in the case of wavetrains of infinite length, an explicit formula for the scattering angle of waves passing a vortex at a distance is derived correct to second order in Froude or Mach number, and cross-checked against numerical integrations of the ray-tracing equations.

This work is part of an ongoing study of internal gravity-wave dynamics in the atmosphere and may be important for the development of future gravity-wave parametrization schemes in numerical models of the global circulation. At present, all such schemes are constrained to neglect refraction effects caused by horizontally inhomogeneous mean flows. Removing this artificial constraint and taking account of remote recoil should make the parametrization schemes significantly more accurate.