We now consider wave refraction due to velocity strain and shear associated with vortical mean flows. Such refraction changes the waves' pseudomomentum field and, arguably, the central topic of wave-mean interactions outside simple geometry is how such pseudomomentum changes are related to the leading-order mean-flow response. The same question was satisfactorily answered in simple geometry by the pseudomomentum rule. However, refractive changes in the pseudomomentum do not rely in any essential way on wave dissipation or external forces, and yet they can irreversibly change the total amount of pseudomomentum in the wave field. This makes clear that the usual pseudomomentum rule of simple geometry, which equates such changes to an effective force exerted on the mean flow, must be modified.

As we shall see, the conservation law for the sum of pseudomomentum and GLM impulse is the key for understanding the wave-mean interactions in the presence of refraction. We will illustrate this by a number of examples consisting of wavepackets and confined wavetrains. The most important result is the following: if the concept of an effective mean force makes sense at all, then this force is not exerted at the location of the wavepacket, but at the location of the vortices that induce the straining field. This gives the wave—mean interactions a non-local character that was clearly absent in simple geometry, where the effective mean force was always exerted at the location of the wavepacket.