Abstract

Four of the simplest examples of interaction between a single wavetrain and a single vortex are analysed, with a focus on effective recoil forces, local and remote. All four examples comply with the pseudomomentum rule. The first three examples are two-dimensional and non-rotating (shallow-water or gas dynamical), and the fourth is rotating, with deep-water waves inducing an Ursell-Hasselmann-Pollard `anti-Stokes flow’. The Froude or Mach number, and the Rossby number in the fourth example, are assumed small. Contrary to a recent suggestion, the anti-Stokes flow does not suppress remote recoil. Remote recoil is all or part of the interaction in all four examples, except in one special limiting case. That is the only case in which, exceptionally, the effective recoil force can be regarded as entirely local, and therefore identifiable with the Craik-Leibovich vortex force. It is the case often focused on in the quantum fluids literature, in connection with phonon-vortex interactions. Another peculiarity of that case is that the only significant wave refraction effect is the Aharonov-Bohm topological phase jump.