Abstract
The second order mean motion induced around an internal Rossby wave packet, having an infinite zonal length and propagating vertically in an inviscid Boussinesq fluid at rest in a channel, is discussed, and the validity of photon analogy to such a wave packet is examined.
It is shown that the second order mean zonal momentum averaged in the meridional direction is just equal to the wave momentum E/C (where E and C are the wave energy and the phase velocity in the zonal direction respectively). This guarantees the validity of photon analogy to the wave packet, and also implies that the treatment done rather intuitively in the previous paper by the author (Uryu, 1974) is essentially correct.
It is shown that, to the first order in ∈ (where ∈ is a small parameter characterizing the slowness of variation of wave amplitude), the vertical component of Lagrangian mean velocity is zero, as a result of the cancellation between the Stokes drift and the Eulerian mean velocity.
The case of propagation in a shear flow is also treated, and it is shown that the absorption of wave at the critical level occurs as a result that the wave momentum is stored up in the mean zonal flow there.
It is also shown that the results obtained in case of Rossby wave packet can be obtained without any essential change also in case of internal gravity wave packet under the same situation.
