On the Mean Motions Induced around a Planetary Wave Packet on a Rotating Sphere

Abstract

The mean motions induced around a planetary wave packet surrounding longitudinally a rotating sphere and propagating meridionally on it are discussed by using a simple model situation of two dimensional motion of an incompressible fluid.
It is shown that the wave packet conserves its angular momentum during the meridional propagation on a sphere, while it conserves its momentum under the beta-plane approximation. It is also shown that the wave packet induces the change of mean angular momentum in case of propagation on a sphere and the magnitude of the induced mean angular momentum is just equal to the wave action which is defined by the ratio of the wave energy and the westward drift angular velocity of the wave packet. Under the beta-plane approximation, this is reduced to the result that the induced mean zonal momentum is just equal to the wave momentum which is defined by the ratio of the wave energy and the ‘local’ westward phase velocity given by Rossby formula.
It is concluded from these results that the photon analogy to such a wave packet is allowed.
Finally, some comments are made upon the origin of westerlies found in the mid-latitudinal regions.