LONG WAVE APPROXIMATION, LINEAR AND NON-LINEAR ROSSBY WAVES

The length scales L_x, L_y in x and y directions respectively are not in the same magnitude usually. For instance, L_x>L_y. This is called the long wave approximation and can be used to simplify the problem. The KdV equation can also be easily derived under this approximation. In this paper the physical foundation of the application of this long wave approximation to the non-linear Rossby wave is analysed The results show that the parameter (L_y/L_x)~2 which denotes the degree of anisotropy in the length scale is an important factor. As it reduces, the motion tends to higher frequency. For the low-latitudes, it is also easy to deriveKdV equation with the same approximation for non-linear Rossby wave. The characteristic features of the non-linear Rossby wave in the low latitudes are similar to those in the midlatitudes.