Interactions between Long and Synoptic-Scale Waves. Part II: Growth Rate of Long Waves

Abstract

The synoptic-scale waves can alter the structure and growth rate of long waves by a two-step process. First, the long wave modulates the synoptic-scale waves on a planetary scale by-changing the local instability characteristics of the flow. This produces planetary-scale variations in the eddy heat flu and. vorticity fluxes. Then, these fluxes can directly force the long wave. This coupling of a synoptic-scale wave and a long wave is studied as a two time-scale process; the synoptic-scale waves vary on a faster time scale than the long waves. In Part 1, we looked at the first step of this two-step process, the effect of a long wave on the synoptic-scale waves. In this paper, we look at the second step, effects of the synoptic-scale waves on long waves. We find two potentially unstable solutions, one is a modification of the linear long wave, and the other is a strongly nonlinear solution. In the latter solution, the long wave has aphase speed approximately equal to Re of the synoptic-scale wave, and its growth rate can be greater than the modified linear long wave.