The algebraic decay of equatorial Rossby waves in a shear flow

Through numerical integration, we show that equatorial Rossby waves, like their midlatitude counterparts, decay algebraically in the limit t → ∞ in a linear shear flow. For small times, the growth expected for some components does not translate into any growth of the wave disturbance as a whole when the initial conditions has a broad Fourier spectrum. The conclusion is that Rossby waves will amplify with time only when the mean flow has an inflection point or when the initial eddy field is strongly concentrated in long waves tilted against the shear.