On the dependence of travelling wave stability on basic state wave phase speed

The dependence of stability on basic state wave phase speed is examined in a nondivergent barotropic model on a sphere for planetary scale waves with phase speeds typical of waves observed in the atmosphere. Triad interactions are examined analytically and compared to numerical results from a full spectral model. A number of triads may result in growth of the perturbation components for each basic state wave; for each triad there is a basic state wave phase speed where it is resonant, identified as the point where the critical amplitude for instability to that perturbation becomes zero. Critical amplitudes for instability obtained using the full spectral model generally agree well with triad results. Since the basic state wave phase speed determines which triad will grow, spatial structure and critical amplitudes for instability for the growing disturbances depend strongly on basic state wave phase speed. The results of this idealized study suggest that phase speed may be an important factor in determining the stability of planetary scale waves in the atmosphere.