Kelvin Wave-CISK Controlled by Surface Friction

Abstract

As a step toward an understanding of the mechanism of super cloud cluster (SCC), the effect of surface friction on the instability of Kelvin wave is discussed, together with the condition of the vertical profile of parameterized convective heating. In this paper (Part I), linear theory is developed with an equatorial beta-plane model in which the amount of convective heating is assumed to be proportional to the vertical velocity at the top of the boundary layer. Results from the eigenvalue problem suggest that the effect of surface friction is, at least under such parameterization, indispensable for essential understanding of SCC; this study is along the same line as Wang (1988) with respect to the importance of surface friction.Issue is focused on three unstable modes. One is a stationary mode excited with much heating at lower levels, and identified with conditional instability of the first kind (CIFK). The other two are Kelvin modes that contrast with each other; one is destabilized by enough heating at upper levels, even without surface friction (referred to as NFK: Non-Frictional Kelvin mode), and the other is destabilized by moderate heating at lower levels under the control of surface friction (FK: Frictional Kelvin mode). NFK has phase velocities of more than 10ms-1, and its growth rates are on the order of 10-3s-1 at small wavelengths. On the contrary, FK is characterized by smaller phase velocities of less than 10ms-l, and by only slight dependence of its growth rates on wavelength. In addition, the convergence in the boundary layer exhibits a phase shift slightly eastward relative to the convergence aloft; this is the key feature that induces effective feedback between convection and the wave.In view of the large phase velocity and the small preferred scale, NFK may be interpreted as a Kelvin mode of the type that has been treated in many previous studies on SCC. Difficulties in explaining the observed phase velocity and preferred scale of SCC are inherent in NFK. By contrast, FK can give a realistic phase velocity and preferred scale, and clear up major difficulties in the previous studies. Inclusion of surface friction is expected not only to serve as the missing link of the past linear theories of SCC, but also as a basis of future non-linear experiments with explicit moisture processes.