Reexamination of Wave-CISK Theory: Existence and Properties of Nonlinear Wave-CISK Modes

Abstract

Linear analyses of wave-CISK models often lead to the conclusion that the mechanism does not explain the scale selection of planetary-scale tropical motions. In particular, Kelvin or gravity wave-CISK tends to prefer cumulus-scale motions. On the other hand, numerical models with ?positive-only? heating did not experience much difficulty in generating large scale disturbances of realistic structure. A previous study explained these numerical results in terms of linear Kelvin wave-CISK modes, whose wave packages exhibit remarkable resemblence to the simulated disturbances. However, the linear theory can not explain how the simulated disturbances can maintain a ?wavenumber-l? structure against the explosive growth of short wavelength components. A reexamination of the wave-CISK theories is carried out in this paper. It is argued that the CISK mechanism possess inherently a very severe form of nonlinearity that takes full effect for even infinitesimal perturbations. The linearized CISK theories, therefore, do not give a correct description of a CISK-driven system at any stage of its development. A simple 5-level 64-wave spectral model demonstrates that the nonlinear effects of wave-CISK alone is able to produce exponentially growing ?wavenumber-1? flow patterns that propagate without change of shape. Since these flow patterns have well-defined structure, growth rate, and propagation speed, it is proposed to call them nonlinear wave-CISK modes. The nonlinear wave-CISK modes exhibit all the characteristics of the linear Kelvin wave-CISK packages of Chang and Lim (1988). The scale selection problem of their linear Kelvin wave-CISK theory has, however, been resolved. Introduction of a diffusion damping has no significant effect on the propagation speed and structure of these modes. The overall structure of the modes depends mainly on the growth rate. Varying other parameters may affect the growth rate; but modes of the same growth rate look rather like each other, irrespective of the other parameters.