ON THE GROWTH OF DISTURBANCES TO FORCED AND DISSIPATED BAROTROPIC FLOWS

We consider the growth of disturbances to large-scale zonally-asymmetr ic steady states in a truncated spectral model for forced and dissipat ed barotropic flow. A variant of the energy method is developed to opt imize the instantaneous disturbance energy growth rate. The method inv olves solving a matrix eigenvalue problem amenable to standard numeric al techniques. Two applications are discussed. (1) The global stabilit y of a family of steady states is assessed in terms of the Ekman dampi ng coefficient r. It is shown that monotonic global stability (i.e., e very disturbances energy monotonically decays to zero) prevails when r greater-than-or-equal-to r(c). (2) Initially fastest-growing disturba nces are constructed in the r < r(c) regime. Particular attention is p aid to a subregion of the r < r(c) regime where initially-growing dist urbances exist despite stability with respect to normal modes. Nonline ar time-dependent simulations are performed in order to appraise the t ime evolution of various disturbances.