On the growth of disturbances to forced and dissipated barotropic flows |
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| Authors: | Jieping Zou John Fyfe |
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| Institution: | 1. University of British Columbia, Department of Oceanography , 6270 University Boulevard, Vancouver, B.C., Canada , V6T 1Z4;2. Institute of Ocean Sciences, Canadian Department of Fisheries and Oceans;3. Climate Modelling and Diagnostics Studies Division, Canadian Climate Centre, Atmospheric Environment Service, Environment Canada |
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| Abstract: | Abstract We consider the growth of disturbances to large-scale zonally-asymmetric steady states in a truncated spectral model for forced and dissipated barotropic flow. A variant of the energy method is developed to optimize the instantaneous disturbance energy growth rate. The method involves solving a matrix eigenvalue problem amenable to standard numerical techniques. Two applications are discussed. (1) The global stability of a family of steady states is assessed in terms of the Ekman damping coefficient r. It is shown that monotonic global stability (i.e., every disturbances energy monotonically decays to zero) prevails when r≥rc . (2) Initially fastest-growing disturbances are constructed in the r<rc regime. Particular attention is paid to a subregion of the r<rc regime where initially-growing disturbances exist despite stability with respect to normal modes. Nonlinear time-dependent simulations are performed in order to appraise the time evolution of various disturbances. |
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| Keywords: | Optimal disturbances global stability energy method |
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