Optimal Excitation of Neutral Rossby Waves

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  • 1 Dept. of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts
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Abstract

Properly configured disturbances are known to be effective in transferring the kinetic energy of a mean shear flow to neutrally stable modal and nonmodal waves. Consideration of perturbation energetics requires that such disturbances produce down-gradient momentum fluxes which are associated with perturbation phase lines oriented against the mean shear. Initial conditions chosen arbitrarily, except that they satisfy this requirement, have been shown to result in robust excitation of neutral waves. A question naturally arising from such studies is whether there exists, in some well-defined sense, a best or most effective choice of initial conditions which optimally excites the waves. This question is addressed as a variational problem, and examples of optimal initial conditions are identified for the barotropic β-plane channel. These examples include the most effective excitation of a given neutral Rossby mode and the most rapidly growing perturbation for a given time period without restriction on spectra composition.

Abstract

Properly configured disturbances are known to be effective in transferring the kinetic energy of a mean shear flow to neutrally stable modal and nonmodal waves. Consideration of perturbation energetics requires that such disturbances produce down-gradient momentum fluxes which are associated with perturbation phase lines oriented against the mean shear. Initial conditions chosen arbitrarily, except that they satisfy this requirement, have been shown to result in robust excitation of neutral waves. A question naturally arising from such studies is whether there exists, in some well-defined sense, a best or most effective choice of initial conditions which optimally excites the waves. This question is addressed as a variational problem, and examples of optimal initial conditions are identified for the barotropic β-plane channel. These examples include the most effective excitation of a given neutral Rossby mode and the most rapidly growing perturbation for a given time period without restriction on spectra composition.

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