On the structure of the stability matrix in the normal mode stability study of zonal incompressible flows on a sphere
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Abstract
A structure of the matrix resulting from the normal mode stability of tonal non-divergent flows on a sphere is analyzed. The analysis is based on using the recurrent formula derived for the nonlinear triad interaction coefficients. As an application, it is shown that a zonal flow of the form of a Legendre polynomial of degree j is exponentially and algebraically stable to all the small-scale perturbations whose zonal wave number is greater than j.
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