Free Solutions of the Barotropic Vorticity Equation

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Abstract
Using a variational procedure, we numerically search for steady solutions to the unforced, inviscid barotropic vorticity equation on the sphere. The algorithm produces many states that have extremely small tendencies within the triangular 15 spherical harmonic truncation employed in the calculation and which can thus be considered to be free modes. Often these states are similar to the planetary scale structure of the first guess fields; when observed 500 mb flow patterns are used as first guesses, the resulting free solutions can have structures reminiscent of time-mean atmospheric states. The functional relationship between streamfunction and absolute vorticity in the solutions is usually nonlinear, and thus the solutions are unlike any previously known free solutions of the barotropic vorticity equation. Each first guess considered in the study leads to a distinct, free, steady stale, but the collection of such states is not dense in phase space. The distribution of these states is nonuniform.... Abstract Using a variational procedure, we numerically search for steady solutions to the unforced, inviscid barotropic vorticity equation on the sphere. The algorithm produces many states that have extremely small tendencies within the triangular 15 spherical harmonic truncation employed in the calculation and which can thus be considered to be free modes. Often these states are similar to the planetary scale structure of the first guess fields; when observed 500 mb flow patterns are used as first guesses, the resulting free solutions can have structures reminiscent of time-mean atmospheric states. The functional relationship between streamfunction and absolute vorticity in the solutions is usually nonlinear, and thus the solutions are unlike any previously known free solutions of the barotropic vorticity equation. Each first guess considered in the study leads to a distinct, free, steady stale, but the collection of such states is not dense in phase space. The distribution of these states is nonuniform....

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