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On the application of the integral invariants and decay laws of vorticity distributions

Unsteady three-dimensional incompressible viscous flow fields induced by initial vorticity distributions are studied. Relevant invariants and decay laws of the moments of vorticity distributions are presented and shown to be useful in the numerical calculation of flow fields in two ways. First, the moments determine the leading terms of the far-field velocity, which can be employed as boundary conditions for the numerical calculation. Secondly, the deviations of the numerical results from the invariants and the decay laws can be used to measure the error of the numerical solution.