An exact series solution of the energy spectrum function for a Gaussian initial velocity field is obtained. It is shown that the energy spectrum function goes quickly to an algebraic form (1/kt)n, where 2 < n < 4, except in the regions of extremely small and large k, the algebraic region extending to larger k as time proceeds. The numerical value of n seems to depend on the initial energy spectrum function.
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Woo-Hyung Kahng (1970) studied this question.
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