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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Complementary remarks to properties of the energy spectrum in Leith's model of turbulence
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Complementary remarks to properties of the energy spectrum in Leith's model of turbulence

机译：利用湍流模型的能谱的互补评论

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摘要

In [1], we found that an anomalous exponent x~* of the power-law asymptotic E(k, t) ～ Ck ~(-x~*) as t → t_* for k 1 in k-space representation occurs into the interval 5/3 < x~* < x_2, where t_* is a finite singular time. Here 5/3 is the Kolmogorov index for the pure Kolmogorov spectrum and x_2 ≈ 1.95 corresponds to a Hopf bifurcation which appears in the dynamical system associated with the Leith model in the form of self-similar representation. This is then births the transient self-similar spectrum of the kinetic energy of turbulence discovered in [2]. The upper estimate was justified only by numerical simulations [2].We prove that the transient self-similar spectrum realised by a heteroclinic connection on the phase plane indeed corresponds to x~* < x_2. Then, we study the behavior of the energy spectrum E(k, t) beyond t_* as t →∞.
机译：在[1]中，我们发现动力法渐近e（k，t）〜ck〜（-x〜*）的异常指数x〜*在k空间表示中为t→t_ *为k 1 发生在间隔5/3

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