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arXiv physics/0607280physics.flu-dynmath-phmath.MP
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分形强迫流中的能量耗散

Energy Dissipation in Fractal-Forced Flow

Alexey Cheskidov, Charles R. Doering, Nikola P. Petrov

摘要:

本文对三维不可压纳维-斯托克斯方程解的能量耗散率进行了严格的估计,重点研究了能量耗散率与驱动力性质的关系。对于平方可积体力,耗散的高雷诺数(低粘性)上界与粘性无关,与传统湍流能量级联的存在一致。另一方面,当体积力不是平方可积时,即,当力的傅立叶频谱在高波数下衰减得足够慢时,在很宽的空间尺度范围内存在显著的直接驱动。然后,耗散率的上限可能在高雷诺数下发散,这与最近对“分形强迫”湍流的实验和计算研究一致。

英文摘要:

The rate of energy dissipation in solutions of the body-forced 3-d incompressible Navier-Stokes equations is rigorously estimated with a focus on its dependence on the nature of the driving force. For square integrable body forces the high Reynolds number (low viscosity) upper bound on the dissipation is independent of the viscosity, consistent with the existence of a conventional turbulent energy cascade. On the other hand when the body force is not square integrable, i.e., when the Fourier spectrum of the force decays sufficiently slowly at high wavenumbers, there is significant direct driving at a broad range of spatial scales. Then the upper limit for the dissipation rate may diverge at high Reynolds numbers, consistent with recent experimental and computational studies of "fractal-forced'' turbulence.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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