The energy spectrum in the universal range of two-dimensional turbulence
The energy spectrum in the universal range of two-dimensional turbulence
复制标题
二维湍流普遍范围内的能谱
DOI：
10.1016/0169-5983(88)90029-9
复制
发表时间：
1988
影响因子：
1.5
通讯作者：
K. Ohkitani
中科院分区：
文献类型：
--
作者：
S. Kida;M. Yamada;K. Ohkitani
从高对称随机初速度场出发，采用谱方法对大雷诺数下的二维Navier-Stokes方程进行了1364个2阶模态的直接数值模拟。在涡度拟能耗散率η（t）取极大值后，出现了两个波数范围，它们受不同的相似律控制。能谱E（k，t）的形状表示为E（k，t）= Aη（t）1/6v 3/2（k/kd）-3exp [-λ 2A（k/kd）]，其中k为波数，t为时间，v为流体的运动粘度，kd = η（t）1/6 v1/2为耗散波数，A = 1.6。关于涡度拟能耗散率，我们观察到下列性质：（1）随着雷诺数R的增加，涡度拟能耗散率最大值出现的时间推迟，可能与ln R成正比。(ii)它接近有限的正值的无粘极限，如果上述的时间滞后被考虑在内，（iii）它的衰减成反比的时间的立方，使拟能表示为一个常数项和一个长期的衰减成反比的时间的平方的总和。本文讨论了为什么在大多数以前报道的二维周期性流动的直接数值模拟中观察到的能谱的幂律比k-3更陡。
Direct numerical simulation of two-dimensional Navier-Stokes equations at large Reynolds numbers is made by the spectral method with 1364 2 modes starting from a high-symmetric random initial velocity field. Two wavenumber ranges, governed by different similarity laws are observed after the enstrophy dissipation rate η (t) takes the maximum value. At small wavenumbers the energy spectrum is stationary in time, while at larger wavenumbers it decays according to the similarity law predicted by the enstrophy cascade theory, and the shape of the energy spectrum E (k, t) is expressed by E (k, t)= Aη (t) 1/6 v 3/2 (k/k d)-3 exp [–√ 2A (k/k d)], where k is the wavenumber, t the time, v the kinematic viscosity of fluid, k d= η (t) 1/6 v 1/2 the dissipation wavenumber, and A≈ 1.6. Concerning the enstrophy dissipation rate the following properties are observed:(i) As the Reynolds number R increases, the time of maximum enstrophy dissipation rate is delayed, probably in proportion to ln R.(ii) It approaches finite positive values in the inviscid limit if the above-mentioned time-lag is taken into account,(iii) It decays inversely proportionally to the cubic of time, so that the enstrophy is expressed as a sum of a constant term and a term which decays inversely proportionally to the square of time. This paper discusses why power laws of the energy spectrum observed in most of previously reported direct numerical simulations of two-dimensional periodic flows were steeper than k-3.
高分辨率湍流直接数值模拟中能量耗散的间歇性
DOI：
--
发表时间：
2007
期刊：
Journal of the Physical Society of Japan 76(7)
影响因子：
--
作者：
Mukougawa;H.;et al.;Y. Kaneda and K. Morishita
通讯作者：
Y. Kaneda and K. Morishita