论文标题
高雷诺数数量湍流中能量光谱的耗散范围
Dissipation range of the energy spectrum in high Reynolds number turbulence
论文作者
论文摘要
我们试图了解完全发育的湍流耗散范围内的动能光谱。数据是通过周期性域中强制的Navier-Stokes方程的直接数值模拟（DNS）获得的，对于泰勒级雷诺数，最高$r_λ= 650 $，非常出色的小尺度分辨率，$ k_ {max}η\ y Max $ r_ / y Max 3 $ aft $ r_ / y Max 3 $ and $ r_ / $ k_ {max} $是最大解析的波数，$η$是kolmogorov长度刻度。我们发现，对于有限范围的bavenumbers $ k $，超过瓶装范围为$ 0.1 \ sillesimkη\ lyssim0.5 $，所有$r_λ$的光谱显示出$ \ exp（-k^{2/3}）$的普遍拉伸指数行为，根据最近的理论预测。在近耗散范围内的拉伸指数拟合$ 1 \ Lessimkη\ Lessim 4 $没有独特的指数，随着$r_λ$的增加而降低。该区域可以被视为拉伸指数行为与远距离耗散范围$kη> 6 $之间的交叉，其中分析论证以及具有超级细胞分辨率的DNS数据（S. Khurshid等，Phys。〜Rev。〜Rev.〜Fluids 3，082601，082601，2018）建议A $ \ exp（-k）$依赖性。我们评论与假设伪代码定律的多重模型的联系。
We seek to understand the kinetic energy spectrum in the dissipation range of fully developed turbulence. The data are obtained by direct numerical simulations (DNS) of forced Navier-Stokes equations in a periodic domain, for Taylor-scale Reynolds numbers up to $R_λ=650$, with excellent small-scale resolution of $k_{max}η\approx 6$ for all cases (and additionally at $R_λ=1300$ with $k_{max}η\approx3$), where $k_{max}$ is the maximum resolved wavenumber and $η$ is the Kolmogorov length scale. We find that, for a limited range of wavenumbers $k$ past the bottleneck in the range $0.1 \lesssim kη\lesssim0.5$, the spectra for all $R_λ$ display a universal stretched exponential behavior of the form $\exp(-k^{2/3})$, in rough accordance with recent theoretical predictions. The stretched exponential fit in the near dissipation range $1 \lesssim kη\lesssim 4$ does not possess a unique exponent, which decreases with increasing $R_λ$. This region can be regarded as a crossover between the stretched exponential behavior and the far dissipation range $kη> 6$, in which analytical arguments as well as DNS data with superfine resolution (S. Khurshid et al., Phys.~Rev.~Fluids 3, 082601, 2018) suggest a $\exp(-k)$ dependence. We remark on the connection to the multifractal model which hypothesizes a pseudo-algebraic law.
