Dissipation range of the energy spectrum in high Reynolds number turbulence

Abstract

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 $R_{\lambda }=650$, with excellent small-scale resolution of $k_{max}\eta \approx 6$ for all cases (and additionally at $R_{\lambda }=1300$ with $k_{max}\eta \approx 3$), where $k_{max}$ is the maximum resolved wavenumber and $\eta$ is the Kolmogorov length scale. We find that, for a limited range of wavenumbers $k$ past the bottleneck in the range $0.1\lesssim k\eta \lesssim 0.5$, the spectra for all $R_{\lambda }$ 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 $1\lesssim k\eta \lesssim 4$ does not possess a unique exponent, which decreases with increasing $R_{\lambda }$. This region can be regarded as a crossover between the stretched exponential behavior and the far dissipation range $k\eta >6$, 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.

arXiv comment6 pages, 4 figures

References in corpus (10)

• Universal intermittent properties of particle trajectories in highly turbulent flows
• Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
• Extreme velocity gradients in turbulent flows
• Far Dissipation Range of Turbulence
• Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence
• Unified Multifractal Description of Velocity Increments Statistics in Turbulence: Intermittency and Skewness
• Reynolds number effect on the velocity increment skewness in isotropic turbulence
• Spatiotemporal velocity-velocity correlation function in fully developed turbulence
• Experimental Study of the Bottleneck in Fully Developed Turbulence
• Analysis of the dissipative range of the energy spectrum in grid turbulence and in direct numerical simulations

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