A physical mechanism of the energy cascade in homogeneous isotropic turbulence

2008 ◽  
Vol 605 ◽  
pp. 355-366 ◽  
Author(s):  
SUSUMU GOTO
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Transfer Rate ◽  
Physical Mechanism ◽  
Isotropic Turbulence ◽  
Scale Space ◽  
Energy Cascade ◽  
Homogeneous Isotropic Turbulence ◽  
Moderate Reynolds Number

In order to investigate the physical mechanism of the energy cascade in homogeneous isotropic turbulence, the internal energy and its transfer rate are defined as a function of scale, space and time. Direct numerical simulation of turbulence at a moderate Reynolds number verifies that the energy cascade can be caused by the successive creation of smaller-scale tubular vortices in the larger-scale straining regions existing between pairs of larger-scale tubular vortices. Movies are available with the online version of the paper.

scholarly journals Direct Numerical Simulation in Two Dimensional Homogeneous Isotropic Turbulence Using Spectral Method

2013 ◽  
Vol 5 (3) ◽  
pp. 435-445
Author(s):  
M. S. I. Mallik ◽  
M. A. Uddin ◽  
M. A. Rahman
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Flow Field ◽  
Direct Numerical Simulation ◽  
Spectral Method ◽  
Isotropic Turbulence ◽  
Qualitative Behavior ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Decaying Turbulence

Direct numerical simulation (DNS) in two-dimensional homogeneous isotropic turbulence is performed by using the Spectral method at a Reynolds number Re = 1000 on a uniformly distributed grid points. The Reynolds number is low enough that the computational grid is capable of resolving all the possible turbulent scales. The statistical properties in the computed flow field show a good agreement with the qualitative behavior of decaying turbulence. The behavior of the flow structures in the computed flow field also follow the classical idea of the fluid flow in turbulence. Keywords: Direct numerical simulation, Isotropic turbulence, Spectral method. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi:http://dx.doi.org/10.3329/jsr.v5i3.12665 J. Sci. Res. 5 (3), 435-445 (2013)  

Turbulent energy density in scale space for inhomogeneous turbulence

2018 ◽  
Vol 842 ◽  
pp. 532-553 ◽  
Author(s):  
Fujihiro Hamba
Keyword(s):  
Energy Spectrum ◽  
Energy Density ◽  
Isotropic Turbulence ◽  
Scale Space ◽  
Scale Dependence ◽  
Energy Cascade ◽  
Homogeneous Isotropic Turbulence ◽  
Velocity Correlation ◽  
Inhomogeneous Turbulence ◽  
Point Velocity

The energy spectrum is commonly used to describe the scale dependence of the turbulent fluctuations in homogeneous isotropic turbulence. In contrast, one-point statistical quantities, such as the turbulent kinetic energy, are employed for inhomogeneous turbulence modelling. To obtain a better understanding of inhomogeneous turbulence, some attempts have been made to describe its scale dependence by using the second-order structure function and the two-point velocity correlation. However, previous expressions for the energy density in the scale space do not satisfy the requirement that it should be non-negative. In this work, a new expression for the energy density in the scale space is proposed on the basis of the two-point velocity correlation; the integral with a filter function is introduced to satisfy the non-negativity of the energy density. Direct numerical simulation (DNS) data of homogeneous isotropic turbulence were first used to assess the role of the energy density by comparing it with the energy spectrum. DNS data of a turbulent channel flow were then used to investigate the energy density and its transport equation in inhomogeneous turbulence. It was shown that the new energy density is positive in the scale space of the homogeneous direction. The energy transfer was successfully examined in the scale space both in the homogeneous and inhomogeneous directions. The energy cascade from large to small scales was clearly observed. Moreover, the inverse energy cascade from large to very large scales was observed in the scale space of the spanwise direction.

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