Fine Scale Eddy Cluster and Energy Cascade in Homogeneous Isotropic Turbulence

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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Particle Dispersion in Fine Scales of Homogeneous Isotropic Turbulence

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2007-37234 ◽

2007 ◽

Author(s):

M. Sato ◽

M. Tanahashi ◽

T. Miyauchi

Keyword(s):

Isotropic Turbulence ◽

Major Axis ◽

Stokes Number ◽

High Energy ◽

Energy Dissipation Rate ◽

Particle Dispersion ◽

Fine Scale ◽

Number Density ◽

Homogeneous Isotropic Turbulence ◽

Preferential Concentration

Direct numerical simulations of homogeneous isotropic turbulence laden with particles have been conducted to clarify the relationship between particle dispersion and coherent fine scale eddies in turbulence. Dispersion of 106 particles are analyzed for several particle Stokes numbers. The spatial distributions of particles depend on their Stokes number, and the Stokes number that causes preferential concentration of particles is closely related to the time scale of coherent fine scale eddies in turbulence. On the plane perpendicular to the rotating axes of fine scale eddies, number density of particle with particular Stokes number is low at the center of the fine scale eddy, and high in the regions with high energy dissipation rate around the eddy. The maximum number density can be observed at about 1.5 to 2.0 times the eddy radius on the major axis of the fine scale eddy.

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A physical mechanism of the energy cascade in homogeneous isotropic turbulence

Journal of Fluid Mechanics ◽

10.1017/s0022112008001511 ◽

2008 ◽

Vol 605 ◽

pp. 355-366 ◽

Cited By ~ 39

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.

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The effect of viscoelasticity on the turbulent kinetic energy cascade

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.585 ◽

2014 ◽

Vol 760 ◽

pp. 39-62 ◽

Cited By ~ 25

Author(s):

P. C. Valente ◽

C. B. da Silva ◽

F. T. Pinho

Keyword(s):

Kinetic Energy ◽

Isotropic Turbulence ◽

Relaxation Times ◽

Turnover Time ◽

Excess Energy ◽

Energy Cascade ◽

Homogeneous Isotropic Turbulence ◽

Total Energy Flux ◽

Strong Depletion ◽

Nonlinear Energy

AbstractDirect numerical simulations of statistically steady homogeneous isotropic turbulence in viscoelastic fluids described by the FENE-P model, such as those laden with polymers, are presented. It is shown that the strong depletion of the turbulence dissipation reported by previous authors does not necessarily imply a depletion of the nonlinear energy cascade. However, for large relaxation times, of the order of the eddy turnover time, the polymers remove more energy from the large scales than they can dissipate and transfer the excess energy back into the turbulent dissipative scales. This is effectively a polymer-induced kinetic energy cascade which competes with the nonlinear energy cascade of the turbulence leading to its depletion. It is also shown that the total energy flux to the small scales from both cascade mechanisms remains approximately the same fraction of the kinetic energy over the turnover time as the nonlinear energy cascade flux in Newtonian turbulence.

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422 Statistics of the Cluster of Coherent Fine Scale Eddies in Homogeneous Isotropic Turbulence

The proceedings of the JSME annual meeting ◽

10.1299/jsmemecjo.2005.2.0_309 ◽

2005 ◽

Vol 2005.2 (0) ◽

pp. 309-310

Author(s):

Kuniharu FUJIBAYASHI ◽

Mamoru TANAHASHI ◽

Toshio MIYAUCHI

Keyword(s):

Isotropic Turbulence ◽

Fine Scale ◽

Homogeneous Isotropic Turbulence

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517 Reynolds Number Dependence of Coherent Fine Scale Eddies in Homogeneous Isotropic Turbulence

The Proceedings of The Computational Mechanics Conference ◽

10.1299/jsmecmd.2001.14.567 ◽

2001 ◽

Vol 2001.14 (0) ◽

pp. 567-568

Author(s):

Mamoru TANAHASHI ◽

Shinichiro KIKUCHI ◽

Shiki IWASE ◽

Toru YANAGAWA ◽

Toshio MIYAUCHI

Keyword(s):

Reynolds Number ◽

Isotropic Turbulence ◽

Fine Scale ◽

Homogeneous Isotropic Turbulence ◽

Reynolds Number Dependence

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Three Dimensional Feature of Coherent Fine Scale Eddies in Homogeneous Isotropic Turbulence.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B ◽

10.1299/kikaib.65.3237 ◽

1999 ◽

Vol 65 (638) ◽

pp. 3237-3243 ◽

Cited By ~ 1

Author(s):

Mamoru TANAHASHI ◽

Md. Ashraf UDDIN ◽

Shiki IWASE ◽

Toshio MIYAUCHI

Keyword(s):

Isotropic Turbulence ◽

Three Dimensional ◽

Fine Scale ◽

Homogeneous Isotropic Turbulence

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The Influence of Polymers on Coherent Structures in Decaying Homogeneous Isotropic Turbulence

ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C ◽

10.1115/fedsm-icnmm2010-30459 ◽

2010 ◽

Author(s):

Wei-Hua Cai ◽

Hong-Na Zhang ◽

Feng-Chen Li

Keyword(s):

Numerical Simulation ◽

Direct Numerical Simulation ◽

Drag Reduction ◽

Coherent Structures ◽

Isotropic Turbulence ◽

Polymer Additives ◽

Fine Scale ◽

Reduction Mechanism ◽

Homogeneous Isotropic Turbulence ◽

Increase Rate

Drag reduction in decaying homogeneous isotropic turbulence (DHIT) with polymer additives has been observed, which leads to weaker turbulent characteristic quantities. Coherent structures play an important role in the understanding of turbulent dynamics, and the introduction of polymer additives can significantly modify their behavior. It is believed the modifications are closely related to drag reduction mechanism. In the present study, we mainly focus on investigating the influence of polymers on coherent structures from phenomenological and energetic viewpoint for DHIT with polymers based on direct numerical simulation (DNS). The results show that polymers can not only suppress the increase rate of the enstrophy and strain but also their productions, leading to a remarkable inhibition of coherent structures especially at fine scale.

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