Geometry of two-point velocity correlation tensor of homogeneous isotropic turbulence with helicity in sol-manifold coordinates

2018 ◽  
Vol 59 (10) ◽  
pp. 103507
Author(s):  
Rohollah Bakhshandeh Chamazkoti ◽  
Martin Oberlack
Keyword(s):  
Isotropic Turbulence ◽  
Homogeneous Isotropic Turbulence ◽  
Velocity Correlation ◽  
Correlation Tensor ◽  
Point Velocity

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.

scholarly journals The Extended Symmetry Lie Algebra and the Asymptotic Expansion of the Transversal Correlation Function for the Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
V. N. Grebenev ◽  
A. N. Grishkov ◽  
M. Oberlack
Keyword(s):  
Correlation Function ◽  
Asymptotic Expansion ◽  
Lie Algebra ◽  
Degrees Of Freedom ◽  
Isotropic Turbulence ◽  
Central Charge ◽  
Riemannian Metrics ◽  
Equivalence Transformation ◽  
Velocity Correlation ◽  
Correlation Tensor

The extended symmetry of the functional of length determined in an affine spaceK3of the correlation vectors for homogeneous isotropic turbulence is studied. The two-point velocity-correlation tensor field (parametrized by the time variablet) of the velocity fluctuations is used to equip this space by a family of the pseudo-Riemannian metricsdl2(t)(Grebenev and Oberlack (2011)). First, we observe the results obtained by Grebenev and Oberlack (2011) and Grebenev et al. (2012) about a geometry of the correlation spaceK3and expose the Lie algebra associated with the equivalence transformation of the above-mentioned functional for the quadratic formdlD22(t)generated bydl2(t)which is similar to the Lie algebra constructed by Grebenev et al. (2012). Then, using the properties of this Lie algebra, we show that there exists a nontrivial central extension wherein the central charge is defined by the same bilinear skew-symmetric formcas for the Witt algebra which measures the number of internal degrees of freedom of the system. For the applications in turbulence, as the main result, we establish the asymptotic expansion of the transversal correlation function for large correlation distances in the frame ofdlD22(t).

The theory of axisymmetric turbulence

1950 ◽  
Vol 242 (855) ◽  
pp. 557-577 ◽  
Keyword(s):  
Differential Equations ◽  
Isotropic Turbulence ◽  
Explicit Representation ◽  
Velocity Correlation ◽  
Correlation Tensor ◽  
Gauge Invariant ◽  
Preferred Direction ◽  
Von Karman ◽  
Von Kármán

The present paper completes the theory of axisymmetric tensors and forms to the extent that is needed for the development of a theory of turbulence in which symmetry about a certain preferred direction is assumed to exist. Particular attention is given to the manner in which tensors, solenoidal in one or more indices, can be derived, uniquely, in a gauge-invariant way, as the curl of a suitably defined skew tensor. The explicit representation of the fundamental velocity correlation tensor ( ) in terms of two defining scalars is found; and the differential equations governing these scalars is also derived. In the theory of axisymmetric turbulence these latter equations replace the equation of von Karman & Howarth in the theory of isotropic turbulence.

scholarly journals A Lagrangian direct-interaction approximation for homogeneous isotropic turbulence

1997 ◽  
Vol 345 ◽  
pp. 307-345 ◽  
Author(s):  
SHIGEO KIDA ◽  
SUSUMU GOTO
Keyword(s):  
Energy Spectrum ◽  
Differential Equations ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Direct Interaction ◽  
Homogeneous Isotropic Turbulence ◽  
Velocity Correlation ◽  
Stationary Turbulence ◽  
Direct Interaction Approximation ◽  
Velocity Derivative

A set of integro-differential equations in the Lagrangian renormalized approximation (Kaneda 1981) is rederived by applying a perturbation method developed by Kraichnan (1959), which is based upon an extraction of direct interactions among Fourier modes of a velocity field and was applied to the Eulerian velocity correlation and response functions, to the Lagrangian ones for homogeneous isotropic turbulence. The resultant set of integro-differential equations for these functions has no adjustable free parameters. The shape of the energy spectrum function is determined numerically in the universal range for stationary turbulence, and in the whole wavenumber range in a similarly evolving form for the freely decaying case. The energy spectrum in the universal range takes the same shape in both cases, which also agrees excellently with many measurements of various kinds of real turbulence as well as numerical results obtained by Gotoh et al. (1988) for a decaying case as an initial value problem. The skewness factor of the longitudinal velocity derivative is calculated to be −0.66 for stationary turbulence. The wavenumber dependence of the eddy viscosity is also determined.

Application of the POD to the Similarity Region of an Axisymmetric Turbulent Jet

2002 ◽  
Author(s):  
Stephan Gamard ◽  
William K. George
Keyword(s):  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Turbulent Jet ◽  
Velocity Correlation ◽  
Azimuthal Mode ◽  
Correlation Tensor ◽  
Double Fourier Transform ◽  
Streamwise Velocity Component ◽  
Point Velocity ◽  
Two Peaks

Multipoint instantaneous measurements of the streamwise velocity component were obtained in the far field region of an axisymmetric turbulent jet from 20 to 69 diameters downstream for jet exit Reynolds numbers ranging from 40,000 to 84,700. The Proper Orthogonal Decomposition (POD) was then applied to a double Fourier transform in time and azimuthal direction of the two-point velocity correlation tensor. The first eigenspectrum, which contains more than 62% of the resolved streamwise energy, has two peaks: one at azimuthal mode-2 at near zero frequency, and another at mode-1 at a local Strouhal number (fx/Uc) of approximately 1. When checked against two-point statistics similarity analysis from Ewing (1995) extended to the POD, the results compare favorably and also give some hints into the resolution necessary to cover the field.

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