Realizability of the rapid distortion theory spectrum: The mechanism behind the Kelvin–Townsend equations

2021 ◽  
Vol 62 (6) ◽  
pp. 063101
Author(s):  
A. Ruiz de Zarate Fabregas ◽  
N. L. Dias ◽  
D. G. Alfaro Vigo
Keyword(s):  
Rapid Distortion Theory

Modelling of rapid pressure—strain in Reynolds-stress closures

1994 ◽  
Vol 269 ◽  
pp. 143-168 ◽  
Author(s):  
Arne V. Johansson ◽  
Magnus Hallbäck
Keyword(s):  
Strain Rate ◽  
Reynolds Stress ◽  
Sudden Change ◽  
Model Parameters ◽  
Rapid Distortion Theory ◽  
Flow Parameters ◽  
Turbulent Reynolds Number ◽  
Principal Axes ◽  
Anisotropy Tensor ◽  
Rapid Pressure

The most general form for the rapid pressure—strain rate, within the context of classical Reynolds-stress transport (RST) closures for homogeneous flows, is derived, and truncated forms are obtained with the aid of rapid distortion theory. By a classical RST-closure we here denote a model with transport equations for the Reynolds stress tensor and the total dissipation rate. It is demonstrated that all earlier models for the rapid pressure—strain rate within the class of classical Reynolds-stress closures can be formulated as subsets of the general form derived here. Direct numerical simulations were used to show that the dependence on flow parameters, such as the turbulent Reynolds number, is small, allowing rapid distortion theory to be used for the determination of model parameters. It was shown that such a nonlinear description, of fourth order in the Reynolds-stress anisotropy tensor, is quite sufficient to very accurately model the rapid pressure—strain in all cases of irrotational mean flows, but also to get reasonable predictions in, for example, a rapid homogeneous shear flow. Also, the response of a sudden change in the orientation of the principal axes of a plane strain is investigated for the present model and models proposed in the literature. Inherent restrictions on the predictive capability of Reynolds-stress closures for rotational effects are identified.

The distortion of turbulence by irrotational plane strain

1968 ◽  
Vol 32 (4) ◽  
pp. 657-673 ◽  
Author(s):  
H. J. Tucker ◽  
A. J. Reynolds
Keyword(s):  
Plane Strain ◽  
Strain Ratio ◽  
Equilibrium Structure ◽  
Turbulence Energy ◽  
Grid Turbulence ◽  
Rapid Distortion Theory ◽  
Degree Of Anisotropy ◽  
The Individual ◽  
Mean Strain

The experiments reported here extend those of Townsend which form the basis of his model of free turbulence. Here straining is carried to a strain ratio of 6:1, while Townsend's straining went only to 4:1. Two kinds of distorting ducts are used to produce the uniform mean strain applied to initially nearly isotropic grid turbulence.The results differ from Townsend's in that: (i) a considerably higher degree of anisotropy is achieved, Townsend's measure of anisotropy attaining values up to 0·6, rather than the maximum of 0·42 he found; (ii) there is no evidence that an equilibrium structure is attained; and (iii) the strained turbulence rapidly becomes less anisotropic when the straining ceases.It is found to be possible to predict the variation of the total turbulence energy using rapid-distortion theory with a correction for decay. However, the individual components cannot be accurately predicted in this way.

The evolution of the coherent structures in a uniformly distorted plane turbulent wake

1995 ◽  
Vol 291 ◽  
pp. 299-322 ◽  
Author(s):  
G. A. Kopp ◽  
J. G. Kawall ◽  
J. F. Keffer
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Turbulent Wake ◽  
Entrainment Rate ◽  
Rapid Distortion Theory ◽  
Vortex Model ◽  
Pattern Recognition Analysis ◽  
Preservation Theory ◽  
Far Wake ◽  
Plane Turbulent Wake

A plane turbulent wake generated by a flat plate is subjected to a uniform distortion. It is observed that nearly two-dimensional, quasi-periodic coherent structures dominate the distorted wake. Rapid distortion theory, applied to a kinematic vortex model of the coherent structures in the undistorted far wake, predicts many of the effects revealed by a hot-wire anemometry/pattern-recognition analysis of these structures. Specifically, rapid distortion theory predicts reasonably well the observed changes in the ensemble-averaged velocity patterns and the disproportionate amplification of the large-scale coherent structures relative to the smaller-scale ‘isotropic’ eddies. These results are consistent with the view that self-preservation of the distorted wake is not possible because of the selective amplification of the coherent structures, which control the development of the wake. As well, the entrainment rate in the distorted wake increases at a rate greater than that predicted by the self-preservation theory.

scholarly journals Rapid distortion theory for compressible homogeneous turbulence under isotropic mean strain

1996 ◽  
Vol 8 (10) ◽  
pp. 2692-2705 ◽  
Author(s):  
G. A. Blaisdell ◽  
G. N. Coleman ◽  
N. N. Mansour
Keyword(s):  
Homogeneous Turbulence ◽  
Rapid Distortion Theory ◽  
Mean Strain

Turbulence amplification by a shock wave and rapid distortion theory

1993 ◽  
Vol 5 (10) ◽  
pp. 2539-2550 ◽  
Author(s):  
L. Jacquin ◽  
C. Cambon ◽  
E. Blin
Keyword(s):  
Shock Wave ◽  
Rapid Distortion Theory

A Rapid Distortion Theory modified turbulence spectra for semi-analytical airfoil noise prediction

2016 ◽  
Vol 383 ◽  
pp. 349-363 ◽  
Author(s):  
Leandro D. Santana ◽  
Julien Christophe ◽  
Christophe Schram ◽  
Wim Desmet
Keyword(s):  
Noise Prediction ◽  
Turbulence Spectra ◽  
Rapid Distortion Theory
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