Spectrum of axi-symmetric turbulence in a contracting stream

Acharya, Y. V. G.

doi:10.1007/bf03048803

Cited by 2 publications

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“…Earlier work on the problem has been incomplete and, in some places, even incorrect. Acharya (1956) and Swamy (1972) both considered what is here called ansatz I1 (see $4.1). Acharya wrote down the expressions for the component energies for the special case of an axisymmetric contraction, in terms of integrals involving the appropriate scalar functions, but made no attempt to evaluate them.…”

Section: K R Sreenivasan and R Narasirnhamentioning

confidence: 99%

Rapid distortion of axisymmetric turbulence

Sreenivasan

Narasimha

1978

J. Fluid Mech.

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A generalization of the isotropic theory of Batchelor & Proudman (1954) is developed to estimate the effect of sudden but arbitrary three-dimensional distortion on homogeneous, initially axisymmetric turbulence. The energy changes due to distortion are expressed in terms of the Fourier coefficients of an expansion in zonal harmonics of the two independent scalar functions that describe the axisymmetric spectral tensor. However, for two special but non-trivial forms of this tensor, which represent possibly the simplest kinds of non-isotropic turbulence and specify the angular distribution but not the wavenumber dependence, the energy ratios have been determined in closed form. The deviation of the ratio from its isotropic value is the product of a factor containing R, the initial value of the ratio of the longitudinal to the transverse energy component, and another factor depending only on the geometry of the distortion. It is found that, in axisymmetric and large two-dimensional contractions, the isotropic theory gives nearly the correct longitudinal energy, but (when R > 1) over-estimates the increase in the transverse energy; the product of the two intensities varies little unless the distortion is very large, thus accounting for the stress-freezing observed in rapidly accelerated shear flows.Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement. The different ansatzes predict results in broad qualitative agreement with a simple strategem suggested by Reynolds & Tucker (1975), but the quantitative differences are not always negligible.

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Section: K R Sreenivasan and R Narasirnhamentioning

confidence: 99%

Rapid distortion of axisymmetric turbulence

Sreenivasan

Narasimha

1978

J. Fluid Mech.

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Small Reynolds number nearly isotropic turbulence in a straight duct and a contraction

Bennett

Corrsin

1978

The Physics of Fluids

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Measurements have been made of nearly isotropic, low Reynolds number, grid-generated turbulence. The decay results agree with the predictions for ’’final period’’ isotropic turbulence decay (in time) by the linear approximation of von Kármán and Howarth, and Batchelor and Townsend. This agreement occurs in spite of the fact that at the smallest turbulence Reynolds number attained, Rλ≈4, the inertial (triple velocity correlation) term in the double velocity correlation equation is not negligible as assumed in the theoretical estimates. As in experiments of Batchelor and Stewart, the turbulence shows appreciable departure from isotropy, indicated by component energy inequality growth downstream. It is also shown by nonzero velocity skewness, not reported heretofore at small Rλ. Measurement of the effect of a secondary contraction on small Reynolds number turbulence indicates that the contraction has less effect than at larger Reynolds numbers.

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Spectrum of axi-symmetric turbulence in a contracting stream

Cited by 2 publications

References 1 publication

Rapid distortion of axisymmetric turbulence

Rapid distortion of axisymmetric turbulence

Small Reynolds number nearly isotropic turbulence in a straight duct and a contraction

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