### Abstract

A generalization of the isotropic theory of G. K. Batchelor and O. Proudman 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. Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement.

Original language | English (US) |
---|---|

Pages (from-to) | 497-516 |

Number of pages | 20 |

Journal | Journal of Fluid Mechanics |

Volume | 84 |

Issue number | pt 3 |

State | Published - Jan 1 1978 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*84*(pt 3), 497-516.

**RAPID DISTORTION OF AXISYMMETRIC TURBULENCE.** / Sreenivasan, K. R.; Narasimha, R.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 84, no. pt 3, pp. 497-516.

}

TY - JOUR

T1 - RAPID DISTORTION OF AXISYMMETRIC TURBULENCE.

AU - Sreenivasan, K. R.

AU - Narasimha, R.

PY - 1978/1/1

Y1 - 1978/1/1

N2 - A generalization of the isotropic theory of G. K. Batchelor and O. Proudman 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. Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement.

AB - A generalization of the isotropic theory of G. K. Batchelor and O. Proudman 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. Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement.

UR - http://www.scopus.com/inward/record.url?scp=0017931025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0017931025&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0017931025

VL - 84

SP - 497

EP - 516

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - pt 3

ER -