### Abstract

Original language | English |
---|---|

Pages (from-to) | 477-512 |

Number of pages | 26 |

Journal | Journal of Fluid Mechanics |

Volume | 824 |

Early online date | 1 Jul 2017 |

DOIs | |

Publication status | Published - 30 Aug 2017 |

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### Keywords

- rapid distortion theory
- turbulence
- aero-acoustics

### Cite this

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*Journal of Fluid Mechanics*, vol. 824, pp. 477-512. https://doi.org/10.1017/jfm.2017.350

**Generalized rapid-distortion theory on transversely sheared mean flows with physically realizable upstream boundary conditions : application to trailing edge problem.** / Goldstein, M. E.; Leib, S. J.; Afsar, M. Z.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalized rapid-distortion theory on transversely sheared mean flows with physically realizable upstream boundary conditions

T2 - application to trailing edge problem

AU - Goldstein, M. E.

AU - Leib, S. J.

AU - Afsar, M. Z.

PY - 2017/8/30

Y1 - 2017/8/30

N2 - This paper is concerned with rapid distortion theory on transversely sheared mean flows which (among other things) can be used to analyze the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It extends previous analyses of Goldstein, Afsar & Leib (2013 a, b) which showed that the unsteady motion is completely determined by specifying two arbitrary convected quantities. The present paper uses a pair of previously derived conservation laws to derive upstream boundary conditions that relate these quantities to experimentally measurable flow variables. The result is dependent on the imposition of causality on an intermediate variable that appears in the conservation laws. Goldstein et al (2013a) related the convected quantities to the physical flow variables at the location of the interaction, but the results were not generic and hard to reconcile with experiment. That problem does not occur in the present formulation which leads to a much simpler and more natural result than the one given in Goldstein et al (2013a). We also show that the present formalism yields better predictions of the sound radiation produced by the interaction of a two-dimensional jet with the downstream edge of a flat plate than the Goldstein et al (2013a) result. The role of causality is also discussed.

AB - This paper is concerned with rapid distortion theory on transversely sheared mean flows which (among other things) can be used to analyze the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It extends previous analyses of Goldstein, Afsar & Leib (2013 a, b) which showed that the unsteady motion is completely determined by specifying two arbitrary convected quantities. The present paper uses a pair of previously derived conservation laws to derive upstream boundary conditions that relate these quantities to experimentally measurable flow variables. The result is dependent on the imposition of causality on an intermediate variable that appears in the conservation laws. Goldstein et al (2013a) related the convected quantities to the physical flow variables at the location of the interaction, but the results were not generic and hard to reconcile with experiment. That problem does not occur in the present formulation which leads to a much simpler and more natural result than the one given in Goldstein et al (2013a). We also show that the present formalism yields better predictions of the sound radiation produced by the interaction of a two-dimensional jet with the downstream edge of a flat plate than the Goldstein et al (2013a) result. The role of causality is also discussed.

KW - rapid distortion theory

KW - turbulence

KW - aero-acoustics

UR - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics

U2 - 10.1017/jfm.2017.350

DO - 10.1017/jfm.2017.350

M3 - Article

VL - 824

SP - 477

EP - 512

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -