### Abstract

Receptivity of high-speed boundary layers in calorically perfect gas is considered within the framework of fluctuating hydrodynamics introduced by Landau and Lifshitz1 for a one-component fluid. It is assumed that kinetic fluctuations (KF) manifest themselves in the governing equations through “stochastic forcing” by a random stress tensor and by a random heat flux. The stochastic forcing generates unstable modes in boundary layers. By solving the KF receptivity problem the root-mean-square amplitudes of instability are expressed in terms of correlations for the random stress tensor and heat flux stemming from the fluctuation-dissipation theorem. The results indicate that the boundary-layer flow is most susceptible to kinetic fluctuations in the critical layer, and the receptivity occurs near the lower branch of the neutral stability curve for the considered instability. Although the initial amplitudes of the unstable modes generated by kinetic fluctuations are small, they go through a significant amplification toward the nonlinear region and may lead to laminar-turbulent transition. The root-mean-square amplitudes of KF-induced instability are expressed in a compact analytical form, which do not contain any empirical quantities. This opens up an opportunity to estimate the upper bound of transition Reynolds number in the framework of physics-based amplitude method. The results are consistent with the previous theoretical findings indicating that kinetic fluctuations at a microscopic scale can trigger a macroscopic phenomenon-laminar-turbulent transition in boundary-layer flows.

Original language | English (US) |
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Title of host publication | 46th AIAA Fluid Dynamics Conference |

Publisher | American Institute of Aeronautics and Astronautics Inc, AIAA |

ISBN (Print) | 9781624104367 |

State | Published - 2016 |

Event | 46th AIAA Fluid Dynamics Conference, 2016 - Washington, United States Duration: Jun 13 2016 → Jun 17 2016 |

### Other

Other | 46th AIAA Fluid Dynamics Conference, 2016 |
---|---|

Country | United States |

City | Washington |

Period | 6/13/16 → 6/17/16 |

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### ASJC Scopus subject areas

- Engineering (miscellaneous)
- Aerospace Engineering

### Cite this

*46th AIAA Fluid Dynamics Conference*American Institute of Aeronautics and Astronautics Inc, AIAA.

**Receptivity of high-speed boundary layers to kinetic fluctuations.** / Fedorov, Alexander; Tumin, Anatoli.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*46th AIAA Fluid Dynamics Conference.*American Institute of Aeronautics and Astronautics Inc, AIAA, 46th AIAA Fluid Dynamics Conference, 2016, Washington, United States, 6/13/16.

}

TY - GEN

T1 - Receptivity of high-speed boundary layers to kinetic fluctuations

AU - Fedorov, Alexander

AU - Tumin, Anatoli

PY - 2016

Y1 - 2016

N2 - Receptivity of high-speed boundary layers in calorically perfect gas is considered within the framework of fluctuating hydrodynamics introduced by Landau and Lifshitz1 for a one-component fluid. It is assumed that kinetic fluctuations (KF) manifest themselves in the governing equations through “stochastic forcing” by a random stress tensor and by a random heat flux. The stochastic forcing generates unstable modes in boundary layers. By solving the KF receptivity problem the root-mean-square amplitudes of instability are expressed in terms of correlations for the random stress tensor and heat flux stemming from the fluctuation-dissipation theorem. The results indicate that the boundary-layer flow is most susceptible to kinetic fluctuations in the critical layer, and the receptivity occurs near the lower branch of the neutral stability curve for the considered instability. Although the initial amplitudes of the unstable modes generated by kinetic fluctuations are small, they go through a significant amplification toward the nonlinear region and may lead to laminar-turbulent transition. The root-mean-square amplitudes of KF-induced instability are expressed in a compact analytical form, which do not contain any empirical quantities. This opens up an opportunity to estimate the upper bound of transition Reynolds number in the framework of physics-based amplitude method. The results are consistent with the previous theoretical findings indicating that kinetic fluctuations at a microscopic scale can trigger a macroscopic phenomenon-laminar-turbulent transition in boundary-layer flows.

AB - Receptivity of high-speed boundary layers in calorically perfect gas is considered within the framework of fluctuating hydrodynamics introduced by Landau and Lifshitz1 for a one-component fluid. It is assumed that kinetic fluctuations (KF) manifest themselves in the governing equations through “stochastic forcing” by a random stress tensor and by a random heat flux. The stochastic forcing generates unstable modes in boundary layers. By solving the KF receptivity problem the root-mean-square amplitudes of instability are expressed in terms of correlations for the random stress tensor and heat flux stemming from the fluctuation-dissipation theorem. The results indicate that the boundary-layer flow is most susceptible to kinetic fluctuations in the critical layer, and the receptivity occurs near the lower branch of the neutral stability curve for the considered instability. Although the initial amplitudes of the unstable modes generated by kinetic fluctuations are small, they go through a significant amplification toward the nonlinear region and may lead to laminar-turbulent transition. The root-mean-square amplitudes of KF-induced instability are expressed in a compact analytical form, which do not contain any empirical quantities. This opens up an opportunity to estimate the upper bound of transition Reynolds number in the framework of physics-based amplitude method. The results are consistent with the previous theoretical findings indicating that kinetic fluctuations at a microscopic scale can trigger a macroscopic phenomenon-laminar-turbulent transition in boundary-layer flows.

UR - http://www.scopus.com/inward/record.url?scp=84980340046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84980340046&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84980340046

SN - 9781624104367

BT - 46th AIAA Fluid Dynamics Conference

PB - American Institute of Aeronautics and Astronautics Inc, AIAA

ER -