### Abstract

Results of eigenvalue analysis based on global and local eigenvalue considerations are presented. A collocation method with the Chebyshev polynomial approximation has been used for the global eigenvalue analysis. The results explain the appearance of a second unstable mode. In the case of real frequencies with Reynolds number R < 381 there is only one unstable mode. This mode coalesces at R ≈ 381 with a stable mode. At R > 381 they become separated by interchannging their branches, then the second unstable mode occurs. The receptivity problem has been considered with respect to perturbations emanating from a wall. The results illustrate that high-frequency modes have a stronger response than low-frequency modes. It is shown that the method of expansion in a biorthogonal eigenfunction system and the method used by Ashpis and Reshotko are equivalent with regard to the receptivity problem solution.

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

Pages (from-to) | 33-45 |

Number of pages | 13 |

Journal | Theoretical and Computational Fluid Dynamics |

Volume | 9 |

Issue number | 1 |

State | Published - 1997 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Theoretical and Computational Fluid Dynamics*,

*9*(1), 33-45.

**Instability and receptivity of laminar wall jets.** / Tumin, Anatoli; Aizatulin, Lolita.

Research output: Contribution to journal › Article

*Theoretical and Computational Fluid Dynamics*, vol. 9, no. 1, pp. 33-45.

}

TY - JOUR

T1 - Instability and receptivity of laminar wall jets

AU - Tumin, Anatoli

AU - Aizatulin, Lolita

PY - 1997

Y1 - 1997

N2 - Results of eigenvalue analysis based on global and local eigenvalue considerations are presented. A collocation method with the Chebyshev polynomial approximation has been used for the global eigenvalue analysis. The results explain the appearance of a second unstable mode. In the case of real frequencies with Reynolds number R < 381 there is only one unstable mode. This mode coalesces at R ≈ 381 with a stable mode. At R > 381 they become separated by interchannging their branches, then the second unstable mode occurs. The receptivity problem has been considered with respect to perturbations emanating from a wall. The results illustrate that high-frequency modes have a stronger response than low-frequency modes. It is shown that the method of expansion in a biorthogonal eigenfunction system and the method used by Ashpis and Reshotko are equivalent with regard to the receptivity problem solution.

AB - Results of eigenvalue analysis based on global and local eigenvalue considerations are presented. A collocation method with the Chebyshev polynomial approximation has been used for the global eigenvalue analysis. The results explain the appearance of a second unstable mode. In the case of real frequencies with Reynolds number R < 381 there is only one unstable mode. This mode coalesces at R ≈ 381 with a stable mode. At R > 381 they become separated by interchannging their branches, then the second unstable mode occurs. The receptivity problem has been considered with respect to perturbations emanating from a wall. The results illustrate that high-frequency modes have a stronger response than low-frequency modes. It is shown that the method of expansion in a biorthogonal eigenfunction system and the method used by Ashpis and Reshotko are equivalent with regard to the receptivity problem solution.

UR - http://www.scopus.com/inward/record.url?scp=0031483906&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031483906&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031483906

VL - 9

SP - 33

EP - 45

JO - Theoretical and Computational Fluid Dynamics

JF - Theoretical and Computational Fluid Dynamics

SN - 0935-4964

IS - 1

ER -