### Abstract

The linear stability of free-shear flows is governed by their dispersion characteristics. The dispersion relation can be obtained by integrating the Rayleigh equation. The integration process can be hampered by the presence of singularities within the domain of integration. A complex-domain contour integration procedure is presented that enables this integration to be performed in a modular and robust fashion. This is accomplished by deforming the original integration contour into piecewise-continuous line-segments in the complex domain to avoid all the singularities. This integration technique can then be used to find absolute and convective instabilities of the medium by a simple procedure. However when the velocity profile for a shear layer is obtained from experiments or numerical simulations, it is available only along the real-axis. Thus the complex-domain integration procedure cannot be applied unless a functional fit is obtained for the velocity profile. For convectively unstable systems, the integration can be carried out along the real-axis only for self-excited systems. However, for a certain class of free-shear flows, it is shown that an absolute instability can still be calculated by integrating the Rayleigh equation along the real-axis. This leads to the development of a fully automatic absolute-instability solver and a semi-automatic convective-instability solver.

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

Pages (from-to) | 1282-1289 |

Number of pages | 8 |

Journal | Computers and Fluids |

Volume | 35 |

Issue number | 10 |

DOIs | |

State | Published - Dec 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Engineering(all)

### Cite this

}

*Computers and Fluids*, vol. 35, no. 10, pp. 1282-1289. https://doi.org/10.1016/j.compfluid.2005.06.003

**Numerical computation of the linear convective and absolute stability of free-shear flows.** / Agarwal, Anurag; Morris, Philip John.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical computation of the linear convective and absolute stability of free-shear flows

AU - Agarwal, Anurag

AU - Morris, Philip John

PY - 2006/12/1

Y1 - 2006/12/1

N2 - The linear stability of free-shear flows is governed by their dispersion characteristics. The dispersion relation can be obtained by integrating the Rayleigh equation. The integration process can be hampered by the presence of singularities within the domain of integration. A complex-domain contour integration procedure is presented that enables this integration to be performed in a modular and robust fashion. This is accomplished by deforming the original integration contour into piecewise-continuous line-segments in the complex domain to avoid all the singularities. This integration technique can then be used to find absolute and convective instabilities of the medium by a simple procedure. However when the velocity profile for a shear layer is obtained from experiments or numerical simulations, it is available only along the real-axis. Thus the complex-domain integration procedure cannot be applied unless a functional fit is obtained for the velocity profile. For convectively unstable systems, the integration can be carried out along the real-axis only for self-excited systems. However, for a certain class of free-shear flows, it is shown that an absolute instability can still be calculated by integrating the Rayleigh equation along the real-axis. This leads to the development of a fully automatic absolute-instability solver and a semi-automatic convective-instability solver.

AB - The linear stability of free-shear flows is governed by their dispersion characteristics. The dispersion relation can be obtained by integrating the Rayleigh equation. The integration process can be hampered by the presence of singularities within the domain of integration. A complex-domain contour integration procedure is presented that enables this integration to be performed in a modular and robust fashion. This is accomplished by deforming the original integration contour into piecewise-continuous line-segments in the complex domain to avoid all the singularities. This integration technique can then be used to find absolute and convective instabilities of the medium by a simple procedure. However when the velocity profile for a shear layer is obtained from experiments or numerical simulations, it is available only along the real-axis. Thus the complex-domain integration procedure cannot be applied unless a functional fit is obtained for the velocity profile. For convectively unstable systems, the integration can be carried out along the real-axis only for self-excited systems. However, for a certain class of free-shear flows, it is shown that an absolute instability can still be calculated by integrating the Rayleigh equation along the real-axis. This leads to the development of a fully automatic absolute-instability solver and a semi-automatic convective-instability solver.

UR - http://www.scopus.com/inward/record.url?scp=33747845278&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747845278&partnerID=8YFLogxK

U2 - 10.1016/j.compfluid.2005.06.003

DO - 10.1016/j.compfluid.2005.06.003

M3 - Article

AN - SCOPUS:33747845278

VL - 35

SP - 1282

EP - 1289

JO - Computers and Fluids

JF - Computers and Fluids

SN - 0045-7930

IS - 10

ER -