## Abstract

A non-parallel analysis of time-oscillatory instability of conical jets reveals important features not found in prior studies. Flow deceleration significantly enhances the shear-layer instability for both swirl-free and swirling jets. In swirl-free jets, flow deceleration causes the axisymmetric instability (absent in the parallel approximation). The critical Reynolds number Re_{a} for this instability is an order of magnitude smaller than the critical Re_{a} predicted before for the helical instability (where Re_{a} = rv_{a}/v, r is the distance from the jet source, v_{a} is the jet maximum velocity at a given r, and v is the viscosity). Swirl, intensifying the divergence of streamlines, induces an additional, divergent instability (which occurs even in shear-free flows). For the swirl Reynolds number Re_{s} (circulation to viscosity ratio) exceeding 3, the critical Re_{a} for the single-helix counter-rotating mode becomes smaller than those for axisymmetric and multi-helix modes. Since the critical Re_{s} is less than 10 for the near-axis jets, the boundary-layer approximation (used before) is invalid, as is Long's Type II boundary-layer solution (whose stability has been extensively studied). Thus, the non-parallel character of jets strongly affects their stability. Our results, obtained in a far-field approximation allowing reduction of the linear stability problem to ordinary differential equations, are more valid for short wavelengths.

Original language | English |
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Pages (from-to) | 283-309 |

Number of pages | 27 |

Journal | Journal of Fluid Mechanics |

Issue number | 480 |

DOIs | |

State | Published - Apr 10 2003 |