Landa, P. S. and McClintock, P. V. E. (2012) *The transition to turbulence in slowly diverging subsonic submerged jets.* Physics of Fluids, 24 (3). -. ISSN 1070-6631

## Abstract

We address the problem of how turbulence is created in a submerged plane jet, near to the nozzle from which it issues. We do so by making use of a WKB-like asymptotic expansion for approximate solution of a complex, linear, fourth-order differential equation describing small deviations from the steady-state stream function. The result is used as a generating solution for application of the asymptotic Krylov-Bogolyubov method, enabling us to find the spatial and temporal spectra of the turbulence in the first approximation. We have thus been able to find the complex eigenvalues and eigenfunctions, i.e., the natural waves. We show that, for any given set of parameters, there is a continuum of frequencies and, for each frequency, a continuum of phase velocities. Correspondingly, there is an infinite number of wavelengths. It follows that there is no unique dispersion law and, because of perturbations (however, small they may be), a regular temporal spectrum does not exist even in cases where the spatial spectrum is regular. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3693141]

Item Type: | Article |
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Journal or Publication Title: | Physics of Fluids |

Uncontrolled Keywords: | differential equations ; eigenvalues and eigenfunctions ; jets ; laminar to turbulent transitions ; nozzles ; subsonic flow ; turbulence ; WKB calculations |

Subjects: | Q Science > QC Physics |

Departments: | Faculty of Science and Technology > Physics |

ID Code: | 54941 |

Deposited By: | ep_importer_pure |

Deposited On: | 07 Jun 2012 15:08 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 07 Jan 2015 17:29 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/54941 |

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