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The unstable temporal development of axi-symmetric jets of incompressible fluid

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Abstract

We study the shear-driven instability, of Kelvin–Helmholtz type, that forms at the interface between a cylindrical jet of flowing fluid and its surroundings. The results of an infinitesimal-amplitude theory based on linearising the system about the undisturbed jet are given. A novel numerical model based on the Galerkin spectral method is developed and employed to simulate the non-linear development of the jet in the weakly-compressible Boussinesq regime. Representative results demonstrating the viability of this model are given, and are shown to agree with the linear analysis for small disturbances, but to develop cylindrical roll-up in the severely non-linear regime.

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  1. Available freely online from https://au.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes?s_tid=prof_contriblnk.

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Acknowledgements

The authors gratefully acknowledge the scholarly assistance of Prof. A. Bassom and Dr S. Walters, as well as the financial assistance of the G.F.R. Ellis Memorial and Tasmania Graduate Research Scholarships. The critical comments from three Anonymous Reviewers improved the presentation and results of this paper significantly.

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Authors and Affiliations

  1. Department of Mathematics and Physics, University of Tasmania, Box 37, Hobart, 7001, Australia

    Earl S. Lester & Lawrence K. Forbes

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  1. Earl S. Lester
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  2. Lawrence K. Forbes
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Correspondence to Earl S. Lester.

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Lester, E.S., Forbes, L.K. The unstable temporal development of axi-symmetric jets of incompressible fluid. J Eng Math 120, 29–42 (2020). https://doi.org/10.1007/s10665-019-10030-w

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