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On the internal structure of weakly nonlinear bores in laminar high Reynolds number flow

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Abstract

The paper deals with the internal structure of hydraulic jumps in near-critical single-layer flows which replaces the discontinuities predicted by hydraulic theory if viscous effects acting inside a thin laminar boundary layer are properly accounted for. In the limit of large Reynolds number this leads to a structure problem formed by the classical triple-deck equations supplemented with a novel nonlinear interaction relationship which allows for the passage through the critical state. Hydraulic jumps are shown to represent eigensolutions of the structure problem where this passage is achieved by the local thickening of the boundary layer which acts as a viscous hump. The effects of detuning and dispersion due to streamline curvature and surface tension on the internal structure of hydraulic jumps are studied in detail. In addition, the interaction of hydraulic jumps with surface mounted obstacles is investigated.

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Authors and Affiliations

  1. Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Resselgasse 3/E322, 1040, Wien, Austria

    Alfred Kluwick, Alfred Exner & Christoph Grinschgl

  2. School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland

    Edward A. Cox

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  1. Alfred Kluwick
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  2. Edward A. Cox
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  3. Alfred Exner
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  4. Christoph Grinschgl
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Correspondence to Alfred Kluwick.

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Kluwick, A., Cox, E.A., Exner, A. et al. On the internal structure of weakly nonlinear bores in laminar high Reynolds number flow. Acta Mech 210, 135–157 (2010). https://doi.org/10.1007/s00707-009-0188-x

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  • DOI: https://doi.org/10.1007/s00707-009-0188-x

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