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Pressure Transfer Functions for Interfacial Fluids Problems

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Abstract

We make a consistent derivation, from the governing equations, of the pressure transfer function in the small-amplitude Stokes wave regime and the hydrostatic approximation in the small-amplitude solitary water wave regime, in the presence of a background shear flow. The results agree with the well-known formulae in the zero vorticity case, but they incorporate the effects of vorticity through solutions to the Rayleigh equation. We extend the results to permit continuous density stratification and to internal waves between two constant-density fluids. Several examples are discussed.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Robin Ming Chen

  2. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Vera Mikyoung Hur

  3. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Samuel Walsh

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  1. Robin Ming Chen
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  2. Vera Mikyoung Hur
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  3. Samuel Walsh
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Correspondence to Samuel Walsh.

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Communicated by A. Constantin

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Chen, R.M., Hur, V.M. & Walsh, S. Pressure Transfer Functions for Interfacial Fluids Problems. J. Math. Fluid Mech. 19, 59–76 (2017). https://doi.org/10.1007/s00021-016-0265-6

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