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Exact Analytic Solutions of the Nonlinear Long-Wave Equations in the Case of Axisymmetric Fluid Vibrations in a Parabolic Rotating Vessel

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Abstract

A class of exact analytic solutions of the system of nonlinear long-wave equations is found. This class corresponds to the axisymmetric vibrations of an ideal incompressible homogeneous fluid in a rotating vessel in the shape of a paraboloid of revolution. The radial velocity of these motions is a linear function, and the azimuthal velocity and free surface displacements are polynomials in the radial coordinate with time-dependent coefficients. The nonlinear vibration frequency is equal to the frequency of the lowest mode of linear axisymmetric standing waves in the parabolic vessel.

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Authors
  1. S. F. Dotsenko
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  2. A. Rubino
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Dotsenko, S.F., Rubino, A. Exact Analytic Solutions of the Nonlinear Long-Wave Equations in the Case of Axisymmetric Fluid Vibrations in a Parabolic Rotating Vessel. Fluid Dynamics 38, 303–309 (2003). https://doi.org/10.1023/A:1024233405221

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  • DOI: https://doi.org/10.1023/A:1024233405221

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