Journal of Mathematical Sciences

, Volume 240, Issue 3, pp 358–373 | Cite as

Nonlinear Boundary-Layer Problems and Laminar Vortical Streams Generated by Resonant Sloshing in a Tank with Circular Base

  • A. N. Timokha

For a viscous incompressible liquid with laminar flows, we deduce nonlinear boundary-layer problems for the near-surface flows near wetted surfaces (wall and bottom) of a rigid tank with circular base partly filled with a liquid of finite depth. Under the assumption that the resonant steady-state inviscid liquid sloshing caused by the horizontal translational orbital motion of the tank with forcing frequency close to the lowest natural sloshing frequency is known, by adopting the Narimanov–Moiseev-type approximation of the above-mentioned inviscid sloshing, we construct an analytic asymptotic solution of the obtained boundary-layer problems. It is shown that the inviscid flows must contain a global stationary vortex component. A new nonlinear boundary-value problem governing this component is proposed.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. N. Timokha
    • 1
    • 2
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  2. 2.Centre for Autonomous Marine Operations and Systems, Department of Marine TechnologyNorwegian University of Science and TechnologyTrondheimNorway

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