Nonlinear Boundary-Layer Problems and Laminar Vortical Streams Generated by Resonant Sloshing in a Tank with Circular Base
- Authors: Timokha A.N.1,2
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Affiliations:
- Institute of Mathematics, Ukrainian National Academy of Sciences
- Centre for Autonomous Marine Operations and Systems, Department of Marine Technology, Norwegian University of Science and Technology
- Issue: Vol 240, No 3 (2019)
- Pages: 358-373
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242749
- DOI: https://doi.org/10.1007/s10958-019-04357-z
- ID: 242749
Cite item
Abstract
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.
About the authors
A. N. Timokha
Institute of Mathematics, Ukrainian National Academy of Sciences; Centre for Autonomous Marine Operations and Systems, Department of Marine Technology, Norwegian University of Science and Technology
Email: Jade.Santos@springer.com
Ukraine, Tereshchenkivs’ka Str., 3, Kyiv, 01004; Trondheim, NO-7491