Nonlinear Boundary-Layer Problems and Laminar Vortical Streams Generated by Resonant Sloshing in a Tank with Circular Base
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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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- 1.H. N. Abramson, The Dynamic Behavior of Liquids in Moving Containers with Applications to Space Vehicle Technology, Tech. Rept. NASA, NASA, Washington (1966).Google Scholar
- 3.J. Bouvard, W. Herreman, and F. Moisy, “Mean mass transport in an orbitally shaken cylindrical container,” Phys. Rev. Fluids, 2, Issue 8, Paper ID 084801 (2017).Google Scholar
- 10.I. Lukovsky and A. N. Timokha, “Combining Narimanov–Moiseev’s and Lukovsky–Miles’ schemes for nonlinear liquid sloshing,” J. Numer. Appl. Math., 105, 69–82 (2011).Google Scholar
- 13.G. S. Narimanov, L. V. Dokuchaev, and I. A. Lukovsky, Nonlinear Dynamics of Flying Vehicles with Liquid [in Russian], Mashinostroenie, Moscow (1977).Google Scholar
- 14.A. D. Polyanin and V. E. Nasaikinskii, Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edn., Taylor & Francis Group, CRC Press, London (2015).Google Scholar
- 17.M. Reclari, Hydrodynamics of Orbital Shaken Bioreactors: Thesis No. 5759, Ecole Polytech. Federale de Lausanne (2013).Google Scholar