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

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.