Nonlinear boundary-layer problems and laminar vortical stream generated by resonant sloshing in a circular- base tank

Abstract

Suggesting a viscous incompressible liquid with laminar flows, nonlinear boundary-layer problems on the wetted tank surface (wall and bottom) of a rigid circular-base tank partly filled with a finite depth are derived assuming known the resonant steady-state inviscid liquid sloshing due to a horizontal translatory orbital tank motion with the forcing frequency close to the lowest natural sloshing frequency. By adopting a Narimanov–Moiseev-type approximation of the above-mentioned inviscid sloshing, an analytical asymptotic solution of the derived boundary-layer problems is constructed to prove that the inviscid flows must contain a global stationary vortex component. A new nonlinear boundary value problem governing this component is derived.