Coupling of a swirl-type resonant sloshing and a mean rotational flow

Abstract

Referring to experimental results by Prandtl (1949) and Hutton (1964) as well as more recent model tests by Royon-Lebeaud, Hopfinger & Cartellier (2007) and Reclari (2013), a Moiseev-type asymptotic almost periodic (steady-state) solution of a resonant sloshing problem is derived to show that a time-averaged rotational liquid flow, if occurs, becomes nonlinearly coupled with the dominant swirl-type wave component. The coupling appears as a necessary solvability condition and consists of nonlinear (differential) equations with respect to four amplitude parameters of the two lowest natural sloshing modes and the time-averaged velocity field, which is governed by a partial differential equation of the first order. Finding its unique solution requires to know the (Stokes) steady-streaming.