Resonant sloshing in an upright annular tank

Resonant sloshing in an upright annular tank is studied by using a new nonlinear modal theory, which is complete within the framework of the Narimanov–Moiseev asymptotics. The applicability is justified for a fairly deep liquid (the liquid-depth-to-outer-tank-radius ratio 1. 5 h=h/r₂) and away from the non-dimensional inner radii r₁=r₁/r₂=0. 08546, 0. 17618, 0. 27826, 0. 31323, 0. 31855, 0. 43444, 0. 46015, 0. 48434, 0. 68655, 0. 70118. The theory is used to describe steady-state (stable and unstable) resonant waves due to a harmonic excitation with the forcing frequency close to the lowest natural sloshing frequency. We show that the surge-sway-pitch-roll excitation is always of either longitudinal or elliptic type. Existing experimental results on the horizontally excited steady-state wave regimes in an upright circular tank (r₁=0) are utilised for validation. Inserting an inner pole with the radii r₁ 0. 25 and 0. 35 (1. 5 h) causes that no stable swirling and/or irregular waves exist. The response curves for an elliptic-type excitation are examined versus the minor-axis forcing-amplitude component. Stable swirling is then expected being co- and counter-directed to the angular forcing direction. Passage to the rotary (circular) excitation keeps the co-directed swirling stable for all resonant forcing frequencies but the stable counter-directed swirling disappears.