Olav F. Rognebakke

Resonant three-dimensional nonlinear sloshing in a square-base basin

An asymptotic modal system is derived for modelling nonlinear sloshing in a rectangular tank with similar width and breadth. The system couples nonlinearly nine modal functions describing the time evolution of the natural modes. Two primary modes are assumed to be dominant. The system is equivalent to the model by Faltinsen et al. (2000) for the two-dimensional case. It is validated for resonant sloshing in a square-base basin. Emphasis is on finite fluid depth but the behaviour with decreasing depth to intermediate depths is also discussed. The tank is forced in surge/sway/roll/pitch with frequency close to the lowest degenerate natural frequency. The theoretical part concentrates on periodic solutions of the modal system (steady-state wave motions) for longitudinal (along the walls) and diagonal (in the vertical diagonal plane) excitations. Three types of solutions are established for each case: (i) ‘planar’/‘diagonal’ resonant standing waves for longitudinal/diagonal forcing, (ii) ‘swirling’ waves moving along tank walls clockwise or counterclockwise and (iii) ‘square’-like resonant standing wave coupling in-phase oscillations of both the lowest modes. The frequency domains for stable and unstable waves (i)–(iii), the contribution of higher modes and the influence of decreasing fluid depth are studied in detail. The zones where either unstable steady regimes exist or there are two or more stable periodic solutions with similar amplitudes are found. New experimental results are presented and show generally good agreement with theoretical data on effective domains of steady-state sloshing. Three-dimensional sloshing regimes demonstrate a significant contribution of higher modes in steady-state and transient flows.

Two-dimensional resonant piston-like sloshing in a moonpool

This paper presents combined theoretical and experimental studies of the two-dimensional piston-like steady-state motions of a fluid in a moonpool formed by two rectangular hulls (e.g. a dual pontoon or catamaran). Vertical harmonic excitation of the partly submerged structure in calm water is assumed. A high-precision analytically oriented linear-potential-flow method, which captures the singular behaviour of the velocity potential at the corner points of the rectangular structure, is developed. The linear steady-state results are compared with new experimental data and show generally satisfactory agreement. The influence of vortex shedding has been evaluated by using the local discrete-vortex method of Graham (1980). It was shown to be small. Thus, the discrepancy between the theory and experiment may be related to the free-surface nonlinearity.

Resonant three-dimensional nonlinear sloshing in a square-base basin. Part 2. Effect of higher modes

The paper continues our investigations of three-dimensional nonlinear resonant fluid sloshing in a square-base basin with finite depth (mean depth/tank length ratio

Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth

h\,{\ge}\, 0.3

Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth

). The sloshing is forced by a combined sway/surge resonant harmonic excitation of the two lowest natural modes. The new studies are strongly motivated by a discrepancy between previous quantitative theoretical results and experimental measurements and consist of a more precise description of the strong nonlinear amplification of higher modes. The latter is justified here by secondary resonance. Effective frequency domains of the secondary resonance are quantified. An adaptive asymptotic modal theory improves agreement with earlier and new experimental data both in the transient and steady-state conditions. Local breaking and overturning near the walls, that may lead to a ‘switch’ between distinct steady regimes, increase both global damping and generate random-like excitation of higher modes, are extensively discussed.

Classification of three-dimensional nonlinear sloshing in a square-base tank with finite depth

An adaptive asymptotic nonlinear modal system is used for systematic quantification of three-dimensional steady-state resonant sloshing in a square base tank with a finite fill depth. The depth/breadth ratios are ⩾0.4. The tank is laterally excited with frequency close to the lowest natural frequency. The main emphasis is on the “swirling” wave regime and its special features, e.g., stability, feedback of higher modes, and regular and irregular switch of the apparent direction of rotation. Theoretical results are validated for both steady-state solutions and “beating” that does not die out in experimental investigations. Frequency domains with no stable steady-state waves and occurrence of “chaotic” waves are discussed.