Hostname: page-component-797576ffbb-lm8cj Total loading time: 0 Render date: 2023-12-04T16:03:30.830Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false

A shallow-water sloshing model for wave breaking in rectangular tanks

Published online by Cambridge University Press:  02 April 2014

Matteo Antuono*
CNR-INSEAN (Marine Technology Research Institute), via di Vallerano 139, 00128 Rome, Italy
Andrea Bardazzi
CNR-INSEAN (Marine Technology Research Institute), via di Vallerano 139, 00128 Rome, Italy
Claudio Lugni
CNR-INSEAN (Marine Technology Research Institute), via di Vallerano 139, 00128 Rome, Italy Centre for Autonomous Marine Operations and Systems (AMOS), Department of Marine Technology, NTNU, 7491 Trondheim, Norway
Maurizio Brocchini
Dipartimento ICEA, Università Politecnica delle Marche, via Brecce Bianche 12, 60121 Ancona, Italy
Email address for correspondence:


We propose a simple, robust and efficient sloshing model that accounts for breaking phenomena evolving in rectangular tanks and in shallow-water conditions. The model has been obtained by applying Fourier analysis to Boussinesq-type equations and using an approximate analytic solution for the vorticity generated by wave breaking. The toe of the breaker and the intensity of the vorticity injected at the free surface are computed on the basis of literature results for coastal-type breakers. A first experimental campaign has been used to calibrate the turbulent viscosity of the sloshing model, while a second campaign has been run as final validation. The overall good agreement between the numerical outputs and the experimental data confirms the reliability and robustness of the proposed model.

© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Antuono, M., Bouscasse, B., Colagrossi, A. & Lugni, C. 2012 Two-dimensional modal method for shallow-water sloshing in rectangular basins. J. Fluid Mech. 700, 419440.Google Scholar
Antuono, M. & Brocchini, M. 2013 Beyond Boussinesq-type equations: semi-integrated models for coastal dynamics. Phys. Fluids 25, 016603.Google Scholar
Antuono, M. & Colagrossi, A. 2013 The damping of viscous gravity waves. Wave Motion 50, 197209.Google Scholar
Antuono, M., Colagrossi, A., Marrone, S. & Lugni, C. 2011 Propagation of gravity waves through an SPH scheme with numerical diffusive terms. Comput. Phys. Commun. 182, 866877.Google Scholar
Ardakani, H. A. & Bridges, T. J. 2012 Shallow-water sloshing in vessels undergoing prescribed rigid-motion in two dimensions. Eur. J. Mech. B/Fluids 31, 4043.Google Scholar
Bouscasse, B., Antuono, M., Colagrossi, A. & Lugni, C. 2013 Numerical and experimental investigation of nonlinear shallow water sloshing. Intl J. Nonlinear Sci. Numer. Simul. 14 (2), 123138.Google Scholar
Bredmose, H., Brocchini, M., Peregrine, D. H. & Thais, L. 2003 Experimental investigation and numerical modelling of steep forced water waves. J. Fluid Mech. 490, 217249.Google Scholar
Chester, W. & Bones, J. A. 1968 Resonant oscillations of water waves. II. Experiment. Proc. R. Soc. Lond. A 306, 2329.Google Scholar
Cox, D. T., Kobayashi, N. & Okayasu, A. 1995 Experimental and numerical modelling of surf zone hydrodynamics. Tech. Rep. University of Delaware.Google Scholar
Faltinsen, O. M., Landrini, M. & Greco, M. 2004 Slamming in marine applications. J. Engng Maths 48, 187217.Google Scholar
Faltinsen, O. M., Rognebakke, O. F., Lukovsky, I. A. & Timokha, A. N. 2000 Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. J. Fluid Mech. 407, 201234.Google Scholar
Faltinsen, O. M. & Timokha, A. N. 2001 An adaptive multimodal approach to nonlinear sloshing in a rectangular tank. J. Fluid Mech. 432, 167200.Google Scholar
Faltinsen, O. M. & Timokha, A. N. 2002 Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth. J. Fluid Mech. 470, 319357.Google Scholar
Faltinsen, O. M. & Timokha, A. N. 2009 Sloshing. Cambridge University Press.Google Scholar
Hill, D. F. 2003 Transient and steady-state amplitudes of forced waves in rectangular basins. Phys. Fluids 39 (6), 15761587.Google Scholar
Lamb, H. 1945 Hydrodynamics. Cambridge University Press.Google Scholar
Lepelletier, T. G. & Raichlen, F. 1988 Nonlinear oscillations in rectangular tanks. J. Engng Maths 114 (1), 123.Google Scholar
Olsen, H. & Johnsen, K. 1975 Nonlinear sloshing in rectangular tanks: a pilot study on the applicability of analytical models. Tech. Rep. 74-72-5, vol. 2. Det Norske Veritas (DNV), Hvik, Norway.Google Scholar
Veeramony, J. & Svendsen, I. A. 2000 The flow in surf-zone waves. Coast. Engng 39, 93122.Google Scholar