Skip to main content Accessibility help

A coupled variational principle for 2D interactions between water waves and a rigid body containing fluid

  • Hamid Alemi Ardakani (a1)


New variational principles are given for the two-dimensional interactions between gravity-driven water waves and a rotating and translating rectangular vessel dynamically coupled to its interior potential flow with uniform vorticity. The complete set of equations of motion for the exterior water waves, the exact nonlinear hydrodynamic equations of motion for the vessel in the roll/pitch, sway/surge and heave directions, and also the full set of equations of motion for the interior fluid of the vessel, relative to the body coordinate system attached to the rotating–translating vessel, are derived from two Lagrangian functionals.


Corresponding author

Email address for correspondence:


Hide All
Alemi Ardakani, H.2010 Rigid-body motion with interior shallow-water sloshing. PhD thesis, University of Surrey, UK.
Alemi Ardakani, H. & Bridges, T. J. 2012 Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in two dimensions. Eur. J. Mech. (B/Fluids) 31, 3043.
Bokhove, O. & Kalogirou, A. 2016 Variational Water Wave Modelling: from Continuum to Experiment (ed. Bridges, T. J., Groves, M. D. & Nicholls, D. P.), Lecture Notes on the Theory of Water Waves, LMS Lecture Notes, vol. 426, pp. 226259. Cambridge University Press.
Broer, L. J. F. 1974 On the Hamiltonian theory for surface waves. Appl. Sci. Res. 29, 430446.
van Daalen, E. F. G.1993 Numerical and theoretical studies of water waves and floating bodies. PhD thesis, University of Twente, Netherlands.
van Daalen, E. F. G., van Groesen, E. & Zandbergen, P. J. 1993 A Hamiltonian formulation for nonlinear wave–body interactions. In Proceedings of the Eighth International Workshop on Water Waves and Floating Bodies, Canada, pp. 159163. Available at
Daniliuk, I. I. 1976 On integral functionals with a variable domain of integration. In Proceedings of the Steklov Institute of Mathematics, vol. 118, pp. 1144. American Mathematical Society.
Flanders, H. 1973 Differentiation under the integral sign. Am. Math. Mon. 80, 615627.
Gagarina, E., Ambati, V. R., Nurijanyan, S., van der Vegt, J. J. W. & Bokhove, O. 2016 On variational and symplectic time integrators for Hamiltonian systems. J. Comput. Phys. 306, 370389.
Gagarina, E., Ambati, V. R., van der Vegt, J. J. W. & Bokhove, O. 2014 Variational space–time (dis)continuous Galerkin method for nonlinear free surface water waves. J. Comput. Phys. 275, 459483.
Gagarina, E., van der Vegt, J. & Bokhove, O. 2013 Horizontal circulation and jumps in Hamiltonian wave models. Nonlinear Process. Geophys. 20, 483500.
van Groesen, E. & Andonowati 2017 Hamiltonian Boussinesq formulation of wave–ship interactions. Appl. Math. Model. 42, 133144.
Kalogirou, A. & Bokhove, O. 2016 Mathematical and numerical modelling of wave impact on wave-energy buoys. In Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, p. 8. The American Society of Mechanical Engineers.
Luke, J. C. 1967 A variational principle for a fluid with a free surface. J. Fluid Mech. 27, 395397.
Miles, J. W. 1977 On Hamilton’s principle for surface waves. J. Fluid Mech. 83, 153158.
Miloh, T. 1984 Hamilton’s principle, Lagrange’s method, and ship motion theory. J. Ship Res. 28, 229237.
Zakharov, V. E. 1968 Stability of periodic waves of finite-amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190194.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

A coupled variational principle for 2D interactions between water waves and a rigid body containing fluid

  • Hamid Alemi Ardakani (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed