Hostname: page-component-cb9f654ff-nr592 Total loading time: 0 Render date: 2025-08-23T20:42:56.299Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  18 August 2017

Hamid Alemi Ardakani Open the ORCID record for Hamid Alemi Ardakani [Opens in a new window]
Hamid Alemi Ardakani*
Affiliation:
Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Penryn, Cornwall TR10 9EZ, UK
*
†Email address for correspondence: alemi.hamid@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Mathematical Foundations: Variational methods

Information

Type
Rapids
Information
Journal of Fluid Mechanics , Volume 827 , 25 September 2017 , R2
Check for updates
Copyright
© 2017 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.)

Article purchase

Temporarily unavailable

References

Alemi Ardakani, H.2010 Rigid-body motion with interior shallow-water sloshing. PhD thesis, University of Surrey, UK.Google Scholar
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, 30–43.CrossRefGoogle Scholar
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. 226–259. Cambridge University Press.Google Scholar
Broer, L. J. F. 1974 On the Hamiltonian theory for surface waves. Appl. Sci. Res. 29, 430–446.Google Scholar
van Daalen, E. F. G.1993 Numerical and theoretical studies of water waves and floating bodies. PhD thesis, University of Twente, Netherlands.Google Scholar
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. 159–163. Available at http://www.iwwwfb.org/Workshops/08.htm.Google Scholar
Daniliuk, I. I. 1976 On integral functionals with a variable domain of integration. In Proceedings of the Steklov Institute of Mathematics, vol. 118, pp. 1–144. American Mathematical Society.Google Scholar
Flanders, H. 1973 Differentiation under the integral sign. Am. Math. Mon. 80, 615–627.Google Scholar
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, 370–389.Google Scholar
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, 459–483.CrossRefGoogle Scholar
Gagarina, E., van der Vegt, J. & Bokhove, O. 2013 Horizontal circulation and jumps in Hamiltonian wave models. Nonlinear Process. Geophys. 20, 483–500.CrossRefGoogle Scholar
van Groesen, E. & Andonowati 2017 Hamiltonian Boussinesq formulation of wave–ship interactions. Appl. Math. Model. 42, 133–144.Google Scholar
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.Google Scholar
Luke, J. C. 1967 A variational principle for a fluid with a free surface. J. Fluid Mech. 27, 395–397.Google Scholar
Miles, J. W. 1977 On Hamilton’s principle for surface waves. J. Fluid Mech. 83, 153–158.Google Scholar
Miloh, T. 1984 Hamilton’s principle, Lagrange’s method, and ship motion theory. J. Ship Res. 28, 229–237.CrossRefGoogle Scholar
Zakharov, V. E. 1968 Stability of periodic waves of finite-amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190–194.Google Scholar