Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 177
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Dutykh, Denys and Goubet, Olivier 2016. Derivation of dissipative Boussinesq equations using the Dirichlet-to-Neumann operator approach. Mathematics and Computers in Simulation, Vol. 127, p. 80.

    Dutykh, Denys and Clamond, Didier 2016. Modified shallow water equations for significantly varying seabeds. Applied Mathematical Modelling,

    Gagarina, E. Ambati, V.R. Nurijanyan, S. van der Vegt, J.J.W. and Bokhove, O. 2016. On variational and symplectic time integrators for Hamiltonian systems. Journal of Computational Physics, Vol. 306, p. 370.

    Kalogirou, Anna Moulopoulou, Erietta E. and Bokhove, Onno 2016. Variational finite element methods for waves in a Hele-Shaw tank. Applied Mathematical Modelling,

    Ohayon, Roger and Soize, Christian 2016. Nonlinear model reduction for computational vibration analysis of structures with weak geometrical nonlinearity coupled with linear acoustic liquids in the presence of linear sloshing and capillarity. Computers & Fluids,

    Panda, Srikumar Mondal, Arpita and Gayen, R 2016. An Efficient Integral Equation Approach to Study Wave Reflection by a Discontinuity in the Impedance-Type Surface Boundary Conditions. International Journal of Applied and Computational Mathematics,

    Rogers, Colin 2016. The Korteweg capillarity system. Integrable reduction via gauge and reciprocal links. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 96, Issue. 7, p. 813.

    Sedletsky, Yu V 2016. Variational approach to the derivation of the Davey–Stewartson system. Fluid Dynamics Research, Vol. 48, Issue. 1, p. 015506.

    Touboul, J. Charland, J. Rey, V. and Belibassakis, K. 2016. Extended mild-slope equation for surface waves interacting with a vertically sheared current. Coastal Engineering, Vol. 116, p. 77.

    Athanassoulis, Gerassimos A. and Papoutsellis, Christos E. 2015. 2015 Days on Diffraction (DD). p. 1.

    Bagri, G. S. and Groves, M. D. 2015. A Spatial Dynamics Theory for Doubly Periodic Travelling Gravity-Capillary Surface Waves on Water of Infinite Depth. Journal of Dynamics and Differential Equations, Vol. 27, Issue. 3-4, p. 343.

    Dutykh, Denys Chhay, Marx and Clamond, Didier 2015. Numerical study of the generalised Klein–Gordon equations. Physica D: Nonlinear Phenomena, Vol. 304-305, p. 23.

    Karczewska, Anna Rozmej, Piotr and Infeld, Eryk 2015. Energy invariant for shallow-water waves and the Korteweg–de Vries equation: Doubts about the invariance of energy. Physical Review E, Vol. 92, Issue. 5,

    Papoutsellis, Christos E. 2015. Numerical Simulation of Non-linear Water Waves over Variable Bathymetry. Procedia Computer Science, Vol. 66, p. 174.

    Sedletsky, Yu. V. 2015. Inclusion of dispersive terms in the averaged Lagrangian method: turning to the complex amplitude of envelope. Nonlinear Dynamics, Vol. 81, Issue. 1-2, p. 383.

    Zhang, Zili Nielsen, Søren R.K. Basu, Biswajit and Li, Jie 2015. Nonlinear modeling of tuned liquid dampers (TLDs) in rotating wind turbine blades for damping edgewise vibrations. Journal of Fluids and Structures, Vol. 59, p. 252.

    Belibassakis, K.A. Athanassoulis, G.A. and Gerostathis, Th.P. 2014. Directional wave spectrum transformation in the presence of strong depth and current inhomogeneities by means of coupled-mode model. Ocean Engineering, Vol. 87, p. 84.

    Dutykh, Denys and Clamond, Didier 2014. Efficient computation of steady solitary gravity waves. Wave Motion, Vol. 51, Issue. 1, p. 86.

    Franken, Norbert 2014. A free boundary and an optimal shape problem of a floating body. Annali di Matematica Pura ed Applicata (1923 -), Vol. 193, Issue. 4, p. 975.

    Gagarina, E. Ambati, V.R. van der Vegt, J.J.W. and Bokhove, O. 2014. Variational space–time (dis)continuous Galerkin method for nonlinear free surface water waves. Journal of Computational Physics, Vol. 275, p. 459.


A variational principle for a fluid with a free surface

  • J. C. Luke (a1)
  • DOI:
  • Published online: 01 March 2006

The full set of equations of motion for the classical water wave problem in Eulerian co-ordinates is obtained from a Lagrangian function which equals the pressure. This Lagrangian is compared with the more usual expression formed from kinetic minus potential energy.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *