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The Pressure Boundary Condition and the Pressure as Lagrangian for Water Waves

Bridges, Thomas J. (2019) The Pressure Boundary Condition and the Pressure as Lagrangian for Water Waves Water Waves: An interdisciplinary journal.

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Abstract

The pressure boundary condition for the full Euler equations with a free surface and general vorticity field is formulated in terms of a generalized Bernoulli equation deduced from the Gavrilyuk–Kalisch–Khorsand conservation law. The use of pressure as a Lagrangian density, as in Luke’s variational principle, is reviewed and extension to a full vortical flow is attempted with limited success. However, a new variational principle for time-dependent water waves in terms of the stream function is found. The variational principle generates vortical boundary conditions but with a harmonic stream function. Other aspects of vorticity in variational principles are also discussed.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Bridges, Thomas J.T.Bridges@surrey.ac.uk
Date : 11 March 2019
DOI : 10.1007/s42286-019-00001-0
Copyright Disclaimer : © The Author(s) 2019. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Uncontrolled Keywords : Oceanography; Lagrangian; Vorticity; Streamfunction; Variational principle
Depositing User : Clive Harris
Date Deposited : 08 Apr 2019 12:27
Last Modified : 08 Apr 2019 12:27
URI: http://epubs.surrey.ac.uk/id/eprint/850994

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