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

被引:1
作者
Bridges, Thomas J. [1 ]
机构
[1] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey, England
关键词
Oceanography; Lagrangian; Vorticity; Streamfunction; Variational principle; VARIATIONAL-PRINCIPLES;
D O I
10.1007/s42286-019-00001-0
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:131 / 143
页数:13
相关论文
共 15 条
[1]  
Ardakani HA, 2018, Arxiv, DOI arXiv:1809.10909
[2]  
Bateman H., 1964, Partial Differential Equations
[3]   On Seliger and Whitham's variational principle for hydrodynamic systems from the point of view of 'fictitious particles' [J].
Casetta, Leonardo ;
Pesce, Celso P. .
ACTA MECHANICA, 2011, 219 (1-2) :181-184
[4]   Practical use of variational principles for modeling water waves [J].
Clamond, Didier ;
Dutykh, Denys .
PHYSICA D-NONLINEAR PHENOMENA, 2012, 241 (01) :25-36
[5]   Variational water-wave model with accurate dispersion and vertical vorticity [J].
Cotter, Colin ;
Bokhove, Onno .
JOURNAL OF ENGINEERING MATHEMATICS, 2010, 67 (1-2) :33-54
[6]   Clebsch Potentials in the Variational Principle for a Perfect Fluid [J].
Fukagawa, Hiroki ;
Fujitani, Youhei .
PROGRESS OF THEORETICAL PHYSICS, 2010, 124 (03) :517-531
[7]  
Gavrilyuk S, 2011, CISM COURSES LECT, V535, P163
[8]   A kinematic conservation law in free surface flow [J].
Gavrilyuk, Sergey ;
Kalisch, Henrik ;
Khorsand, Zahra .
NONLINEARITY, 2015, 28 (06) :1805-1821
[9]   Clebsch representation near points where the vorticity vanishes [J].
Graham, CR ;
Henyey, FS .
PHYSICS OF FLUIDS, 2000, 12 (04) :744-746
[10]   Existence and conditional energetic stability of solitary gravity-capillary water waves with constant vorticity [J].
Groves, M. D. ;
Wahlen, E. .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2015, 145 (04) :791-883