TITLE:
Hamiltonian Formulation for Water Wave Equation
AUTHORS:
Shamima Sultana, Zillur Rahman
KEYWORDS:
Water Wave Equation; Lagrangian Function; Hamiltonian Function; Hamilton’s Canonical Equation of Motion
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.3 No.2,
June
26,
2013
ABSTRACT: This paper concerns the development and application of the Hamiltonian function which is the sum of kinetic energy and potential energy of the system. Two dimensional water wave equations for irrotational, incompressible, inviscid fluid have been constructed in cartesian coordinates and also in cylindrical coordinates. Then Lagrangian function within a certain flow region is expanded under the assumption that the dispersion μ and the nonlinearity ε satisfied . Using Hamilton’s principle for water wave evolution Hamiltonian formulation is derived. It is obvious that the motion of the system is conservative. Then Hamilton’s canonical equation of motion is also derived.