A new form of governing equations of fluids arising from Hamilton's principle

Details A new form of governing equations of fluids arising from Hamilton's principle A new form of governing equations of fluids arising from Hamilton's principle

2008-01-15

arxiv.org/abs/0801.2333v1

International Journal of Engineering Science / International Journal of Engineering Sciences 37, 12 (1999) 1495-1520

Physics

Fluid Dynamics

28 pages

Scientific paper

10.1016/S0020-7225(98)00131-1

A new form of governing equations is derived from Hamilton's principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws both for non-dispersive case (Lagrangian depends only on conserved quantities) and dispersive case (Lagrangian depends also on their derivatives). For non-dispersive case the set of conservation laws allows to rewrite the governing equations in the symmetric form of Godunov-Friedrichs-Lax. The linear stability of equilibrium states for potential motions is also studied. In particular, the dispersion relation is obtained in terms of Hermitian matrices both for non-dispersive and dispersive case. Some new results are extended to the two-fluid non-dispersive case.

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