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Simple water waves in Lagrangian description

Chybicki W.

Archives of Hydro-Engineering and Environmental Mechanics

2006

Vol. 53, nr 4

381-387

Details of the model of long water waves in the Lagrangian description are presented. The equation of motion is derived from variational formulation of the problem. Only two important cases are considered: when the water depth changes uniformly in space or the depth is constant. For quasilinear hyperbolic system obtained in this description the Riemann invariants and equation of simple waves are found. For constant depth, the Riemann invariants are exactly the same as in the Euler description, however, the velocity of wave propagation is different. In case of uniform slope the velocity, as well as the Riemann invariants are different. In the Lagrangian description the free surface is described in parametric form.