This paper studies the continuous evolution of breaking wave for the surface water waves propagating on a sloping beach.A Lagrangian asymptotic solution is derived.According to the solution coupled with the wave breaking criteria and the equations of water particles motion,the wave deformation and the continuous wave breaking processes for the progressive water waves propagating on a sloping bottom can be derived.A series of experiments are also conducted to compare with the theoretical solution.The results show that the present solution can reasonably describe the plunging or spilling wave breaking phenomenon.
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