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This paper reports study on the mechanism of long-wave breaking in a one-dimensional open chan-nel,without bottom friction,or with linear bottom friction.In general,the wave breaking phenomenon is related to the notion of“blow-up of solution”and can be studied by using the blow-up theory of par-tial differential equations(PDE).A pair of Riemann invariants are introduced to transform the governingequations into ordinary differential equations(ODE)along the characteristic directions of the governingequations.From the properties of the solutions of the ODE,the time and location of wave breakingare estimated and the criterion of long-wave breaking for the case with linear bottom friction is obtained.
This paper reports study on the mechanism of long-wave breaking in a one-dimensional open chan-nel, without bottom friction, or with linear bottom friction. In general, the wave breaking phenomenon is related to the notion of “blow-up of solution ”and can be studied by using the blow-up theory of par differential differential equations (PDE). A pair of Riemann invariants are introduced to transform the governingequations into ordinary differential equations (ODE) along the characteristic directions of the governingequations .From the properties of the solutions of the ODE, the time and location of wave breakingare estimated and the criterion of long-wave breaking for the case with linear bottom friction is.