The simulation of nonlinear surface waves is significant importance in safety studies fluid containers and reservoirs. In this paper, free flows are simulated using a fixed grid method which employs local exponential basis functions (EBFs). Assuming the flow to be inviscid irrotational, velocity potential Laplace’s equation spatially discretized solved by considering Bernoulli’s for irrotationa...

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We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As a critical control parameter is surpassed, small amplitude surface waves bifurcate subcritically toward highly nonlinear ones with twice their amplitude. We ...

Systems of three or more conservation laws in which a conserved quantity is passively transported have a contact eld; sometimes, the contact speed and the speed of one of the nonlinear waves coincide on a surface in state space. We prove that this resonance surface contains the equilibrium points of the contact eld. We construct locally the Riemann solution for an example of such a system of th...

We consider the Euler equations describing nonlinear waves on the free surface of a twodimensional inviscid, irrotational fluid layer of finite depth. For large surface tension, Bond number larger than 1=3, and Froude number close to 1, the system possesses a one-parameter family of small-amplitude, traveling solitary wave solutions. We show that these solitary waves are spectrally stable with ...

We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent as the one found in the stationary regime, in agreement with weak turbulence predictions. The amplitude of all Fourier modes are found to decrease exponentially with time at the same...