Related papers: Wave breaking for the Kakutani-Matsuuchi model
We show wave breaking for the Whitham equation in a range of fractional dispersion, i.e. the solution remains bounded but its slope becomes unbounded in finite time, provided that the initial datum is sufficiently steep.
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
A family of Camassa-Holm type equations with a linear term and cubic and quartic nonlinearities is considered. Local well-posedness results are established via Kato's approach. Conserved quantities for the equation are determined and from…
This paper aims to give a refined wave breaking description of the Cauchy problem to the one-dimensional nonlinear shallow water equations providing a sharp estimate of the lifespan of the solutions depending on the amplitude and topography…
We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations, and which generalize the Whitham…
In this paper we study wave breaking in the unidirectional non-local wave model describing the motion of a collision-free plasma in a magnetic field. By analyzing the monotonicity and continuity properties of a system of the Riccati-type…
We introduce a numerical strategy to study the evolution of 2D water waves in the presence of a plunging jet. The free-surface Navier-Stokes solution is obtained with a finite but small viscosity. We observe the formation of a surface…
We modify the nonlinear shallow water equations, the Korteweg-de Vries equation, and the Whitham equation, to permit constant vorticity, and examine wave breaking, or the lack thereof. By wave breaking, we mean that the solution remains…
Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the…
The KdV equation is a model equation for waves at the surface of an inviscid incompressible fluid, and it is well known that the equation describes the evolution of unidirectional waves of small amplitude and long wavelength fairly…
We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope…
For models describing water waves, Constantin and Escher's works have long been considered as the cornerstone method for proving wave breaking phenomena. Their rigorous analytic proof shows that if the lowest slope of flows can be…
Two methods to treat wave breaking in the framework of the Hamiltonian formulation of free-surface potential flow are presented, tested, and validated. The first is an extension of Kennedy et al (2000)'s eddy-viscosity approach originally…
Theoretical results on water waves almost always start by assuming irrotationality of the flow in order to simplify the formulation. In this work, we investigate the well-foundedness of this hypothesis via numerical simulations of the…
Many supervised machine learning methods have revolutionised the empirical modelling of complex systems. These empirical models, however, are usually "black boxes" and provide only limited physical explanations about the underlying systems.…
This paper aims to show that the Cauchy problem of the Burgers equation with a weakly dispersive perturbation involving the Bessel potential (generalization of the Fornberg-Whitham equation) can exhibit wave breaking for initial data with…
We review here the derivation of many of the most important models that appear in the literature (mainly in coastal oceanography) for the description of waves in shallow water. We show that these models can be obtained using various…
The present study focuses on direct numerical simulations of breaking waves generated by a wave plate at constant water depths. The aim is to quantify the dynamics and kinematics in the breaking process, together with the air entrainment…
Wave breaking is a critical process in the upper ocean: an energy sink for the surface wave field and a source for turbulence in the ocean surface boundary layer. We apply a novel multi-layer numerical solver resolving upper-ocean dynamics…
The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been…