Jean-Marc Vanden-Broeck

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Recently developed techniques in exponential asymptotics beyond all orders are employed on the problem of potential flows with a free surface and small surface tension, in the absence of gravity. Exponentially small capillary waves are found to be generated on the free surface where the equipotentials from singularities in the flow (for example, stagnation(More)
Nonlinear waves in a forced channel flow of two contiguous homogeneous fluids of different densities are considered. Each fluid layer is of finite depth. The forcing is due to an obstruction lying on the bottom. The study is restricted to steady flows. First a weakly nonlinear analysis is performed. At leading order the problem reduces to a forced(More)
Hybrid free-surface flows past disturbances in a two-dimensional channel are identified and studied. The fluid is assumed to be inviscid and incompressible, and the flow to be steady and irrotational. The disturbances consist of a step in the bottom of the channel and a flat object lying on the free-surface (e.g., a sluice gate). A weakly nonlinear(More)
Solutions of the nonlinear water wave equations under an ice sheet are computed using a boundary integral equation method. The ice sheet is modelled as a thin elastic plate and the fluid equations are nonlinear. Depending on the velocity of the moving disturbance generating the flow, different types of responses of the floating ice sheet are discussed.
Hydroelasticity brings together hydrodynamics and elastic theories. It is concerned with deformations of elastic bodies responding to hydrodynamic excitations, which themselves depend on elastic deformation. This Theme Issue is intended to identify and to outline mathematical problems of modern hydroelasticity and to review recent developments in this area,(More)
We study the formation and dynamics of interfacial waves on a perfect dielectric ideal fluid layer of finite depth, wetting a solid wall, when the region above the fluid is hydrodynamically passive but has constant permittivity, for example, air. The wall is held at a constant electric potential and a second electrode having a different potential is placed(More)