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Author: search.filters.author.Roberto Ribeiro‐Jr

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    Nonlinear wave dynamics under the presence of a strong horizontal electric field and a bathymetry
    (Elsevier BV, 2024-12-13)
    In this letter, we explore free-surface flow of an ideal dielectric liquid subjected to a strong tangential electric field in the presence of variable bottom topographies. Analytically, we demonstrate that nonlinear waves of arbitrary shape can propagate at a critical speed without distortion, provided they are in resonance with a moving localized obstacle at the bottom. Numerical solutions of the full model for various obstacle types yield two key results: (i) For localized obstacles, a wave forms above the obstacle, then splits into symmetric waves traveling in opposite directions at the same speed and a stationary disturbance formed due to electric field inhomogeneities. (ii) Periodic spatial bathymetries induce periodic motion in both space and time. Additionally, considering traveling solitary waves, we show that a small dispersive tail arises when they interact with the bathymetry.
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    FULL EULER EQUATIONS FOR WAVES GENERATED BY VERTICAL SEABED DISPLACEMENTS
    (Society for Industrial and Applied Mathematics, 2025-01-01)
    We present a numerical method for simulating the generation and propagation of surface gravity waves by vertical seabed displacements. The cornerstone of our method is the computation of a time-dependent conformal map that incorporates the time-dependent geometry of the seabed in the physical domain and the dynamic wave profile at the free surface, thus enabling us to spectrally integrate the fully nonlinear Euler equations without further restrictions in nonlinearity or dispersion. We validate our numerical method using the linear model for waves generated by small vertical seabed displacements. Comparisons are made between the linear and fully nonlinear models. Finally, we compare the active and passive generation approaches. Solutions of the fully nonlinear Euler equations reveal shortcomings of the passive generation approach; while it yields accurate predictions during the generation stage and propagation of the leading waves, it underestimates the waveheight and wave profiles of subsequent waves.
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