Particle Trajectories Beneath Fully Nonlinear Waves Generated by Horizontal Seabed Motion

Abstract

We investigate fully nonlinear water waves and fluid-particle dynamics generated by the horizontal motion of a seabed obstacle with prescribed time-dependent velocity. The governing equations are the full Euler equations, formulated in a time-dependent conformal domain that simultaneously maps the moving free surface and seabed onto fixed boundaries. The main contribution of this work is a Lagrangian formulation for computing particle trajectories in the resulting genuinely unsteady conformal domain. We derive a closed-form trajectory system in the canonical domain in which the time dependence of the conformal map is entirely represented by the real and imaginary parts of an analytic function that can be evaluated spectrally from the surface. We apply the formulation to waves generated by horizontal submarine landslide motion and characterize particle displacements throughout the fluid as functions of the initial particle position and Froude number. Our findings identify distinct regions in which particle motion is predominantly associated with the moving seabed, the generated wave, or the combined action of both. The results reveal a transition in the dominant mechanism driving particle motion: at low Froude numbers, particle displacements are primarily associated with the moving seabed, whereas at high Froude numbers the generated wave becomes increasingly dominant, particularly near the free surface and away from the obstacle path.The numerical predictions are benchmarked against laboratory data available in the literature, showing good agreement and providing a quantitative assessment of the model accuracy. Moreover, laboratory topographies beyond those considered here can be readily incorporated into the numerical framework through a Hermite interpolation procedure.