Non-hydrostatic shallow flow model of particle tracking in basin with various bathymetry

Abstract

In the present paper, Green-Naghdi (GN) model is applied to investigate the movement of particles in a basin with flat and non-flat bathymetry. Two numerical discretisation, second-order central difference and fourth-order central difference, are used as numerical solvers of GN model. The developed GN model is verified against the analytical solution of the linearised shallow water equations by using benchmark test of free surface sloshing of an initial Gaussian hump in a closed square basin. Then, the flow fields of evolution of sloshing motion of Gaussian hump are used to perform Lagrangian particle tracking. Four scenarios of particle tracking are studied for a basin with flat and non-flat bathymetry. First, is the case of flat-bed basin. Second, is where the bed topography of basin contains rocky hump in its centre. Third, is where the bed topography of basin contains rocky trough in its centre and in the fourth case bed topography of basin containing rocky hump in its corner is studied. Particle positions are predicted for each scenario and are compared with each other. The developed model shows remarkable capability to correctly predict the positions of particles of all scenarios.