Lagrangian modelling of nonlinear viscous waves generated by moving seabed deformation

Water waves generated by a moving bottom

Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.

Long waves over a bi-viscous seabed: transverse patterns

The coupled interaction of long standing hydrodynamic waves with a deformable non-Newtonian seabed is examined using a two-layer model for which the upper layer fluid is inviscid and the lower layer is bi-viscous. The two-dimensional response of the system to forcing by a predominantly longitudinal (cross-shore) standing wave perturbed by a small transverse (along-shore) component is determined...

Numerical study of nonlinear shallow water waves produced by a submerged moving disturbance in viscous flow

Two-dimensional solitary waves generated by a submerged body moving near the critical speed in a shallow water channel are studied numerically. The incompressible Navier–Stokes equations in a curvilinear free-surface-fitted coordinate system are solved by the finite difference method. The present numerical results are compared with the existing experimental data, and with the numerical solution...

Nonlinear Stability of Viscous Roll Waves

Extending results of Oh–Zumbrun and Johnson–Zumbrun for parabolic conservation laws, we show that spectral stability implies nonlinear stability for spatially periodic viscous roll wave solutions of the one-dimensional St. Venant equations for shallow water flow down an inclined ramp. The main new issues to be overcome are incomplete parabolicity and the nonconservative form of the equations, w...

Nonlinear Stability of Viscous Shock Waves