Numerical study on three-dimensional waves produced by a bottom jet

• A wave model is simulated for the wave motions induced by a bottom jet.
• A set of gB equations are solved for comparison with fully nonlinear model.
• Jet types: sudden eruption, initial transient, and periodic transient are discussed.

The eruption of an underwater volcano can initiate the disturbances of the sea surface and subsequently generate a group of outward-propagating tsunamis. The theme of this study is to introduce a three-dimensional (3D) fully nonlinear wave model for the simulation of wave motions induced by a bottom jet. A boundary-fitted coordinate system is utilized to conveniently adjust grids according to the transient moving free surface. The governing Laplace equation of the velocity potential is solved by an implicit finite-difference scheme while a mixed explicit/implicit iteration procedure is applied to solve the free-surface boundary conditions. In addition, a set of generalized Boussinesq equations are solved for comparison with the fully nonlinear model. Good agreements in comparisons with the existing numerical and analytical solutions are achieved for cases investigated. Waves induced by three types of bottom jets: namely (1) sudden eruption, (2) initial transient, and (3) periodic transient are discussed in this paper. For the case of sudden erupted jet, a system of 3D outgoing waves as the cylindrical wave pattern are presented and discussed. For the initial transient types, it shows the transition in the incipient stage has a great influence on the initial rising of the water surface and the induced leading waves. Furthermore, an interesting up-down phenomenon in the center of disturbed free surface due to the type of periodic jet is revealed.