Numerical Simulation of the Kelvin Wake Patterns

Abstract

The ship wave is of great interest for wave drag and coastal erosion. This paper proposes a mechanism of ship wave transformation to explore the effects of ship speed and ship size on the waveform. Firstly, based on the theory of potential flow, the boundary integral equations for the Kelvin ship waves are obtained by deploying the different Kelvin sources or Rankine sources. Then, these integral equations are numerically discretized to a set of nonlinear equations. Finally, the Jacobian−free Newton–Krylov method with a preconditioner is adopted to solve the nonlinear equations. Though imitating plenty of different Kelvin wave patterns, the mechanism of ship wave transformation is proposed to conveniently generate the polymorphic Kelvin wake patterns. The above numerical simulation scheme is verified by comparing simulation results with real ship waves. After that, the wake angle is discussed with the effects of Froude number, source strength and source type by following the mechanism of ship wave transformation. The results show that the wake angle tends to decrease with ship speed but increase with ship size. In addition, for high ship speeds, the effect on the wake angle can be more dramatic.