The surface gravity wave pattern that forms behind a steadily moving disturbance is well-known to comprise divergent waves and transverse waves, contained within a distinctive V-shaped wake. For sufficiently fast-moving disturbances (large Froude numbers), the wake is dominated by divergent waves, and the apparent wake angle is less than the classical Kelvin angle. This issue has received significant attention in recent years. In this paper, we are concerned with a theoretical study of the complementary limit of a slow-moving disturbances (small Froude numbers), which is much less studied. In this regime, the wake is dominated by transverse waves, and it turns out the apparent wake angle is also less than the classical Kelvin angle. We consider three configurations: flow past a submerged source singularity, a submerged doublet, and a pressure distribution applied to the surface. We treat the linearised version of these problems and use the method of stationary phase and exponential asymptotics to quantify the decrease in apparent wake angle as the Froude number decreases. We also study the fully nonlinear problems under various limits to demonstrate the unique and interesting features of Kelvin wake patterns at small Froude numbers.
|Journal||arXiv.org e-Print archive|
|Publication status||Submitted - 9 Sep 2020|