Stern Trace The Wave Theory

As is well known, when a ship moves on the water, there are steady V-shaped waves behind it. The wake angle is 38°56′and is usually called the Kelvin ship wave. The Kelvin wave system is composed of diverging waves and transverse waves. At the two Kelvin arms diverging waves and transverse waves intersect. There the undulation is especially obvious. Synthetic Aperture Radar (SAR) images of the sea surface can show the Kelvin wakes with many studies on it. Many scholars have also studied the waves including regarding the water as an inviscid fluid and as viscous fluid.Some problems about ship waves are investigated and analyzed theoretically in this dissertation. some new phenomena about ship waves have been explained and obtained. The originalities and the main results in this dissertation are:1.The singularity at the critical lines of ship waves on a viscous fluid is avoided.The ship waves mode on a viscous fluid have been obtained. The effect of viscosity on ship waves can been seen clearly. When the viscosity become bigger, the effect of diverging waves disappears slowly and transverse waves dominates. The velocity fields are also obtained. The velocity changes continuously on the critical lines. At the outside of the critical lines, the dispersive relation has no real solution, but the disturbances still exist.2. The formation of narrow ship waves has been explored and studiedThe paper makes reference to the lifting theory of the submerged hydrofoil of finite span and establishes a model of the interaction between a submerged horseshoe vortex and a free surface far from the ship. smooth region. In the region with an included angle of just a few degrees the free surface is smooth. Then the fast oscillation begins when the angle becomes larger. We get the exact angle expression. It is trusted that this region has important effect on the SAR image of narrow V-images. In addition, the interaction between a submerged circle vortex and a free surface has also been considered. The circle vortex could be exist if the submerged body such as a submarine moves under the water.3. Study the ship waves on an ideal fluid of finite depthIt's difficulty to obtain the expression of wave elevation because of the hyperbolic function. We extended Radko's method and studied the effects of Froude number on ship wave modes and made some phenomena clear.