变深度浅水域中非定常船波

UNSTEADY SHIP WAVES IN SHALLOW WATER OF VARYING DEPTH ~1)

以Green-Naghdi(G-N)方程为基础,采用波动方程/有限元法计算船舶经过变深度浅水域时非定常波浪特性.把运动船舶对水面的扰动作为移动压强直接加在Green-Naghdi方程里,以描述运动船体和水面的相互作用.以series 60 CB=0.6船为算例,给出自由面波高,波浪阻力在船舶经过一个水下凸包时变化规律,并与浅水方程的结果进行了比较.计算结果表明,当船舶经过凸包时,波浪阻力先增加,后减少,并逐渐趋于正常.同时发现,当船速小于临界速度时(Fr=gh<1.0),G-N方程给出的船后尾波比浅水方程的结果明显,波浪阻力也比浅水方程的结果有所提高,频率散射必须考虑.当船速大于临界速度时(Fr=gh>1.0),G-N方程的计算结果与浅水方程差别不大,频率散射的影响可以忽略.

This paper employs Green-Naghdi (G-N) equation to study unsteady ship waves in shallow water of varying depth. The ship body is considered as a moving pressure disturbance on free surface. The moving pressure is added to Green-Naghdi equation to formulate interaction of ship body and free surface. The frequency dispersion term of G-N equation accounts for the effects of finite varying water depth on ship waves. Wave Equation/Finite Element Method (WE/FEM ) is used to solve the Green-Naghdi equation. In most areas of shallow water, the water depth is about 10 meters, the ship length is about 50-100 meters. The kh value of ship waves in shallow water is generally small, unless the ship speed is very low. The varying finite depth, non-linearity, frequency dispersion, free surface disturbance, energy dissipation and boundary reflection are hardly studied together for ship waves based on potential theory. Ship wave is a combination of multi-frequencies water waves. The wave components with finite kh could have effect on ship waves due to frequency dispersion. Green-Naghdi equation is one of Boussinesq-type equations that reasonably account for frequency dispersion. Furthermore, varying depth, non-linearity, free surface disturbance, energy dissipation and boundary reflection can also be involved in Green-Naghdi equation.The numerical examples of Series 60 with CB = 0.6 ship are presented in this paper. Three-dimensional free surface elevations and wave resistance are given as the ship passing over a floor bump. The numerical results indicate that the wave resistance increases at first, then decreases, and finally approaches to normal as the ship passing the bump. A comparison between the results predicted by the G-N equation and the shallow water equation is made. It is found that the stern waves are more significant, and the wave resistance predicted by G-N equation is lager than that predicted by shallow water equation in subcritical flows. In supercritical flows, the G-N equation and the shallow water equation give almost the same results, the frequency dispersion may be neglected.