摘要
This paper presents a method for solving Lagrangian version of governing equations that allows boundary conditions at the free surface to be satisfied exactly, which is a three-dimensional generalization of a method first put forward by Stoker. Analytical expressions of nonlinear hydrodynamic pressure up to the third order and of free surface displacement up to the fourth order of an accelerating cylindrical tank were obtained. Here only the motions of objects in their early stage after initial impulses was considered. As a justification of the method, the important special case when the ratio of tank diameter to fluid depth tends to infinity was taken as an example, which shows that the linear hydrodynamic pressure obtained agrees completely with Westergaard or von Karman's classical result.
This paper presents a method for solving Lagrangian version of governing equations that allows boundary conditions at the free surface to be satisfied exactly, which is a three-dimensional generalization of a method first put forward by Stoker. Analytical expressions of nonlinear hydrodynamic pressure up to the third order and of free surface displacement up to the fourth order of an accelerating cylindrical tank were obtained. Here only the motions of objects in their early stage after initial impulses was considered. As a justification of the method, the important special case when the ratio of tank diameter to fluid depth tends to infinity was taken as an example, which shows that the linear hydrodynamic pressure obtained agrees completely with Westergaard or von Karman's classical result.
