When an air cushion supported vessel navigates in the waves, the air pressure in the cushion pulsates due to the pumping effect of waves. The pulsating pressure could induce significant waves to have an impact on the aerodynamics of air cushion. To evaluate the waves, a linear 3D potential method has been proposed by Doctors (1974) and Kim and Tsakonas (1981). However, the algorithm of the 3D method is too complicated and so far the 3D method has not been widely utilized in the air cushion hydrodynamics. In this paper, a 2.5D method for calculating the waves due to the pulsating pressure was firstly presented. The 2.5D method is much simpler and more efficient than the 3D method. The numerical results suggest the sufficient conditions for the 2.5D method to perform as well as the 3D method.
The problem of pulsating pressure induced waves, which is also known as the free surface Dirichlet problem, is common in air cushion hydrodynamics. When an ACV (air cushion vehicle) or a SES (surface effect ship) navigates in waves, the air cushion pressure pulsates due to the wave pumping effect. The pulsating air cushion pressure inversely reacts on the free surface in the cushion and makes waves that could influence the dynamics of the air cushion by changing the cushion volume or air leakage area. Therefore, it is important to evaluate the air cushion hydrodynamics.
The pulsating pressure induced waves or the free surface Dirichlet problems were concerned long time ago. Stoker (1957) and Wehausen et al. (1960) deduced the mathmatic models for solving the free surface Dirichlet problems in 2D case and 3D case, respectively. The 2D model is not practical since the air cushion is always three-dimensional. Meanwhile, it is difficult to directly perform the calculation under the 3D model given by Wehausen. Later Doctors (1974), Kim and Tsakonas (1981) made great efforts to develop a more solvable 3D linear potential method for evaluating the free surface elevation due to a rectangular uniformly-distributed pulsating pressure patch. In order to calculate the waves due to a non-rectangular pulsating pressure patch under an air-lifted vessel, Xie et al. (2008) discretized the irregular pressure patch to a set of rectangular ones, using the method developed by Kim and Tsakonas (1981) to obtain the free surface elevation due to each rectangular patch, and then linearly superimposed them as the final results. In another case, Guo et al. (2016) discretized the nonuniformly-distributed pulsating pressure patch to a series of approximately uniformly-distributed pulsating pressure patches, and then adopted similar procedures to get the free surface elevation. However, it is still not trivial to solve the free surface Dirichlet problem using the upper mentioned 3D linear potential method, since there exist some singular and oscillating integrals.