Using linear water wave theory, we consider the wave radiation (both heave and sway) by a sphere submerged in a three-layer fluid consisting of a layer of finite depth bounded above by a fresh water of finite depth with free surface and below by an infinite layer of water of greater density. The sphere is submerged in either of the three-layers. Each problem is reduced to an infinite system of linear equations by employing the method of multipoles and the system of equations are solved numerically by standard technique. The hydrodynamic forces (added-mass coefficients and damping coefficients) for both the heaving and swaying problems are obtained and depicted graphically against the wave number. When the density ratio of upper and middle layer made to approximately one, curves for added-mass and damping coefficients almost coincide with the corresponding curves for the case of a two-layer fluid with free surface. This means that in the limit, the density ratio of upper and middle layer go to approximately one, the solution agrees with solution for the case of a two-layer fluid with free surface.

使用线性水波理论，我们考虑了球体浸没在三层流体中的波辐射（升沉和摇摆），三层流体由一层有限深度的层组成，该层的上方由一层有限深度的淡水包围，而该有限深度的淡水具有自由表面，而在下方则由一个无限层的更大密度的水。球体浸没在三层中的任何一层中。通过采用多极法将每个问题简化为一个无限的线性方程组，并且通过标准技术对方程组进行数值求解。获得了用于波动问题和摇摆问题的流体动力（附加质量系数和阻尼系数），并根据波数进行了图示。在上层和中间层的密度比约为1的情况下，对于具有自由表面的两层流体，附加质量和阻尼系数的曲线几乎与相应曲线重合。这意味着在极限情况下，上层和中间层的密度比接近于1，该解与具有自由表面的两层流体情况下的解一致。