New expressions are derived for the Green function (GF) for diffraction and radiation of waves by a two-dimensional (2D) body in finite water depth. The finite depth GF is expressed as a sum of singularities, the infinite depth GF and smoothly-varying integrals that are convergent for all parameter values. The infinite depth component is given explicitly, making it very fast to compute. Explicit expressions are derived for the limiting cases of zero and infinite frequency, for both finite and infinite water depth. The low frequency limit of the 2D GF is inconsistent with the zero-frequency 2D GF, with the real part tending to infinity when the water depth is infinite and the imaginary part tending to infinity in finite water depth. The inconsistencies with the zero frequency GF differ between the 2D and 3D cases. These inconsistencies lead to differences between the low-frequency behaviour of the added mass and damping of an oscillating body and the values at zero frequency. It is shown that these differences can be inferred directly from the behaviour of the GF at low frequencies.

为格林函数（GF）导出了新的表达式，用于在有限水深中二维（2D）物体对波的衍射和辐射。有限深度GF表示为奇点，无限深度GF和对于所有参数值收敛的平滑变化积分的总和。明确给出了无限深度分量，使其计算速度非常快。对于有限和无限水深的零和无限频率的极限情况，得出了明确的表达式。2D GF的低频极限与零频率2D GF不一致，当水深无限大时，实部趋于无穷大，而虚部在有限水深中趋于无穷大。在2D和3D情况下，零频率GF的不一致有所不同。这些不一致导致所添加质量的低频行为和振动体的阻尼与零频率值之间的差异。结果表明，这些差异可以直接从GF在低频下的行为推断出来。