Based on the equations of the f-plane shallow water model, a new set of nonlinear models for the interaction of the vortices in the f-plane shallow water system are established by using perturbation expansion and multi-scale method. These models have different nonlinear characteristics. The asymptotic analytical solution(vortex solution) is obtained by using Newton iteration method and quasi-spectral method. In the simulation process, different from the previous studies, the initial values were constructed by using the asymptotic analytical solution for the first time to simulate the interaction process of the vortices. The result shows that the single vortex maintains a stable state for a long time under fixed parameters. The approximate critical distances of the binary vortices are different under different nonlinear effects. When the distance between binary vortices is less than, equal to, or greater than the critical distance, the binary vortices merge, rotate or separate. In addition, when the vortices interact, the critical distance of mKdV-type vortex is slightly larger than that of KdV-type vortex. This indicates that the nonlinear effect increases the energy loss rate during the interaction of the vortices and weakens the intensity of the interaction until the vortices are separated and do not affect each other.

在f平面浅水模型方程的基础上，采用扰动展开和多尺度方法，建立了一套新的f平面浅水系统涡旋相互作用的非线性模型。这些模型具有不同的非线性特性。采用牛顿迭代法和拟谱法得到渐近解析解（涡旋解）。在模拟过程中，不同于以往的研究，首次采用渐近解析解构造初始值，模拟涡流的相互作用过程。结果表明，在固定参数下，单涡流长期保持稳定状态。在不同的非线性效应下，二元涡旋的近似临界距离是不同的。当二元旋涡之间的距离小于、等于或大于临界距离时，二元旋涡会合并、旋转或分离。此外，当涡流相互作用时，mKdV 型涡旋的临界距离略大于 KdV 型涡旋的临界距离。这表明非线性效应增加了涡流相互作用过程中的能量损失率，减弱了相互作用的强度，直到涡流分离且互不影响。