A third-order analytical solution for the gravity–capillary standing wave is derived in Lagrangian coordinates through the Lindstedt–Poincare perturbation method. By numerical computation, the dynamical properties of nonlinear standing waves with surface tension in finite water depth, including particle trajectory and surface profile are investigated. We find that the presence of surface tension leads to a change of the crest form. Moreover, we also find that the particle trajectories near the surface oscillate back and forth along the arcs which will change from concave to convex as the inverse Bond number increases. There is no mass transport of the particles in a wave period.

通过Lindstedt-Poincare摄动法，在拉格朗日坐标中得出了重力-毛细管驻波的三阶解析解。通过数值计算，研究了有限水深中具有表面张力的非线性驻波的动力学特性，包括粒子轨迹和表面轮廓。我们发现表面张力的存在导致波峰形式的改变。此外，我们还发现，表面附近的粒子轨迹沿着弧线来回振荡，随着反键数的增加，弧线将从凹面变为凸面。在波浪周期中没有粒子的质量传输。