缓变主流中三维气泡的非线性振动

NONLINEAR OSCILLATION OF A 3D GAS BUBBLE MOVING IN A SLOWLY VARYING FLOW

空化现象和水下噪声机制与液体中气泡的动力学行为密切相关．在无粘势流的假定下，采用多参数摄动分析，研究了缓变主流中三维气泡的非线性体积模态振动．推导了关于缓变泡形展开的各阶扰动方程，获得了一阶振动的演化方程和一些特殊情况下的解析解；并采用高阶有限元离散的边界积分方程方法。

Cavitation phenomena and underwater noise mechanism are closely related to bubble dynamics. Under the assumption of inviscid potential flow, a multiple parameter perturbation analysis is carried out for the nonlinear volume mode oscillation of a 3D gas bubble moving in a slowly varying flow in the paper. The perturbation equations are deduced by expanding the nonlinear boundary conditions to be satisfied on the slowly varying shape. The evolution equation and some analyticalsolutions of the first order oscillation are derived. The natural frequency of a gas bubble moving near a flat wall or a free surface are calculated by using the boundary integral equation method and high order finite element representation.