涡旋流动中轴对称和非轴对称扰动的相互作用

本文研究涡旋流动中轴对称和非轴对称扰动的相互作用。在无粘、不可压涡旋流动中引进轴对称和非轴对称扰动,将扰动速度展开成傅立叶级数,代入到无粘、不可压流基本方程组中,使用多重尺度摄动方法,获得轴对称和非轴对称弱非线性扰动波振幅的调幅过程所满足的联立方程组。数值计算表明,在满足轴对称扰动和非轴对称扰动耦合的条件下,可以得到具有孤立子性质的轴对称扰动和非轴对称扰动。最后简要地从能量观点讨论了轴对称和非轴对称扰动的干扰机理。

Interaction Between the Axisymmetric and Nonaxisymmetric Disturbances in a Vortex Flow

Interaction between the axisymmetric and non-axisymmetric disturbances in a vortex flow is investigated. The axisymmetric and non-axisymmetric disturbances are introduced in an inviscid, incompressible vortex flow. The perturbation velocities are expanded into Fourier series, and substituted in the governing equations. By using multiple singular perturbation method, the simultaneous equations, which are satisfied by the modulation process of the weakly nonlinear wave's amplitude, are derived. Numerical computation shows that axisymmetrie and nonaxisymmetric solitary waves could be obtained under the conjugate conditions. The interaction mechanism of the axisymmetric and nonaxisymmetric disturbances are briefly discussed from the energy viewpoint.