摘要
本文利用奇异摄动理论的两时间变量展开法 ,研究了垂直强迫圆柱形容器中的单一水表面驻波模式。假设流体是无粘、不可压且运动是无旋的 ,在忽略了表面张力的影响下 ,得到一个具有立方项以及底部驱动项影响的非线性振幅方程。对上述方程进行了数值计算 ,研究了特定 ( 9,6)模式的表面驻波结构和特性 ,如驻波的节点分布及驻波随某些参数的变化规律等 ,从计算的等高线的图象来看 。
The single standing wave mode in a circular cylinder subjected to a vertical oscillation was studied by employing two-time-scale perturbation expansions. It was assumed that the fluid in circular cylindrical vessel is inviscid incompressible and the motion is irrotational, and a dimensionless nonlinear evolution equation of slowly varying complex amplitude was derived without considering the effect of surface tension. The nonlinear amplitude equation is simular to the cubic nonlinear Schrdinger equation and incorporates the effect of parametric excitation. The structure of standing surface wave and characteristics of (9,6) mode, such as the distribution of its nodes and its variations as some parameters changes, were investigated with the help of numerical computation. The contour of the free surface displacement agrees well with experimental results.
出处
《水动力学研究与进展（A辑）》
CSCD
北大核心
2003年第2期135-147,共13页
Chinese Journal of Hydrodynamics
基金
国家自然科学基金资助项目 ( 19772 0 63 )
