中文摘要：

利用Green函数法解析求得Couette流流函数的精确解,通过定义Couette能量、相对能量和能量增长率讨论了初始场结构对Couette流能量演变的影响、能量达到最大值时对应的时间与初始场的关系、最有利于Couette流能量在有限时段快速增长的初始场结构,并对Farrell的研究结果进行了补充和完善.在此基础上,进一步探讨了初值扰动对Couette流能量演变的影响.

英文摘要：

In this paper, the Green function method is used to obtain the exact solution of Couette flow. By defining the Couette flow energy, the relative energy and the energy increase ratio, we discuss the relations between the structure of initial field and the evolution of Couette flow energy, the relations between the time corresponding to Couette flow energy attaining to its maximum and the structure of initial field together with the structure of initial field which can optimal excitated Couette flow energy increasing within a finite time interval. We further investigate the relations between the perturbed initial field and the evolution of Couette flow energy. The conclusions of this paper are supplementary to Farrell’s conclusions.