Study and turbulence control of the laminar-turbulent transition in the spherical Couette flow

采用实验室实验、理论分析和数值模拟相结合的方法，研究了球形Couette流的层流-湍流转变过程。计算关联维并绘制庞加莱截面，当间隙比β=0.14时，流场呈现如下情形：稳态--&gt；周期--&gt；准周期--&gt；混沌--&gt；稳态--&gt；周期--&gt；混沌。结果还表明，在准周期状态下，随着雷诺数的增加，第一返回映射变得不可逆。对于间隙比的其他情况，发现在β=0.13-0.17的范围内出现波动消失现象。提出了一种在球极坐标下求解三维、含时不可压N-S方程的有限差分方法。考虑了一种在时间和空间上都是二阶精度的新算法，并利用该算法实现了速度和压力之间的解耦。计算结果表明，该程序对求解三维不可压缩的Navier-Stokes方程的球极坐标是有效的。在此基础上，用该程序计算了间隙比β=0.14时内球旋转的两球间的球形Couette流动，成功地模拟了亚临界和超临界流动。特别是对螺旋TG涡流进行了细致的直接数值模拟，并进行了系统的分析，探讨了螺旋TG涡流的详细结构、演化过程和产生机理。

The laminar-turbulent transition of spherical Couette flow was investigated by laboratory experiment, theoretical analysis and numerical simulations. Calculating the correlation dimension and drawing the Poincare section, it is revealed for case of clearance ratio beta=0.14 that the flow field traces a scenario as follows ; steady state--> periodic state --> quasi-periodic state --> chaos --> periodic state --> steady state --> periodic state --> chaos. It is also shown that in the quasi-periodic state the first return map becomes irreversible as the Reynolds number increases. For other cases of clearance ratio, it is found that fluctuation disappearance phenomenon occurs in a range of beta=0.13-0.17. A finite-difference method for solving three-dimensional, time-dependent incompressible Navier-Stokes equations in spherical polar coordinates is presented. A new algorithm, which is second-order accurate in time and space, is considered, and decoupling between the velocity and the pressure is achieved by this algorithm. It is demonstrated that the numerical code is valid for solving three-dimensional, unsteady incompressible Navier-Stokes equations spherical polar coordinates. The numerical code was then used to compute the spherical Couette flow between two spheres with the inner sphere rotating for case of clearance ratio beta=0.14, and we successfully simulated the subcritical and supercritical flows. In particular, careful direct numerical simulations on the spiral TG vortex flow has been performed, and systematical analysis has been carried out to explore the detailed structure, evolution process and generation mechanism of the spiral TG vortex flow.