AI 中文总结
研究三角形腔内流动角涡的形成、量化及分形特征，用数值求解纳维-斯托克斯方程并结合莫法特理论分析涡旋级联，通过面积-周长法研究分形性质，提出经验关系，发现角涡分形维数与涡旋大小强度相关，不同形状腔内角涡级联有稳健分形行为。
AI 中文摘要
本研究考察了三角形腔内缓慢粘性不可压缩流中角涡的形成、量化及分形特征。采用基于压力的耦合求解器对控制纳维-斯托克斯方程进行数值求解，根据莫法特角涡理论，通过连续涡旋的尺寸和强度比分析产生的涡旋级联。然后用面积-周长法研究涡旋序列的分形性质。提出了一个经验关系式来估计任意网格分辨率下级联中任意连续涡旋的分形维数。结果表明角涡具有1到2之间的非整数分形维数，且该维数与涡旋大小和强度系统相关。还考察了雷诺数对分形标度的影响。最后，对三角形和方形腔内自相似性的对比分析证实，观察到的角涡级联在不同几何形状和流动状态下表现出稳健的分形行为。
英文摘要
This study examines the formation, quantification, and fractal characterization of corner vortices in slow viscous incompressible flow within a triangular cavity. The governing Navier-Stokes equations are solved numerically using a pressure-based coupled solver, and the resulting vortex cascade is analyzed through the size and intensity ratios of successive eddies in the spirit of Moffatt's theory of corner vortices. The fractal properties of the vortex sequence are then investigated using the area-perimeter method. An empirical relation is proposed to estimate the fractal dimension of any successive vortex in the cascade for arbitrary grid resolution. The results demonstrate that the corner vortices possess non-integer fractal dimensions between 1 and 2, and that this dimension is systematically linked to vortex size and intensity. The influence of Reynolds number on the fractal scaling is also examined. Finally, a comparative analysis of self-similarity in triangular and square cavities confirms that the observed corner-vortex cascade exhibits robust fractal behavior across geometries and flow regimes.
Comments33 pages, 24 figures and 7 tables
