The Lid-Driven Square Cavity Flow: From Stationary to Time Periodic and Chaotic (Communications in Computational Physics, 2007)
Ranging from Re=100 to Re=20,000, several computational experiments areconducted, Re being the Reynolds number. The primary vortex stays put, and the long-term dynamic behavior of the small vortices determines the nature of the solutions. Forlow Reynolds numbers, the solution is stationary; for moderate Reynolds numbers, it istime periodic. For high Reynolds numbers, the solution is neither stationary nor timeperiodic: the solution becomes chaotic. Of the small vortices, the merging and thesplitting, the appearance and the disappearance, and, sometimes, the dragging awayfrom one corner to another and the impeding of the merging—these mark the routeto chaos. For high Reynolds numbers, over weak fundamental frequencies appearsa very low frequency dominating the spectra—this very low frequency being weakerthan clear-cut fundamental frequencies seems an indication that the global attractorhas been attained. The global attractor seems reached for Reynolds numbers up toRe=15,000. This is the lid-driven square cavity flow; the motivations for studying thisflow are recalled in the Introduction.