Study of a 3D Cavity Flow using the Numerical Scheme with High Accuracy

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Numerical simulations are carried out for the three-dimensional steady flow in a lid-driven rectangular cavity using the combined compact scheme with high accuracy and high resolution. We study the incompressible flow in a cavity with spanwise aspect ratio 1. 0 and 6. 55, and aspect ratios 0. 4, 0. 6, 1. 0 and 1. 4. Streamlines are obtained from the steady velocity field data with high accuracy and Poincare sections are plotted from the streamlines for Reynolds numbers ranging from 100 to 500. There are two types of streamlines : localized streamlines near a closed curve and chaotic streamlines. In the Poincare sections we can find various structures of ovals of invariant tori and resonant islands by localized streamlines in the regions near the end-wall and irregularly distributed points by chaotic streamlines. The structures in the Poincare sections are similar to those in the phase portraits of one-dimensional non-autonomous Hamiltonian system. In particular, we found that the Poincare sections of streamlines show striking similarities for the 3 : 1 and 2 : 1 resonances as the Reynolds number is changed. When the Reynolds number is larger than that in the 2 : 1 resonance, we obtained the chaotic streamlines in the whole flow region. The present study show that existence of the invariant tori and disruption by the resonances are generally observed in steady cavity flows in cavities with different aspect ratios and spanwise aspect ratios.