Lineare und nichtlineare Stabilität inkompressibler Strömungen im zweiseitig angetriebenen Rechteckbehälter (English shop)

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This dissertation systematically investigates the linear and non-linear stability of incompressible fluid flows within a double-lid-driven rectangular cavity. The study centers on the decay of the stationary, two-dimensional primary flow and provides a physical interpretation of the hydrodynamic mechanisms driving the transition to three-dimensional structures. Utilizing numerical methodologies, specifically a finite volume method coupled with the Newton-Raphson algorithm, the exact stability boundaries are mapped across a three-dimensional parameter space governed by Reynolds numbers and aspect ratios. Complementary three-dimensional direct simulations are deployed to resolve the non-linear bifurcation behavior unfolding beyond the critical thresholds. The work classifies dominant instability regimes—including centrifugal, elliptical, and quadripolar instabilities—induced by near-wall velocity gradients or specialized vortex stretching fields. These findings refine several previous assumptions in fluid dynamics literature and contribute high-precision benchmark data for computational fluid mechanics.