Chaos in the lid-driven square cavity

Salvador Garcia

Mathematics and Computers in Simulation (MATCOM), 2017, vol. 142, issue C, 98-112

Abstract: As the Reynolds number Re⟶∞ the primary eddy switches from clockwise- to counterclockwise-rotating, a switching repeatedly reversing as the time t⟶∞. The primary eddy is the eddy leading the dynamics. Marking the genesis of chaos, the switching first is observed at Re=307,000 at the upper side of the total kinetic energy range. But then, it is observed at Re=310,000 at the lower side of the total kinetic energy range and unexpectedly relies upon the occurrence of a unique lowest spike in the total kinetic energy range. However, this reliance is not observed at Re=307,000, even when the lowest spike is more pronounced herein, but continues occurring systematically beyond Re=310,000. At extreme Reynolds numbers Re=O(1eps)=O(1015), where eps is the machine epsilon in double precision, as the time t⟶∞, an interesting dynamics still endures where the switching repeatedly reverses or where it stays put, the primary eddy rotating solely counterclockwise.

Keywords: Navier–Stokes equations; Lid-driven square cavity flow; Chaos (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:142:y:2017:i:c:p:98-112

DOI: 10.1016/j.matcom.2017.04.010

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