Abstract
Kármán Vortex Street,a fascinating phenomenon of fluid dynamics,has intrigued the scientific community for a long time.Many researchers have dedicated their efforts to unraveling the essence of this intriguing flow pattern.Here,we apply the lattice Boltz-mann method with curved boundary conditions to simulate flows around a circular cylinder and study the emergence of Kármán Vortex Street using the eigen microstate approach,which can identify phase transition and its order-parameter.At low Reynolds number,there is only one dominant eigen microstate W1 of laminar flow.At Re1c=53.6,there is a phase transition with the emergence of an eigen microstate pair W2,3 of pressure and velocity fields.Further at Re2c=56,there is another phase transition with the emergence of two eigen microstate pairs W4,5 and W6,7.Using the renormalization group theory of eigen microstate,both phase transitions are determined to be first-order.The two-dimensional energy spectrum of eigen microstate for W1,W2,3 after Rec 1,W4-7 after Re2 exhibit-5/3 power-law behavior of Kolnogorov's K41 theory.These results reveal the complexity and provide an analysis of the Kármán Vortex Street from the perspective of phase transitions.
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