Exploring multiple phases and first-order phase transitions in Kármán Vortex Street

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 Boltzmann 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 Re _c ¹ = 53.6, there is a phase transition with the emergence of an eigen microstate pair W^2,3 of pressure and velocity fields. Further at Re _c ² . = 56, there is another phase transition with the emergence of two eigen microstate pairs W^4,5 and W^6,7. 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, W^2,3 after Re_c¹, W^4–7 after Re _c ² 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.