On the bi-stabilities of vortex shedding flows behind a pair of square solids

[[abstract]]Low Reynolds number flows behind two side-by-side square solids with a gap were studied by both numerical simulation and experimental flow-visualization methods. The numerical simulations were conducted by solving the two-dimensional incompressible Navier-Stokes equations. The spatial discretization consists of a seventh-order accurate upwind-biased method for the convective terms and a sixth-order central difference method for the diffusive terms. Arranging the shedding vortices from the upper and lower solids in a synchronal phase and non-synchronal phase as the initial conditions, the stationary in-phase and anti-phase vortex shedding flows take place, respectively. The anti-phase vortex streets remain stable and proceed to the far wake zone. While the in-phase vortex pair, during downstream motion, is observed to rotate around one another. The process eventually leads to the development of a single large-scale wake. The vortex shedding patterns are experimentally studied in a water tunnel by using a Particle Tracing Visualization (PTV) method. The developed in-phase and anti-phase vortex shedding flows along with time-velocity histories are presented and analyzed with the help of signal analysis, i.e., Fourier power spectrum analysis of the velocity evolution and the phase-space trajectory of the velocities. Interestingly, spatially inverse period-doubling phenomena are observed for the in-phase vortex shedding flows.[[note]]SC