Cylinder wakes in quasi-two-dimensional flows with surface friction I: instability and scaling

We measured the frequency of vortex shedding produced by cylinders in a quasi-two-dimensional system with homogenous drag. The system is characterized by the Reynolds number Re $=$ U$_{\mathrm{0}}$D/$\nu $ (U$_{\mathrm{0}}=$ flow speed without the obstacle, D $=$ cylinder diameter, $\nu =$ kinematic viscosity), and a dimensionless drag parameter, $\alpha $* $=$ D$^{\mathrm{2}}$/(L$_{\mathrm{s}}^{\mathrm{2}}$Re) (L$_{\mathrm{s}}=$ length scale above which drag force exceeds viscous force). We investigated the scaling of the Strouhal number St $=$ fD/U$_{\mathrm{o\thinspace }}$(f $=$ vortex shedding frequency) and compared it with conventional measurements in flows without homogenous drag. The dynamics bifurcates above a critical diameter D$_{\mathrm{c}}\sim $L$_{\mathrm{s}}$,$_{\mathrm{\thinspace }}$indicating that the effect of surface friction becomes important. Increased fluctuations beyond the bifurcation indicate the onset of a previously unobserved instability associated with the drag. Also, near some critical parameters, shear instability without vortex shedding is observed, with vortex streets appearing at both higher and lower Reynolds number; the mode at lower Reynolds number has not previously been observed.