Wake modes of a freely vibrating square cylinder

The cross-stream flow-induced vibrations of a square cylinder of mass ratio, m*=10, are studied numerically at a fixed Reynolds number, Re, of 250. The reduced speed, U*, is varied from 1 to 10 independent of Re. The flow-induced vibrations of a square cylinder have been previously investigated either by decoupling U* from Re or by coupling U* with Re. While most of the studies available in the literature follow the former approach, those dealing with m*=10 do not provide a detailed account of the branches of dynamic response, hysteresis, and wake patterns. The current effort aims at contributing to these research gaps. The vibrations are purely vortex-induced, and the dynamic response within synchronization is found to be composed of an initial branch, its extension or extended initial branch, and lower branch. For a square-section oscillator, the extended initial branch is resolved for the first time. The most noteworthy outcome of this work is perhaps the resolution of asymmetric as well as one-sided wake modes at certain reduced speeds. The one-sided shedding occurs either from the top or bottom surface of the oscillator. At U*=4.6, the non-zero mean lift changes sign in successive oscillation cycles, indicating that the solutions are bistable. The resolved asymmetric and one-sided modes are associated with positive and negatives values of mean lift, respectively. A very interesting result of this study is the mismatch of wake modes obtained at non-hysteretic U*=4.6 using forward and backward computations.