Nonlinear optimal transient growth in the wake of a transversely oscillating cylinder

【摘要】：We study numerically the two-and three-dimensional incompressible flow in the wake of a circular cylinder forced to oscillate transversely at Re = 230.The oscillation amplitude and frequency are fixed at A~* = 0.1 and f~* = fU/D = 0.2 respectilvey.We note that this frequency is very close to the natural shedding frequency for the flow around a static cylinder at the same Reynolds number.First,we perform nonlinear optimal transient growth analysis,which takes the two-dimensional result as the base flow and solve the three-dimensional nonlinear perturbation equations.The results show that the growth of the optimal perturbation is linear at small magnitude of initial perturbation,or perturbation energy,with the perturbation vorticity concentrates around the cylinder.Whereas,at large magnitude of initial perturbation,the growth of the optimal perturbation is nonlinear,with the vorticity in the upstream of the lower surface observed to spread downstream of the wake.We also carry out three-dimensional direct simulations with the flow field initialized by a superposition of the base flow and a linearly optimal disturbance.For small magnitude,the perturbation is predominantly monochromatic in the span and always exists in pairs.The dominant modes are even,showing that the wake is a superposition of mode 0,2 and 4.Here mode 0 represents the spanwise mean flow.For large magnitude,the positive and negative streamwise velocity perturbations are coupled and the positive perturbations cover a large area than the negative ones.In this situation,the wake is a superposition of mode 0,2 and 1.With the evolution of nonlinearity,mode 1 gradually overtakes mode 2.