Mode-C transition to three-dimensionality in the wake behind a circular cylinder undergoing 2-DOF VIV*

We have performed the three-dimensional numerical simulations using the open-source Finite Volume-based solver of OpenFOAM. In the simulations, the 2-DOF VIV system is modelled by solving the spring-damper equations allowing the movement of the cylinder in both the inline and cross-flow directions. The cylinder is 9.6 times the cylinder diameter (D) in length and corresponds to a low mass ratio of m^* = 2.546. The Reynolds number is varied from 100 (corresponding to fully 2D wake) to 600 (corresponding to 3D/chaotic wake) to assess the transition to three-dimensionality in the wake. The damping ratio (ζ) is 0 (to maximize the oscillation amplitude), and the velocity ratio (U_r) is chosen to be U_r = 6, which corresponds to the lock-in regime. The data are parametrized using the frequency ratio (f^* = f_nx/f_ny), which is defined as the ratio of inline frequency (f_nx) to cross-flow frequency (f_ny). We have systematically varied this ratio from zero (corresponding to a 1-DOF VIV system with transverse oscillation only) to eight. Further, to represent the 3-D vortex patterns in the cylinder wake, we have used the iso-surfaces of the second eigenvalue (λ₂) of the tensor S² + Ω², where S and Ω are the symmetric and antisymmetric parts of the velocity gradient tensor ▽u, is used to identify the vortex core. An elastically mounted circular cylinder, with the varying inline to transverse oscillation frequency ratios (f^* = f_nx/f_ny), shows a drastic change in the transition Reynolds number and the wake-mode transition to the three-dimensional wake from a fully two-dimensional wake in the lock-in regime. The 2-DOF VIV system follows Mode-C instability for the transition from 2D to 3D wake instead of Mode-B transition observed in the 1-DOF VIV system.