Vortex-induced vibration forever of an extreme-light cylinder in an unsteady wake

Vortex-induced vibration forever (VIVF) is classically associated with a single elastically mounted cylinder, for which oscillations persist at infinite reduced velocity when the mass ratio ( m Superscript asterisk m ∗ $m^*$ ) falls below a critical value ( m Subscript c r Superscript asterisk m c r ∗ $m_{cr}^*$ ). The existence and characteristics of such permanent vibration under unsteady wake conditions remain unclear. This study investigates the vibration response of an extreme-light cylinder placed in the wake of an upstream fixed cylinder without restoring forces, with particular emphasis on the existence and variation of a critical mass ratio m Subscript c r Superscript asterisk m c r ∗ $m_{cr}^*$ with the spacing ratio ( upper L divided by upper D L / D $L/D$ ). The Reynolds number is set to 60, the mass ratio m Superscript asterisk m ∗ $m^*$ ranges from 0.2 to 14 and the spacing ratio upper L divided by upper D L / D $L/D$ ranges from 1.1 to 6.0. Three vibration regimes are identified in the left parenthesis upper L divided by upper D comma m Superscript asterisk Baseline right parenthesis ( L / D , m ∗ ) $(L/D,\, m^*)$ parameter space: non-vibration (NV), limited-range vibration (LRV) and infinite-range vibration (IRV). A critical mass ratio