The primary instability of the wake behind a two-dimensional freely falling circular cylinder is investigated. Numerical simulations are carried out by using the arbitrary Lagrangian-Eulerian (ALE) lattice Boltzmann flux solver, with which the critical Reynolds number ${\mathrm{Re}}_{cr}$ for the Hopf bifurcation is identified. Results show that ${\mathrm{Re}}_{cr}$ decreases from 46.1 for a fixed circular cylinder to approximately 42.3 for a light freely falling body with the density ratio of ${\rho }^{*}=1.01$. A series of stability analyses for various degree of freedom (DOF) combinations are performed, indicating that the streamwise degree of freedom exerts marginal effects on the primary instability of the wake, whereas the transverse motion can significantly destabilize the wake. In contrast, the rotational motion exhibits a stabilizing effect, thereby increasing the critical Reynolds number ${\mathrm{Re}}_{cr}$. It is also demonstrated that, as the density ratio increases, the primary instability characteristics gradually converge to those of the fixed circular cylinder, confirming that the larger inertia weakens the structural mobility. Finally, the underlying mechanism is interpreted through the maximum energy of the perturbation velocity $k_{\max }$, which gives a robust scaling law to quantify the primary instability of the wake.

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• Flow instability
• Flow-structure interactions