Mass and moment of inertia govern the transition in the dynamics and wakes of freely rising and falling cylinders

Abstract

In this Letter, we study the motion and wake-patterns of freely rising and falling cylinders in quiescent fluid. We show that the amplitude of oscillation and the overall system-dynamics are intricately linked to two parameters: the particle's mass-density relative to the fluid $m^{\ast }\equiv {\rho }_p/{\rho }_f$ and its relative moment-of-inertia $I^{\ast }\equiv I_p/I_f$. This supersedes the current understanding that a critical mass density ($m^{\ast }\approx$ 0.54) alone triggers the sudden onset of vigorous vibrations. Using over 144 combinations of $m^{\ast }$ and $I^{\ast }$, we comprehensively map out the parameter space covering very heavy ($m^{\ast }>10$) to very buoyant ($m^{\ast }<0.1$) particles. The entire data collapses into two scaling regimes demarcated by a transitional Strouhal number, $S{t}_t\approx 0.17$. $S{t}_t$ separates a mass-dominated regime from a regime dominated by the particle's moment of inertia. A shift from one regime to the other also marks a gradual transition in the wake-shedding pattern: from the classical $2S$~(2-Single) vortex mode to a $2P$~(2-Pairs) vortex mode. Thus, auto-rotation can have a significant influence on the trajectories and wakes of freely rising isotropic bodies.

Phys. Rev. Lett. (accepted): 5 pages and supplemental material

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