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

## TL;DR

This study reveals that the dynamics and wake patterns of freely rising and falling cylinders are governed by both mass-density and moment of inertia, identifying a transitional regime characterized by a specific Strouhal number and wake mode change.

## Contribution

It provides a comprehensive mapping of the parameter space for mass and moment of inertia effects, surpassing the previous focus on critical mass density alone.

## Key findings

- Two distinct scaling regimes separated by a transitional Strouhal number.
- Transition from $2S$ to $2P$ vortex wake mode with changing parameters.
- Auto-rotation significantly influences trajectories and wake patterns.

## 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 $m^* \equiv \rho_p/\rho_f$ and its relative moment-of-inertia $I^* \equiv {I}_p/{I}_f$. This supersedes the current understanding that a critical mass density ($m^*\approx$ 0.54) alone triggers the sudden onset of vigorous vibrations. Using over 144 combinations of ${m}^*$ and $I^*$, we comprehensively map out the parameter space covering very heavy ($m^* > 10$) to very buoyant ($m^* < 0.1$) particles. The entire data collapses into two scaling regimes demarcated by a transitional Strouhal number, $St_t \approx 0.17$. $St_t$ 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.