# Bistability in the wake of a wavy cylinder

## TL;DR

This study explores the bistable wake dynamics of a wavy cylinder that can suppress vortex shedding but may revert to unsteady flow depending on initial conditions and forcing frequency, highlighting complex flow control behavior.

## Contribution

It reveals the existence of bistable states in the wake of a wavy cylinder, showing flow control effectiveness depends on initial conditions and forcing parameters.

## Key findings

- Critical forcing frequency determines vortex shedding suppression
- Unsteady vortex shedding can persist without forcing
- Bistability affects flow control in complex inflow conditions

## Abstract

We investigate the wake dynamics of an optimally designed wavy cylinder that completely suppresses the K\'arm\'an vortex shedding. Such a wavy cylinder is forced to oscillate with a sinusoidal motion in the crossflow direction. Examination of the lift force spectrum reveals that a critical forcing frequency exists, below which the flow control effectiveness of the wavy cylinder is retained, and beyond which the inherent vortex shedding resurrects. Moreover, the resurrected unsteady vortex shedding can persist even without sustained forcing, leading to the loss of control efficacy. This suggests that in addition to the steady state developed from uniform initial condition, an oscillatory state exists in the wake of wavy cylinder if the initial state is sufficiently perturbed. The discovery of the bistable states calls for examination of the flow control effectiveness of the wavy cylinder in more complicated inflow conditions.