Rare Event-Triggered Transitions in Aerodynamic Bifurcation

Abstract

The transitions between two states of a bistable system are investigated experimentally and analyzed in the framework of rare-event statistics. Considering a disk pendulum swept by a flow in a wind tunnel, bistability between two aerodynamic branches is observed, with spontaneous transitions from one branch to the other. The waiting times before spontaneous transition are distributed following a double exponential as a function of the control parameter, spanning 4 orders of magnitude in time, for both transitions. Inspired by a model originally applied to the transition to turbulence, we show that, for the disk pendulum, both transitions are controlled by rare events of the aerodynamic forces acting on the disk which we propose to link in particular to the vortex shedding-induced fluctuations. Beyond the aerodynamic aspects, this work has interesting fundamental outcomes regarding the broad field of rare events in out-of-equilibrium systems.

Degeneracy of turbulent states in two-dimensional channel flow

“…Jiménez (1990) gathered statistics over periods up to 6000 time units while Umeki (1994) used a window of only 32 time units). Our results then add 2-D channel flow to the list of other turbulent flows where multistability has also been observed such as Rayleigh-Bénard convection (Xi & Xia 2008), von Kármán flow (Ravelet et al 2004;Faranda et al 2017), Taylor-Couette flow (Huisman et al 2014), rotating spherical Couette flow (Zimmerman, Triana & Lathrop 2011), spanwise-rotating plane Couette flow (Xia et al 2018), 2-D forced shear flow (Dallas, Seshasayanan & Fauve 2020), flow in a T-mixer (Schikarski et al 2019) and the flow past a pendular disk in a wind tunnel (Gayout, Bourgoin & Plihon 2021).…”

“…2018), 2-D forced shear flow (Dallas, Seshasayanan & Fauve 2020), flow in a T-mixer (Schikarski et al. 2019) and the flow past a pendular disk in a wind tunnel (Gayout, Bourgoin & Plihon 2021).…”

Nonlinear interactions of ion acoustic waves explored using fast imaging decompositions

“…The distributions are compatible with an exponential distribution, which implies that the transition events are not correlated. Such distributions of residence times or waiting times are ubiquitous to transitions observed in aerodynamics 57 , turbulent flows 58,59 or convection 60 , to the waiting time between reversals in dynamo experiments 61 , or the turbulent dynamics of the scrape-off layer in tokamaks 62,63 .…”

Game-environment feedback dynamics in growing population: Effect of finite carrying capacity

“…It is the phenomenon of bistability in the presence of finite carrying capacity. The bistability is an omnipresent feature of many physical, chemical, and biological systems; there is a lot of current interest in its presence in the phenomena witnessed in quantum [61][62][63], thermal [64][65][66], electrical [67], optical [68,69], and mechanical [70][71][72][73] systems. Consequently, it is exciting to find the bistability in an eco-evolutionary dynamical scenario and that too resulting in counterintuitive conclusions: e.g., the bistability makes it possible to sustain cooperation-and hence to avert the TOC-in the finite population even when every individual faces the prisoner's dilemma.…”