Characterisation of a multistable turbulent wake: application of an improved regime identification with analytical model training

Abstract

This article presents the experimental study and the modelling of the multistable jet in the wake of two side by side square bars separated by a distance $G$ at Reynolds number $R=U_\infty H/\nu=10000$ (with $U_\infty$ the velocity of the incoming flow, $H$ the bar side and $\nu$ the kinematic viscosity). The velocity field downstream of the bars is measured by means of two dimensional two components Particle Image Velocimetry (PIV). We use the weighted transverse position of the jet $Y_m$ and the jet width $w$ to characterise the regimes of multistability as the gap ratio $G/H$ is increased. Three main regimes of multistability are possible: tristability, bistability, and monostability. In our wind tunnel, tristability is observed for $G/H\in [1.15,1.25]$, bistability is observed for $G/H\in [1.5,2.65]$ and monostability is observed for $G/H\in [3.0,3.5]$. Within the first two ranges of $G/H$, there exists gap ratios for which multistability is more complex. In order to analyse the simple and complex multistability regimes as well as the transition from bistable to monostable, we construct an analytical stochastic differential equation (SDE) modelling $Y_m$ for each gap ratio. These SDEs are written with polynomial drift and diffusion. For this matter we use a data based method that finds an trade--off between simplicity of the model (smaller number of monomials) and precision. A first key advantage of the use of the data-based model fitting method is that when the flow is tristable, bistable or monostable, we recover the drifts expected from the theory of bifurcations, but we are now able to correct it with the right multiplicative noise expressed by the diffusion. The second key advantage is that we can also fit atypical drift expressions when the multistability regime is complex that help us make sense of the jet behaviour.