Minimal modeling of the intrinsic cycle of turbulence driven by steady forcing

Abstract

Quasi-Cyclic Behavior (QCB) is a common feature of various laminar and turbulent flows. We conduct Direct Numerical Simulations (DNS) of three-dimensional flow driven by the steady Taylor--Green forcing to find a silent similarity between a stable periodic flow at a small Reynolds number ($\mathrm{Re}$) and turbulent QCB at higher $\mathrm{Re}$. These two temporal dynamics are continuously connected by varying $\mathrm{Re}$. A close examination of the periodic flow allows the formulation of a simple three-equation model, representing the evolution of Fourier modes in three distinct scales. The model reproduces the continuously connected periodic solution and QCB when $\mathrm{Re}$ is varied. We find that non-local triad interactions are necessary to maintain the periodic solution and QCB. Bifurcation analyses illustrate that the model can also reproduce several critical features of turbulence, such as sudden relaminarization of transient chaos. These findings suggest that the model is not specific to the studied flow in a periodic domain but is of more general importance in investigating turbulence in different flow configurations