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
(Re) and turbulent QCB at higher Re. These two temporal
dynamics are continuously connected by varying 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 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