LOW-ORDER MODELLING OF TURBULENT QUASI-CYCLIC BEHAVIOUR AND SUDDEN RELAMINARISATION

We propose a three-equation model which reproduces the quasi-cyclic behaviour of turbulent flow [Araki et al. (2022)]. We examine a 3D flow driven by steady forcing at various Reynolds numbers (Re) to find a perfectly time-periodic flow at a specific low Re and quasi-cyclic flow at higher Re. The two states are continuously connected when changing Re. A mode-by-mode analysis of the periodic flow allows us to formulate the minimal model, which describes the evolution of three families of scales with their nonlinear interactions, dissipation, and driving terms. By calibrating the model parameters to the DNS results, when possible, we find a qualitatively similar periodic solution to the DNS. By increasing the “Reynolds number” of the model, we find permanent chaos, which we compare to turbulence. The same model also reproduces probabilistic transitions between chaotic and steady states for the different parameter sets. The scaling of this sudden relaminarisation agrees with the ones observed in turbulence to some extent. We consider that our minimal model reproduces several key properties of turbulence.