Some dynamical properties of a differential model for the bursting cycle in the near-wall turbulence

In the last years several investigations have been devoted to model the bursting cycle in the near-wall turbulence by means of low-dimensional systems, with the aim of having simple mathematical models for the dynamics of coherent structures. The present paper deals with a low-dimension differential model, recently proposed by the authors. It is directly deduced from the velocity time series measured in a turbulent flow and well mimics the velocity oscillations typical of the bursting events. After studying the linear stability of the model, its behavior when an external forcing is added, both deterministic and stochastic, is analyzed. It is found that the essential characteristic of the dynamics described by the model is a Hopf bifurcation that, when excited by a stochastic forcing, produces time series with fluctuations that have similarities with the real turbulence signals.