Symbolic dynamics and nonlinear forecasting of a low-Reynolds-number turbulent channel flow*

We numerically study the dynamic state and predictability of streamwise velocity in a low-Reynolds-number turbulent channel flow from the viewpoint of symbolic dynamics and nonlinear forecasting. We conduct direct numerical simulation (DNS) under the friction Reynolds number of 180. Applying two sophisticated analytical methods, i.e., orbital-instability-based forecasting method (OIFM) and ordinal partition transition network (OPTN), in combination with the surrogate data method to the time series data obtained by DNS, a low-dimensionally and high-dimensionally chaotic states of the streamwise velocity fluctuations emerge at a viscous sublayer and a logarithmic layer, respectively. The present method identifies the possible presence. The predictable time of the low-dimensional chaotic state in the streamwise velocity at the viscous sublayer is about 100 times as long as the time resolution of DNS. The OIFM has a high potential for predicting the chaotic streamwise velocity from the viscous sublayer to the logarithmic layer.