Nonlinear determinism in time series measurements of two-dimensional turbulence

Experiments on two-dimensional and three-dimensional turbulent flows in a rotating annulus are analyzed using linear and nonlinear time series predictors. The models are used to predict the time series, a time S ahead and to calculate the velocity increment ΔuS=u(sn+S)−u(sn) between the current value of the time series sn and a point time S apart. For two-dimensional flow, the nonlinear model provides superior predictions to the linear model for ΔuS positive and large. In contrast, for three-dimensional turbulence the prediction of the nonlinear model is no better than the linear model. For two-dimensional turbulence, the probability density functions for the predicted ΔuS from the linear model have an exponential tail, while for the nonlinear model the tail exhibits power law decay. The scaling exponent of this power law can be explained using arguments of the Kolmogorov 1941 theory. Our findings contradict the common assumption that two-dimensional turbulence shares the unpredictability properties of three-dimensional turbulent flows.