Chaotic measure of the transition between two- and three-dimensional turbulence

Abstract

Using direct numerical simulation we study the behavior of the maximal Lyapunov exponent in thin-layer turbulence, where one dimension of the system is constrained geometrically. Such systems are known to exhibit transitions from fully three dimensional turbulence through a mixed two and three dimensional phenomenology state and then onto fully two dimensional dynamics. We find a discontinuous jump in the Lyapunov exponent at this second transition implying the predictability of such systems can change dramatically. Such transitions are seen in a number of different turbulent systems, for example those undergoing strong rotation, hence these results may be relevant for the predictability of complicated real world flows. The Lyapunov exponent is found to provide a particularly clear measure of the transition to two dimensional dynamics. Finally, the application of these results to atmospheric predictability with regard to high-resolution modeling is examined.