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

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.