Velocity-dependent Lyapunov exponents as a measure of chaos for open-flow systems

Abstract Many flows in nature are “open flows” (e.g. pipe flow). We study two open-flow systems driven by low-level external noise: the time-dependent generalized Ginzburg-Landau equation and a system of coupled logistic maps. We find that a flow which gives every appearance of being chaotic may nonetheless have no positive Lyapunov exponents. By generalizing the notions of convective instability and Lyapunov exponents we define a measure of chaos for these flows.

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