Rényi entropy and finite Lyapunov exponents as metrics of transport and mixing in an idealised stratosphere

Abstract

Most numerical metrics for diagnosing transport and mixing in fluid flows are based on calculating trajectories and thus knowing the velocity fields of the flows. Velocity fields are however difficult to measure globally on Earth. Tracer fields are on the other hand easier to measure and tracer based metrics could therefore prove to be valuable. A newly proposed metric based on the Rényi entropy of tracer values is examined. Although the metric has been used before, the exact theoretical connection to transport and mixing appears to be unclear to us. This motivates us to examine the metric under controlled circumstances. A simple model, defined by only a few parameters, is implemented and used as a test bench for comparing the metric with conventional trajectory based metrics. In particular, the finite time and the finite size Lyapunov exponents are considered for the comparison. We show that the Rényi entropy metric features the main transport barriers of the model and a positive correlation to the finite Lyapunov exponents is found.