Jakob Grahn will present his master's thesis entitled "Comparing Rényi entropy and finite Lyapunov exponents as metrics of mixing in an idealised stratosphere".

Opponent: Jakob Süld

Supervisor: Donal Murtagh

Abstract

Most metrics of mixing in fluids are based on calculated trajectories and thus knowing the velocity field of the flow. Velocity fields are however difficult to measure globally on Earth. Tracer fields are on the other hand easier to measure and tracer based mixing metrics could therefore be valuable. A newly proposed metric based on the Rényi entropy of tracer values is therefore examined. Although the metric has been studied before, the theoretical connection to mixing is not known to the authors. This motivates an examination of the metric under controlled circumstances. A model based on velocity fields defined by only a few parameters is implemented and used as a test bench for comparing the entropy metric with conventional trajectory based metrics. In particular finite time and finite size Lyapunov exponents are used for comparison. The Rényi entropy metric features the main transport barriers of the model and a positive correlation to the Lyapunov exponents are found. It is concluded that, under the right circumstances, the Rényi entropy metric can be related to mixing.