Transport and mixing of geophysical systems from finite-size Lyapunov exponent calculations

The finite-size Lyapunov exponent (FSLE) calculation is a simple Lagrangian technique able to detect various characteristics of transport and mixing in two-dimensional geophysical flows. In my talk I will show some atmospheric and
oceanographic examples of application of the FSLEs on real data. I will discuss
some open theoretical problems and show how the FSLEs can be used as a building
block for defining new useful diagnostics. For the case of the North-Atlantic and the Algerian basin, the FSLEs can compute the unstable manifolds of hyperbolic points for predicting mesoscale fronts and filaments observed in patterns of chlorophyll and sea surface temperature. Moreover, the convolution of the manifolds can be used to evaluate the role of chaotic transport in submesoscale structures of tracer patches. For the case of the atmosphere, the FSLE alone fails in detecting mixing. However, forward and backward Lyapunov exponents and vectors can be combined, defining a mixing measure that
takes into account the stretching of the field and the gradients of passive tracers. I will show some applications to the upper troposphere-lower stratosphere region, discussing the modulation of large-scale transport barriers due to the El Niño oscillations.