| In recent years there has been a lot of progress in the application of dynamical systems concepts to the description of transport in oceanic flows. In these flows the classical dynamical system theory does not apply since they are aperiodic and finite-time defined. Recently, for describing these flows a new definition of distinguished trajectory has been proposed (Madrid & Mancho, Chaos, 2009). Distinguished trajectories act as organizing centres of the geometrical template of aperiodic time-dependent flows, like fixed points and periodic orbits do in time independent or periodic flows. The computation of distinguished trajectories makes use of a function M of which for the 2D case I show contains a lot of Lagrangian information. I prove that the directions of the stable and unstable subspaces of the distinguished hyperbolic trajectory (DHT) are aligned near almost singular structures of the function M. This fact allows an accurate computation of the linear stable and unstable subspaces of the DHT. I show how in a general geophysical flow a DHT presents a non uniform exponential behaviour and I compute this non uniform dependence. This is possible due to the special structure of the linear time depedent flow in the neighbourhood of the DHT. |
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