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Stochastic processes
Abstract:
Quasi two-dimensional turbulent flows, like mesoscale oceanic and large-scale atmospheric flows, create finite-time coherent structures, compact fluid masses that resist mixing for finite-time despite the turbulent nature of the ambient flow. These coherent structures significantly affect the mixing and transport of fluid elements. In return, the transport of passive scalars like heat, humidity, salinity, chemical concentration, nutrients and even algae has a substantial impact on countless geophysical phenomena. Thus, in order to understand these effects reliable methods for coherent structure detection and the identification of their boundaries are necessary. Here, in this thesis, we present two contributions in this regard. First, we present improvements of the transfer operator approach, an established stochastic approach for the detection of almost-invariant and coherent sets. The approach approximates the transport properties of a complicated flow by a linear transfer operator and aims to partition a given domain in multiple sets such that the inter-set mass transport is minimized. The improvements include the introduction of mixing boundary conditions in stationary and time-dependent flows. By modifying the transfer operator we couple the filaments that surround the coherent and jointly rotating fluid volume such that effectively only two non-communicating sets remain: the coherent eddy core and the ambient flow. This significantly stabilizes the inference of coherent eddy cores and makes the use of popular but error-prone clustering techniques unnecessary. In addition, we discuss the identification of temporally consistent areas of increased coherence. Instead of coherent structures that are defined by advected non-filamenting masses, the concept describes consistent and moving patches of reduced mixing whose mass can change over time. This permits the decoupling of the coherence time scale from the time window under consideration. Both modifications are used to study the transport properties of eight selected Baltic Sea eddies. Secondly, we introduce the MSCS-search, a new algorithm for the inference of finite-time coherent volumes that is solely based upon the concept of convexity. Persistent convexity is a sufficient condition for coherence in two-dimensional flows if coherent structures are understood as non-filamenting volumes. However, convexity has never been considered as condition of coherence, even though some methods use it, for practical reasons, as an explicit constraint. The approach identifies the largest structure inside a given volume that remains star-convex with respect to a given reference trajectory within a given time window. We test the approach thoroughly and our results show that the approach yields good and reliable estimations of coherent structures in all test cases. Moreover, since the results depend explicitly on the considered time window, the results are intuitive and enable the identification and study of filaments. The novel approach is then used to re-evaluate transport processes in the data set of Baltic eddies.
