Dynamical Analysis On The Geometrical Properties Of Turbulent Coherent Structures

We study Ekman flow simulations which describe the Atmospheric Boundary Layer (ABL) in terms of its coherent structures. We classify coherent structures into six categories, all of which can be identified by using scalar criteria. An optimum threshold τ_p is defined for each scalar field by identifying the region of percolation transition. At τ_p, we extract the structures and follow them in time with in-house codes. We study their geometrical evolution with three parameters: Shape Index, Curvedness and Stretching. A point on a feature space with these parameters identifies whether a structure is rod-like, blob-like or sheet-like. If we follow the evolution of a rod-like structure, every transient state ζ is indicated by a point in the feature space. We can now think of this feature space as a phase space which hosts all possible geometrical states of coherent structures in the system. We use two instantaneous metrics to determine the dynamical properties of these geometrical states: the local dimension of the phase space d(ζ) and its persistence in time θ(ζ), where ζ denotes a location in the geometrical phase space. We compute these quantities for numerous samples of rod-like, blob-like and sheet-like structures in order to gain insight into the preferred shape of a structure.