Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing attention in recent years. Similar objectives also arise in diverse fields such as turbulence and combustion research, image analysis, and medical diagnostics under the headlines of "feature tracking", "coherent structure detection" or "image registration" -to name just a few. A host of different approaches to addressing the underlying, often very similar, tasks have been developed and successfully used. Here, several typical examples of such approaches are summarized, further developed and applied to meteorological data sets. Common abstract operational steps form the basis for a unifying framework for the specification of "persistent structures" involving the definition of the physical state of a system, the features of interest, and means of measuring their persistence.
A recent work of Harikrishnan et al. [“Geometry and organization of coherent structures in stably stratified atmospheric boundary layers,” arXiv:2110.02253 (2021)] has revealed an abundance of hairpin-like vortex structures, oriented in a similar direction, in the turbulent patches of a stably stratified Ekman flow. In this study, hairpin-like structures are investigated by treating them as slender vortex filaments, i.e., a vortex filament whose diameter d is small when compared to its radius of curvature R. The corrected thin-tube model of Klein and Knio [“Asymptotic vorticity structure and numerical simulation of slender vortex filaments,” J. Fluid Mech. 284, 275 (1995)] is used to compute the motion of these filaments with the atmospheric boundary layer as a background flow. Our results suggest that the orientation of the hairpin filament in the spanwise direction is linked to its initial starting height under stable stratification, whereas no such dependency can be observed with the neutrally stratified background flow. An improved feature tracking scheme based on spatial overlap for tracking Q-criterion vortex structures on the direct numerical simulation data is also developed. It overcomes the limitation of using a constant threshold in time by dynamically adjusting the thresholds to accommodate the growth or deterioration of a feature. A comparison between the feature tracking and the filament simulation reveals qualitatively similar temporal developments. Finally, an extension of the asymptotic analysis of Callegari and Ting [“Motion of a curved vortex filament with decaying vortical core and axial velocity,” J. Appl. Math. 35, 148–175 (1978)] is carried out to include the effect of gravity. The results show that, in the regime considered here, a contribution from the gravity term occurs only when the tail of an infinitely long filament is tilted at an angle relative to the wall.
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