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On the motion of hairpin filaments in the atmospheric boundary layer

Abhishek HarikrishnanMarie RodalRupert KleinDaniel MargeritNikki Vercauteren
Mar 2023
A recent work of Harikrishnan et al. [arXiv:2110.02253 (2021)] has revealedan abundance of hairpin-like vortex structures, oriented in a similardirection, in the turbulent patches of a stably stratified Ekman flow. TheEkman flow over a smooth wall is a simplified configuration of the AtmosphericBoundary Layer (ABL) where effects of both stratification and rotation arepresent. In this study, hairpin-like structures are investigated by treatingthem as slender vortex filaments, i.e., a vortex filament whose diameter $d$ issmall when compared to its radius of curvature $R$. The corrected thin-tubemodel of Klein and Knio [J. Fluid Mech. (1995)] is used to compute the motionof these filaments with the ABL as a background flow. The influence of the meanbackground flow on the filaments is studied for two stably stratified cases anda neutrally stratified case. Our results suggest that the orientation of thehairpin filament in the spanwise direction is linked to its initial startingheight under stable stratification whereas no such dependency can be observedwith the neutrally stratified background flow. An improved feature trackingscheme based on spatial overlap for tracking $Q$-criterion vortex structures onthe Direct Numerical Simulation (DNS) data is also developed. It overcomes thelimitation of using a constant threshold in time by dynamically adjusting thethresholds to accommodate the growth or deterioration of a feature. Acomparison between the feature tracking and the filament simulation revealsqualitatively similar temporal developments. Finally, an extension of theasymptotic analysis of Callegari and Ting [J. App. Math (1978)] is carried outto include the effect of gravity. The results show that, in the regimeconsidered here, a contribution from the gravity term occurs only when the tailof an infinitely long filament is tilted at an angle relative to the wall.