On the Motion of Hairpin Filaments in the Atmospheric Boundary Layer

Recent results from Harikrishnan et al. [arXiv:2110.02253 (2021)] have revealed that an abundance of hairpin-like structures oriented in a similar direction can be observed in the turbulent patches of a stably stratified Ekman flow. Understanding the dynamics of these inclined features are of immediate importance as they could lead to better subgrid-scale models for large eddy simulation (LES) of stably stratified atmospheric boundary layers (ABL). In this work, we use the corrected thin-tube model of Klein and Knio [J. Fluid Mech. (1995)] to compute the motion of hairpin filaments with the ABL as a background flow. The influence of the mean background flow on the motion of hairpin filaments is examined under neutral, weak and strong stratification. These simulations are then compared to feature tracking of Q-criterion structures performed directly on the direct numerical simulation (DNS) data. Finally, an extension of the asymptotic analysis of Callegari and Ting [J. App. Math. (1978)] is carried out to include the influence of gravity. The results show that a contribution from the gravity term occurs only when the tail of a infinitely long filament is tilted at an angle relative to the wall.