74th Annual Meeting of the APS Division of Fluid Dynamics (November 21, 2021 — November 23, 2021)

P0018: Lagrangian hairpins in atmospheric boundary layers

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Authors

• Abhishek Paraswarar Harikrishnan, Free University of Berlin
• Natalia Ernst, Zuse Institute Berlin
• Cedrick Ansorge, University of Cologne
• Rupert Klein, Free University of Berlin
• Nikki Vercauteren, University of Oslo

DOI: https://doi.org/10.1103/APS.DFD.2021.GFM.P0018

In this poster, we have shown beautiful direct volume renders of finite-time Lyapunov exponent (FTLE) fields applied to a highly stratified Ekman flow. This flow describes the atmospheric boundary layer (ABL) over a smooth flat plate driven by a uniform pressure gradient and experiencing steady rotation in the wall-normal direction. 

An interesting result can be observed here. We note that hairpins extracted from different regions in the flow field are oriented in a similar direction i.e., the head of the hairpins point to a similar direction. These results are in-line with our previous observation with the Eulerian Q-criterion [1, 2].

For further details on FTLE, please refer to the work of [3, 4]. FTLE is sometimes referred in literature as direct Lyapunov exponent (DLE). 

The Reynolds number is described in terms of the geostrophic wind velocity (G), the laminar Ekman-layer depth (D) and the kinematic viscosity (ν) as Re = GD/ν.

References:

[1] Harikrishnan, A., Ansorge, C., Klein, R., and Vercauteren, N. (2020). The curious nature of hairpin vortices. 
https://doi.org/10.1103/APS.DFD.2020.GFM.P0019.

[2] Harikrishnan, A., Ansorge, C., Klein, R., and Vercauteren, N. (2021). Geometry and organization of coherent structures in stably stratified atmospheric boundary layers. https://arxiv.org/abs/2110.02253.

[3] Haller, G. (2001). Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D: Nonlinear Phenomena, 149(4), 248-277.

[4] Shadden, S. C., Lekien, F., & Marsden, J. E. (2005). Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D: Nonlinear Phenomena, 212(3-4), 271-304.