Designing vortices in pipe flow with topography-driven Langmuir circulation. (10th November 2021)

• Record Type: Journal Article
• Authors: Ellingsen, Simen Å.; Akselsen, Andreas H.; Chan, Leon
• Is Part Of: Journal of fluid mechanics. Volume 926(2021)
• Publication Date: 2021-11-10
• Subjects: vortex dynamics -- microfluidics -- pipe flow; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2021.696
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : We present direct numerical simulation of a mechanism for creating longitudinal vortices in pipe flow, compared with a model theory. By furnishing the pipe wall with a pattern of crossing waves, secondary flow in the form of streamwise vortex pairs is created. The mechanism, 'CL1', is kinematic and known from oceanography as a driver of Langmuir circulation. CL1 is strongest when the 'wall wave' vectors make an acute angle with the axis, $\varphi =10^{\circ }$ – $20^{\circ }$, changes sign near $45^{\circ }$ and is weak and of opposite sign beyond this angle. A competing, dynamic mechanism driving secondary flow in the opposite sense is also observed, created by the azimuthally varying friction. Whereas at smaller angles 'CL1' prevails, the dynamic effect dominates when $\varphi \gtrsim 45^{\circ }$, reversing the flow. Curiously, the circulation strength is a faster-than-linearly increasing function of Reynolds number for small $\varphi$ . We explore an analogy with Prandtl's secondary motion of the second kind in turbulence. A transport equation for average streamwise vorticity is derived, and we analyse it for three different crossing angles, $\varphi =18.6^{\circ }, 45^{\circ }$ and $60^{\circ }$ . Mean-vorticity production is organised in a ring-like structure with the two rings contributing to rotating flow in opposite senses. For the larger $\varphi$, the inner ring decides the main swirling motion, whereas for $\varphi =18.6^{\circ }$, outer-ring production dominates. For the larger angles, the outer ring is mainly driven by advection of vorticity and the inner by deformation (stretching) whereas, for $\varphi =18.6^{\circ }$, both contribute approximately equally to production in the outer ring.