Quasi-equilibrium states for helical vortices with swirl. (10th August 2022)

• Record Type: Journal Article
• Authors: Xu, Yonghui; Delbende, Ivan; Rossi, Maurice
• Is Part Of: Journal of fluid mechanics. Volume 944(2022)
• Publication Date: 2022-08-10
• Subjects: general fluid mechanics; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2022.500
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : We present a family of exact equilibrium solutions of the Euler equations consisting of a single helical vortex with an axial flow component along the vortex core. Relations between vorticity, velocity and streamfunction are analytically derived in the inviscid framework and constitute a generalization of relations valid for vortex rings (Batchelor, 1967 An Introduction to Fluid Dynamics . Cambridge University Press). Through Navier–Stokes simulations, it is shown that these relations hold for quasi-steady viscous solutions and become independent of the Reynolds number when sufficiently large. We also elaborate a procedure which generates a quasi-equilibrium with prescribed characteristics (circulation, helix radius, helical pitch, vortex core size, swirl level) and compare the obtained state with the results of an asymptotic theory. Finally, we illustrate how a strong axial flow jeopardizes such an evolution towards a quasi-equilibrium.