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Journal Articles Journal of Fluid Mechanics Year : 2022

Quasi-equilibrium states for helical vortices with swirl

Yonghui Xu
Ivan Delbende
Maurice Rossi


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.

Dates and versions

hal-03844474 , version 1 (08-11-2022)



Yonghui Xu, Ivan Delbende, Maurice Rossi. Quasi-equilibrium states for helical vortices with swirl. Journal of Fluid Mechanics, 2022, 944, pp.A24. ⟨10.1017/jfm.2022.500⟩. ⟨hal-03844474⟩
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