Finite-thickness effect on speed of a counter-rotating vortex pair at high Reynolds numbers. (29th March 2018)

• Record Type: Journal Article
• Authors: Habibah, Ummu; Nakagawa, Hironori; Fukumoto, Yasuhide
• Is Part Of: Fluid dynamics research. Volume 50:Number 3(2018:Jun.)
• Publication Date: 2018-03-29
• Subjects: counter-rotating vortex pair -- traveling speed -- finite-thickness effect -- matched asymptotic expansions -- viscous lateral motion; Fluid dynamics -- Periodicals; 620.106
• DOI: 10.1088/1873-7005/aaa5c8
• Languages: English
• ISSNs: 0169-5983

Abstract

Abstract: We establish a general formula for the translational speed of a counter-rotating vortex pair, valid for thick cores, moving in an incompressible fluid with and without viscosity. We extend to higher order the method of matched asymptotic expansions developed by Ting and Tung (1965 Phys. Fluids 8 1039–51). The solution of the Euler or the Navier–Stokes equations is constructed in the form of a power series in a small parameter, the ratio of the core radius to the distance between the core centers. For a viscous vortex pair, the small parameter should be ν / Γ where ν is the kinematic viscosity of the fluid and Γ is the circulation of each vortex. A correction due to the effect of finite thickness of the vortices to the traveling speed makes its appearance at fifth order. A drastic simplification is achieved of expressing it solely in terms of the strength of the second-order quadrupole field associated with the elliptical deformation of the core. For a viscous vortex pair, we exploit the conservation law for the hydrodynamic impulse to derive the growth of the distance between the vortices, which is cubic in time.