Finite-thickness effect on speed of a counter-rotating vortex pair at high Reynolds numbers

Ummu Habibah, Hironori Nakagawa, Yasuhide Fukumoto

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 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.

Original languageEnglish
Article number031401
JournalFluid Dynamics Research
Volume50
Issue number3
DOIs
Publication statusPublished - Mar 29 2018

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high Reynolds number
counters
Vortex flow
Reynolds number
vortices
Fluids
Tolnaftate
Viscosity
viscosity
fluids
incompressible fluids
power series
conservation laws
simplification
Navier-Stokes equation
Navier Stokes equations
impulses
Conservation
kinematics
Hydrodynamics

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes

Cite this

Finite-thickness effect on speed of a counter-rotating vortex pair at high Reynolds numbers. / Habibah, Ummu; Nakagawa, Hironori; Fukumoto, Yasuhide.

In: Fluid Dynamics Research, Vol. 50, No. 3, 031401, 29.03.2018.

Research output: Contribution to journalArticle

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