Analysis of Reynolds number scaling for viscous vortex reconnection

Qionglin Ni; Fazle Hussain; Jianchun Wang; Shiyi Chen

doi:10.1063/1.4757658

Analysis of Reynolds number scaling for viscous vortex reconnection

Qionglin Ni, Fazle Hussain, Jianchun Wang, Shiyi Chen

Mechanical Engineering

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5 Scopus citations

Abstract

A theoretical analysis of viscous vortex reconnection is developed based on scale separation, and the Reynolds number, Re (= circulation/viscosity), scaling for the reconnection time Trec is derived. The scaling varies continuously as Re increases from T_rec ~Re^-T_rec ~Re. This theoretical prediction agrees well with direct numerical simulations by Garten et al. [J. Fluid Mech.426, 1 (2001)]10.1017/S0022112000002251 and Hussain and Duraisamy [Phys. Fluids23, 021701 (2011)]10.1063/1.3532039. Moreover, our analysis yields two Re's, namely, a characteristic Re Re0.75 ε[o(10³O(10³)for the T_rec Re^0.75scaling given by Hussain and Duraisamy and the critical Re Re_cO(10⁴) for the transition after which the first reconnection is completed. For >, a quiescent state follows, and then, a second reconnection may occur.

Original language	English
Article number	105102
Journal	Physics of Fluids
Volume	24
Issue number	10
DOIs	https://doi.org/10.1063/1.4757658
State	Published - Oct 3 2012

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title = "Analysis of Reynolds number scaling for viscous vortex reconnection",

abstract = "A theoretical analysis of viscous vortex reconnection is developed based on scale separation, and the Reynolds number, Re (= circulation/viscosity), scaling for the reconnection time Trec is derived. The scaling varies continuously as Re increases from Trec ~Re-Trec ~Re. This theoretical prediction agrees well with direct numerical simulations by Garten et al. [J. Fluid Mech.426, 1 (2001)]10.1017/S0022112000002251 and Hussain and Duraisamy [Phys. Fluids23, 021701 (2011)]10.1063/1.3532039. Moreover, our analysis yields two Re's, namely, a characteristic Re Re0.75 ε[o(103O(103)for the Trec Re0.75scaling given by Hussain and Duraisamy and the critical Re RecO(104) for the transition after which the first reconnection is completed. For >, a quiescent state follows, and then, a second reconnection may occur.",

author = "Qionglin Ni and Fazle Hussain and Jianchun Wang and Shiyi Chen",

note = "Funding Information: We thank Yipeng Shi and Jianjun Tao for many useful discussions. This work was supported by the National Natural Science Foundation of China (Grant No. 10921202) and the National Science and Technology Ministry under a sub-project of the “973” program (Grant No. 2009CB724101).",

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T1 - Analysis of Reynolds number scaling for viscous vortex reconnection

AU - Ni, Qionglin

AU - Hussain, Fazle

AU - Wang, Jianchun

AU - Chen, Shiyi

N1 - Funding Information: We thank Yipeng Shi and Jianjun Tao for many useful discussions. This work was supported by the National Natural Science Foundation of China (Grant No. 10921202) and the National Science and Technology Ministry under a sub-project of the “973” program (Grant No. 2009CB724101).

PY - 2012/10/3

Y1 - 2012/10/3

N2 - A theoretical analysis of viscous vortex reconnection is developed based on scale separation, and the Reynolds number, Re (= circulation/viscosity), scaling for the reconnection time Trec is derived. The scaling varies continuously as Re increases from Trec ~Re-Trec ~Re. This theoretical prediction agrees well with direct numerical simulations by Garten et al. [J. Fluid Mech.426, 1 (2001)]10.1017/S0022112000002251 and Hussain and Duraisamy [Phys. Fluids23, 021701 (2011)]10.1063/1.3532039. Moreover, our analysis yields two Re's, namely, a characteristic Re Re0.75 ε[o(103O(103)for the Trec Re0.75scaling given by Hussain and Duraisamy and the critical Re RecO(104) for the transition after which the first reconnection is completed. For >, a quiescent state follows, and then, a second reconnection may occur.

AB - A theoretical analysis of viscous vortex reconnection is developed based on scale separation, and the Reynolds number, Re (= circulation/viscosity), scaling for the reconnection time Trec is derived. The scaling varies continuously as Re increases from Trec ~Re-Trec ~Re. This theoretical prediction agrees well with direct numerical simulations by Garten et al. [J. Fluid Mech.426, 1 (2001)]10.1017/S0022112000002251 and Hussain and Duraisamy [Phys. Fluids23, 021701 (2011)]10.1063/1.3532039. Moreover, our analysis yields two Re's, namely, a characteristic Re Re0.75 ε[o(103O(103)for the Trec Re0.75scaling given by Hussain and Duraisamy and the critical Re RecO(104) for the transition after which the first reconnection is completed. For >, a quiescent state follows, and then, a second reconnection may occur.

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VL - 24

JO - Physics of Fluids

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SN - 1070-6631

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M1 - 105102

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Analysis of Reynolds number scaling for viscous vortex reconnection

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