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

Houston Methodist

Research output: Contribution to journal › Article › peer-review

11 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(10 ³O(10 ³)for the T _rec Re ^0.75scaling given by Hussain and Duraisamy and the critical Re Re _cO(10 ⁴) 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 (US)
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

ASJC Scopus subject areas

Computational Mechanics
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Fluid Flow and Transfer Processes

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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 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(10 3O(10 3)for the T rec Re 0.75scaling given by Hussain and Duraisamy and the critical Re Re cO(10 4) 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). Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

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AU - Hussain, Fazle

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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). Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

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 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(10 3O(10 3)for the T rec Re 0.75scaling given by Hussain and Duraisamy and the critical Re Re cO(10 4) 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 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(10 3O(10 3)for the T rec Re 0.75scaling given by Hussain and Duraisamy and the critical Re Re cO(10 4) 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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Analysis of Reynolds number scaling for viscous vortex reconnection

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