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Transient response of enstrophy transport to opposition control in turbulent channel flow

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Abstract

The transient response of the turbulent enstrophy transport to opposition control in the turbulent channel flow is studied with the aid of direct numerical simulation. It is found that the streamwise enstrophy and the spanwise enstrophy are suppressed by the attenuation of the stretching terms at first, while the vertical enstrophy is reduced by inhibiting the tilt of the mean shear. In the initial period of the control, the streamwise enstrophy evolves much slower than the other two components. The vertical vorticity component exhibits a rapid monotonic decrease and also plays an important role in the attenuation of the other two components.

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Abbreviations

D i :

viscous diffusion term of ith component of enstrophy

H :

half channel width

p :

static pressure

P i ,P ij :

production terms of ith component of enstrophy

Re :

Reynolds number

T i :

turbulent diffusion term of ith component of enstrophy

u :

streamwise velocity

u′ :

fluctuating velocity in streamwise direction

U m :

bulk mean velocity

υ′ :

fluctuating velocity in vertical direction

w′ :

fluctuating velocity in spanwise direction

x, x 1 :

streamwise coordinate

y, x 2 :

vertical coordinate

z, x 3 :

spanwise coordinate

ɛ i :

dissipation term of ith component of enstrophy

ω i :

ith component of vorticity vector

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Correspondence to Chun-xiao Xu  (许春晓).

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Project supported by the National Natural Science Foundation of China (Nos. 10925210, 11002081, and 11132005)

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Ge, Mw., Xu, Cx., Huang, Wx. et al. Transient response of enstrophy transport to opposition control in turbulent channel flow. Appl. Math. Mech.-Engl. Ed. 34, 127–138 (2013). https://doi.org/10.1007/s10483-013-1658-x

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  • DOI: https://doi.org/10.1007/s10483-013-1658-x

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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