Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant

M. Monuar Hossain; M. Abu Bkar Pk; M. S. Alam Sarker

doi:doi:10.11648/j.ajtas.20140304.11

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Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant

M. Monuar Hossain, M. Abu Bkar Pk, M. S. Alam Sarker

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 4)

Received: 6 June 2014 Accepted: 27 June 2014 Published: 30 June 2014

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Abstract

Following Deissler’s approach, the decay in homogeneous turbulence at times preceding to the ultimate phase for the concentration fluctuation of a dilute contaminant undergoing a first-order chemical reaction in a rotating system for the case of four-point correlation is studied. Two-, three-, and four-point correlation equations have been obtained and the correlation equations are converted to spectral form by their Fourier-transform, the terms containing quintuple correlations are neglected in comparison to the third and fourth order correlation terms. Finally, integrating the energy spectrum over all wave numbers, the energy decay law of homogeneous turbulent flow for the concentration fluctuations ahead of the ultimate phase in a rotating system for four-point correlation has been obtained and it is shown by graphically in the text.

Published in	American Journal of Theoretical and Applied Statistics (Volume 3, Issue 4)
DOI	10.11648/j.ajtas.20140304.11
Page(s)	81-89
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Chemical Reactant, Deissler’s Method, Fourier-Transformation, Navier-Stokes Equation, Turbulent Flow, Correlation Function

References

[1]	Aziz, M.A, M.A.K. Azad and M.S. Alam Sarker, “First order reactant in MHD turbulence before the final period of decay for the case of multi-point and multi-time in a rotating system in presence of dust particle,” Res. J. Math. Stat. vol. 2, pp. 56–68, 2010.
[2]	Batchelor, G.K., “The Theory of Homogeneous Turbu lence.” Cambridge University press, Cambridge, 1953. pp: 79.
[3]	Bkar Pk, M.A., M.A.K. Azad and M.S.Alam Sarker, “Decay of energy of MHD turbulence for four-point correlation.” International Journal of Engineering & Technology.1 (9):pp1-13. 2012.
[4]	Bkar Pk. M.A., M.A.K.Azad and M.S.Alam.Sarker, “First-order reactant in homogeneou turbulence prior to the ultimate phase of decay for four-point correlation in presence of dust particle,”Res.J.Appl.Sci.Eng. Technol.,5(2):585-595. 2013(a).
[5]	Bkar Pk, M.A., M.S.Alam Sarker and M.A.K. Azad, “Decay of MHD turbulence before the final period for four-point correla-tion in a rotating system.” Res. J. Appl. Sci. Eng. Technol., 6(15), 2789-2798. 2013(b).
[6]	Chandrasekhar, S., “The invariant theory of isotropic turbulence in magne-to-hydrodynamics,” Proc. Roy.Soc., London, and A204:435-449. 1951.
[7]	Corrsin, S., “On the spectrum of isotropic temperature fluctuations in isotropic turbulence.J.Apll.Phys,”.J.Apll.Phys 22:469-473.1953.
[8]	Deissler, R.G., “On the decay of homogeneous turbulence before the final period.” Phys.Fluid, 1:111-121. 1958.
[9]	Deissler, R.G., “A theory of decaying homoge-neous turbu lence.” Phys. Fluid, 3:176-187. 1960.
[10]	Islam, M.A. and M.S.A Sarker, “First order reactant in MHD turbulence before the final period of decay for the case of multi-point and multi-time.” Indian J. pure appl. Math., 32(8):1173-1184. 2001.
[11]	Kumar, P. and S.R.Patel, “First-order reactant in homogeneous turbulence before the final period of decay.” Phys .Fluids, 17: 1362-1368. 1974.
[12]	Kumar, P. and S.R.Patel, “On first-order reactant in homogeneous turbulence.”Int. J. Eng. Sci., 13:305-315. 1975.
[13]	Loeffler, A.L and R.G. Deissler, “Decay of temperature fluctuations in homogeneous turbulence before the final period.” Int. J. Heat Mass Trans., 1: 312-324. 1961.
[14]	Mondal, M.N.I., “Energy decay law of dusty fluid turbulent flow in a rotating system.” J. Eng. Applied Sci., 1:71. 2006.
[15]	Sarker, M. S. A. and N. Kishore, “Decay of MHD turbulence before the final period.” Int. J. Engng Sci., 29(11):1479-1485. 1991.
[16]	Sarker, M. S. A. and M.A. Islam, “Decay of dusty fluid MHD turbulence before the final period in a rotating system.” J. Math. & Math. Sci, 16:35. 2001.
[17]	Sultan, S., “Energy decay law of dusty fluid turbulent flow in a rotating system.” J.Eng. Applied Sci., 3:166. 2008.

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APA Style

M. Monuar Hossain, M. Abu Bkar Pk, M. S. Alam Sarker. (2014). Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant. American Journal of Theoretical and Applied Statistics, 3(4), 81-89. https://doi.org/10.11648/j.ajtas.20140304.11

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ACS Style

M. Monuar Hossain; M. Abu Bkar Pk; M. S. Alam Sarker. Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant. Am. J. Theor. Appl. Stat. 2014, 3(4), 81-89. doi: 10.11648/j.ajtas.20140304.11

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AMA Style

M. Monuar Hossain, M. Abu Bkar Pk, M. S. Alam Sarker. Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant. Am J Theor Appl Stat. 2014;3(4):81-89. doi: 10.11648/j.ajtas.20140304.11

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@article{10.11648/j.ajtas.20140304.11,
  author = {M. Monuar Hossain and M. Abu Bkar Pk and M. S. Alam Sarker},
  title = {Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {4},
  pages = {81-89},
  doi = {10.11648/j.ajtas.20140304.11},
  url = {https://doi.org/10.11648/j.ajtas.20140304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140304.11},
  abstract = {Following Deissler’s approach, the decay in homogeneous turbulence at times preceding to the ultimate phase for the concentration fluctuation of a dilute contaminant undergoing a first-order chemical reaction in a rotating system for the case of four-point correlation is studied. Two-, three-, and four-point correlation equations have been obtained and the correlation equations are converted to spectral form by their Fourier-transform, the terms containing quintuple correlations are neglected in comparison to the third and fourth order correlation terms. Finally, integrating the energy spectrum over all wave numbers, the energy decay law of homogeneous turbulent flow for the concentration fluctuations ahead of the ultimate phase in a rotating system for four-point correlation has been obtained and it is shown by graphically in the text.},
 year = {2014}
}

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TY  - JOUR
T1  - Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant
AU  - M. Monuar Hossain
AU  - M. Abu Bkar Pk
AU  - M. S. Alam Sarker
Y1  - 2014/06/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140304.11
DO  - 10.11648/j.ajtas.20140304.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 81
EP  - 89
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140304.11
AB  - Following Deissler’s approach, the decay in homogeneous turbulence at times preceding to the ultimate phase for the concentration fluctuation of a dilute contaminant undergoing a first-order chemical reaction in a rotating system for the case of four-point correlation is studied. Two-, three-, and four-point correlation equations have been obtained and the correlation equations are converted to spectral form by their Fourier-transform, the terms containing quintuple correlations are neglected in comparison to the third and fourth order correlation terms. Finally, integrating the energy spectrum over all wave numbers, the energy decay law of homogeneous turbulent flow for the concentration fluctuations ahead of the ultimate phase in a rotating system for four-point correlation has been obtained and it is shown by graphically in the text.
VL  - 3
IS  - 4
ER  -

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Author Information

M. Monuar Hossain

Department of Civil & Environmental Engineering, Uttra University, Dhaka-1230, Bangladesh
M. Abu Bkar Pk

Department of Applied Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh
M. S. Alam Sarker

Department of Applied Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh

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APA Style

M. Monuar Hossain, M. Abu Bkar Pk, M. S. Alam Sarker. (2014). Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant. American Journal of Theoretical and Applied Statistics, 3(4), 81-89. https://doi.org/10.11648/j.ajtas.20140304.11

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ACS Style

M. Monuar Hossain; M. Abu Bkar Pk; M. S. Alam Sarker. Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant. Am. J. Theor. Appl. Stat. 2014, 3(4), 81-89. doi: 10.11648/j.ajtas.20140304.11

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AMA Style

M. Monuar Hossain, M. Abu Bkar Pk, M. S. Alam Sarker. Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant. Am J Theor Appl Stat. 2014;3(4):81-89. doi: 10.11648/j.ajtas.20140304.11

Copy | Download

@article{10.11648/j.ajtas.20140304.11,
  author = {M. Monuar Hossain and M. Abu Bkar Pk and M. S. Alam Sarker},
  title = {Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {4},
  pages = {81-89},
  doi = {10.11648/j.ajtas.20140304.11},
  url = {https://doi.org/10.11648/j.ajtas.20140304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140304.11},
  abstract = {Following Deissler’s approach, the decay in homogeneous turbulence at times preceding to the ultimate phase for the concentration fluctuation of a dilute contaminant undergoing a first-order chemical reaction in a rotating system for the case of four-point correlation is studied. Two-, three-, and four-point correlation equations have been obtained and the correlation equations are converted to spectral form by their Fourier-transform, the terms containing quintuple correlations are neglected in comparison to the third and fourth order correlation terms. Finally, integrating the energy spectrum over all wave numbers, the energy decay law of homogeneous turbulent flow for the concentration fluctuations ahead of the ultimate phase in a rotating system for four-point correlation has been obtained and it is shown by graphically in the text.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Homogeneous Fluid Turbulence before the Final Period of Decay for Four-Point Correlation in a Rotating System for First-Order Reactant
AU  - M. Monuar Hossain
AU  - M. Abu Bkar Pk
AU  - M. S. Alam Sarker
Y1  - 2014/06/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140304.11
DO  - 10.11648/j.ajtas.20140304.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 81
EP  - 89
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140304.11
AB  - Following Deissler’s approach, the decay in homogeneous turbulence at times preceding to the ultimate phase for the concentration fluctuation of a dilute contaminant undergoing a first-order chemical reaction in a rotating system for the case of four-point correlation is studied. Two-, three-, and four-point correlation equations have been obtained and the correlation equations are converted to spectral form by their Fourier-transform, the terms containing quintuple correlations are neglected in comparison to the third and fourth order correlation terms. Finally, integrating the energy spectrum over all wave numbers, the energy decay law of homogeneous turbulent flow for the concentration fluctuations ahead of the ultimate phase in a rotating system for four-point correlation has been obtained and it is shown by graphically in the text.
VL  - 3
IS  - 4
ER  -

Copy | Download