Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay

Ripan Roy; M. Abu Bkar Pk

doi:doi:10.11648/j.pamj.20160502.11

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Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay

Ripan Roy, M. Abu Bkar Pk

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 2)

Received: 26 February 2016 Accepted: 8 March 2016 Published: 21 March 2016

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Abstract

Following Deissler’s approach the magnetic field fluctuation in MHD turbulence prior to the ultimatephase of decay is studied. Two and three point correlation equations have been obtained and the set of equations is made determinate by neglecting the quadruple correlations in comparison with second and third order correlations. The correlation equations are changed to spectral form by taking their Fourier transforms. The decay law for magnetic field fluctuations is obtained and discussed the problem numerically and represented the results graphically.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 2)
DOI	10.11648/j.pamj.20160502.11
Page(s)	32-38
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), 2016. Published by Science Publishing Group

Keywords

Correlation Function, Deissler’s Method, Fourier-Transformation, Matlab, Navier-Stokes Equation

References

[1]	Biskamp, D., “Magnetohydrodynamic turbulence.” Cambridge U. P., UK, pp. 75-77, 2003.
[2]	Bkar Pk, M. A. Abdul Malek, M. A. K. Azad, “Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation.” Applied and Computational Mathematics, Vol. 4, Issue 1, pp. 11-19, 2015.
[3]	Bkar Pk., M. A., M. S. A. Sarker and M. A. K. Azad, “Decay of MHD turbulence prior to the ultimate phase in presence of dust particle for four-point correlation.” International Journal of Applied Mathematics and Mechanics, Vol. 9(10), pp.34-57, 2013.
[4]	Boyd, J. P., “Chebyshev and Forier spectral method.” second edition, Dover, Mineola, NY, 2001.
[5]	Chandrasekhar, S., “The invariant theory of isotropic turbulence in magneto-hydrodynamics.” Proc. Roy. Soc. London, A 204, 435, 1951.
[6]	Corrsin, S., “The spectrum of isotropic temperature fluctuations in isotropic turbulence.” Journal of Applied Physics, Vol. 22, pp. 469-473, 1951.
[7]	Deissler, R. G., “A theory of decaying homogeneous turbulence.” Physics of Fluids, Vol. 3, pp. 176-187, 1960.
[8]	Deissler, R. G., “On the decay of homogeneous turbulence for times before the final period.” Physics of Fluids, Vol. 1, pp. 111-121, 1958.
[9]	Islam, M. A. and M. S. A. Sarker, “The first order reactant in MHD turbulence before the final period of decay for the case of multi-point and multi-time.” Indian Journal of Pure and Applied Mathematics, Vol. 32, pp. 1173-1184, 2001.
[10]	Loeffler, A. L. and R. G. Deissler, “Decay of temperature fluctuations inhomogeneous turbulence before the final period.” International Journal of Heat Mass Transfer, Vol. 1, 312-324, 1961.
[11]	Monuar Hossain, M., 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.” American Journal of Theoritical and Applied Statistics, Vol. 3, Issue 4, pp. 81-89, 2014.
[12]	Rahaman, M. L., “Decay of first order reactant in incompressible MHD turbulence before the final period for the case of multi-point and multi-time in a rotating system.” J. Mech. Cont. & Math. Sci. Vol. 4(2), pp. 509-522, 2010.
[13]	Sarker, M. S. A. and N. Kishore, “Decay of the MHD turbulence before the final period.” Intenational Journal of Engineering Science, Vol. 29(11), pp. 1479-1485, 1991.
[14]	Shebalin, J. V., “Ideal homogeneous magnetohydrodynamic turbulence in the presence of rotation and a mean magnetic field.” Journal of Plasma Physics, Vol. 72, part 4, pp. 507-524, 2006.
[15]	Shebalin, J. V., “The statistical mechanics of ideal homogeneous turbulence.” NASA TP-2002-210783, NASA JSC, Houston, TX, 2002.

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Ripan Roy, M. Abu Bkar Pk. (2016). Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay. Pure and Applied Mathematics Journal, 5(2), 32-38. https://doi.org/10.11648/j.pamj.20160502.11

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ACS Style

Ripan Roy; M. Abu Bkar Pk. Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay. Pure Appl. Math. J. 2016, 5(2), 32-38. doi: 10.11648/j.pamj.20160502.11

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AMA Style

Ripan Roy, M. Abu Bkar Pk. Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay. Pure Appl Math J. 2016;5(2):32-38. doi: 10.11648/j.pamj.20160502.11

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@article{10.11648/j.pamj.20160502.11,
  author = {Ripan Roy and M. Abu Bkar Pk},
  title = {Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {2},
  pages = {32-38},
  doi = {10.11648/j.pamj.20160502.11},
  url = {https://doi.org/10.11648/j.pamj.20160502.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160502.11},
  abstract = {Following Deissler’s approach the magnetic field fluctuation in MHD turbulence prior to the ultimatephase of decay is studied. Two and three point correlation equations have been obtained and the set of equations is made determinate by neglecting the quadruple correlations in comparison with second and third order correlations. The correlation equations are changed to spectral form by taking their Fourier transforms. The decay law for magnetic field fluctuations is obtained and discussed the problem numerically and represented the results graphically.},
 year = {2016}
}

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TY  - JOUR
T1  - Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay
AU  - Ripan Roy
AU  - M. Abu Bkar Pk
Y1  - 2016/03/21
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160502.11
DO  - 10.11648/j.pamj.20160502.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 32
EP  - 38
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160502.11
AB  - Following Deissler’s approach the magnetic field fluctuation in MHD turbulence prior to the ultimatephase of decay is studied. Two and three point correlation equations have been obtained and the set of equations is made determinate by neglecting the quadruple correlations in comparison with second and third order correlations. The correlation equations are changed to spectral form by taking their Fourier transforms. The decay law for magnetic field fluctuations is obtained and discussed the problem numerically and represented the results graphically.
VL  - 5
IS  - 2
ER  -

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Author Information

Ripan Roy

Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
M. Abu Bkar Pk

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

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APA Style

Ripan Roy, M. Abu Bkar Pk. (2016). Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay. Pure and Applied Mathematics Journal, 5(2), 32-38. https://doi.org/10.11648/j.pamj.20160502.11

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ACS Style

Ripan Roy; M. Abu Bkar Pk. Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay. Pure Appl. Math. J. 2016, 5(2), 32-38. doi: 10.11648/j.pamj.20160502.11

Copy | Download

AMA Style

Ripan Roy, M. Abu Bkar Pk. Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay. Pure Appl Math J. 2016;5(2):32-38. doi: 10.11648/j.pamj.20160502.11

Copy | Download

@article{10.11648/j.pamj.20160502.11,
  author = {Ripan Roy and M. Abu Bkar Pk},
  title = {Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {2},
  pages = {32-38},
  doi = {10.11648/j.pamj.20160502.11},
  url = {https://doi.org/10.11648/j.pamj.20160502.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160502.11},
  abstract = {Following Deissler’s approach the magnetic field fluctuation in MHD turbulence prior to the ultimatephase of decay is studied. Two and three point correlation equations have been obtained and the set of equations is made determinate by neglecting the quadruple correlations in comparison with second and third order correlations. The correlation equations are changed to spectral form by taking their Fourier transforms. The decay law for magnetic field fluctuations is obtained and discussed the problem numerically and represented the results graphically.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Numerical Representation of MHD Turbulence Prior to the Ultimate Phase of Decay
AU  - Ripan Roy
AU  - M. Abu Bkar Pk
Y1  - 2016/03/21
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160502.11
DO  - 10.11648/j.pamj.20160502.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 32
EP  - 38
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160502.11
AB  - Following Deissler’s approach the magnetic field fluctuation in MHD turbulence prior to the ultimatephase of decay is studied. Two and three point correlation equations have been obtained and the set of equations is made determinate by neglecting the quadruple correlations in comparison with second and third order correlations. The correlation equations are changed to spectral form by taking their Fourier transforms. The decay law for magnetic field fluctuations is obtained and discussed the problem numerically and represented the results graphically.
VL  - 5
IS  - 2
ER  -

Copy | Download