Conversion of Energy Equation for Turbulent Motion and its Applications

Shams Forruque Ahmed

doi:doi:10.11648/j.acm.20140303.16

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Conversion of Energy Equation for Turbulent Motion and its Applications

Shams Forruque Ahmed

Published in Applied and Computational Mathematics (Volume 3, Issue 3)

Received: 26 June 2014 Accepted: 4 July 2014 Published: 20 July 2014

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Abstract

Turbulent energy has developed revolutionary technology in the form of a portfolio of devices for the mixing, separation and the homogenization of liquids with liquids, liquids with gasses and gasses with gasses. The mixing technology may be applied to a wide variety including chemicals, pharmaceuticals, cosmetics, foods, agricultural, water treatment with purification and hybrid fuels. The paper reports the transformation of energy equation for turbulent flow in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between two points, one point has been taken as the origin of the coordinate system. Correlation between pressure fluctuations and velocity fluctuations at the two points of flow field is applied to the turbulent energy equation. The applications of turbulent energy are discussed for the source of oceanic turbulence by means of Richardson number. A multiplication factor in terms of kinetic energy and potential energy is considered for finding the correlation between the multiplication factor and critical flux Richardson number and to signify the relative efficiency of mixing by Kelvin-Helmholtz billows and the critical flux Richardson number.

Published in	Applied and Computational Mathematics (Volume 3, Issue 3)
DOI	10.11648/j.acm.20140303.16
Page(s)	110-116
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), 2014. Published by Science Publishing Group

Keywords

Turbulent Energy, Turbulent Motion, Richardson Number, Two-Point Correlation, Correlation Tensor

References

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[2]	T. R. Osborn, “Estimates of the local rate of vertical diffusion from dissipation measurements,” Journal of Physical Oceanography, vol.10, pp.83-89, 1980.
[3]	N. S. Oakey, “Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements,” Journal of Physical Oceanography, vol.12, pp.256-271, 1982.
[4]	D. A. Luketina and J. Imberger, “Determining turbulent kinetic energy dissipation from batchelor curve fitting,” Journal of Atmospheric and Oceanic Technology, vol.18, pp.100-113, 2001.
[5]	J. N. Moum, M. C. Gregg, R. C. Lien and M. E. Carr, “Comparison of turbulence kinetic energy dissipation rate estimates from two ocean microstructure profilers,” Journal of Atmospheric and Oceanic Technology, vol.12, pp.346-366, 1995.
[6]	S. Kassinos, W. Reynolds and M. Rogers, “One-point turbulence structure tensors,” Journal of Fluid Mechanics, vol.428, pp.213-248, 2001.
[7]	J. N. Moum, “Energy-containing scales of turbulence in the ocean thermo cline,” Journal of Geophysical Research, vol.101, no.C6, pp.14095-14109, 1996b.
[8]	J. Sheng, H. Meng and R.O. Fox, “A large eddy PIV method for turbulence dissipation rate estimation,” Chemical Engineering Science, vol.55, pp.4423-4434, 2000.
[9]	J. D. Nash and J. N. Moum, “Microstructure estimates of turbulent salinity flux and the dissipation spectrum of salinity,” Journal of Physical Oceanography, vol.32, pp.2312-2333, 2002.
[10]	A. Bhattacharya, S. C. Kassinos and R.D. Moser, “Representing anisotropy of two-point second-order turbulence velocity correlations using structure tensors,” Physics of Fluids, vol.20, pp.1015021-13, 2008.
[11]	V. Carbone, L. Sorriso-Valvo and R. Marino, “On the turbulent energy cascade in anisotropic magneto hydrodynamic turbulence,” Europhysics Letters, vol.88, pp.25001-5, 2009.
[12]	J.O. Hinze, Turbulence, 2nd ed., McGraw-Hill, New York, 1975.
[13]	S. F. Ahmed and M. S. A. Sarker, “Fiber suspensions in turbulent flow with two-point correlation,” Bangladesh Journal of Scientific and Industrial Research, vol.46, no.2, pp.265-270, 2011.
[14]	M. S. A. Sarker and S. F. Ahmed, “Fibre Motion in Dusty Fluid Turbulent Flow with Two-point Correlation,” Journal of Scientific Research, vol.3, no.2, pp.283-290, 2011.
[15]	S. F. Ahmed and M. S. A. Sarker, “Motion of Fibres in Turbulent Flow in a Rotating System,” Rajshahi University Studies Part-B, Journal of Science, vol.37, pp.107-117, 2009.
[16]	S.F. Ahmed, “Derivation of Energy Equation for Turbulent Flow with Two-point Correlation,” Pure and Applied Mathematics Journal, vol.2, no.6, pp.191-194, 2013.
[17]	S. F. Ahmed, “Derivation of Turbulent Energy in Presence of Dust Particles,” American Journal of Applied Mathematics, 1(4), pp.71-77, 2013.
[18]	S. F. Ahmed, “Derivation of Turbulent Energy in a Rotating System,” Journal of Computational and Applied Research in Mechanical Engineering, vol.3, no.1, pp.75-83, 2013.
[19]	S. F. Ahmed, “Turbulent Energy for Dusty Fluid in a Rotating System,” International Journal of Applied Mathematics and Mechanics, vol.9, no.1, pp.50-61, 2012.
[20]	S. Chandrasekhar, “Hydro magnetic Turbulence.II. An Elementary Theory,” Proceedings of the Royal Society, vol.233, pp.330-350, 1955.

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APA Style

Shams Forruque Ahmed. (2014). Conversion of Energy Equation for Turbulent Motion and its Applications. Applied and Computational Mathematics, 3(3), 110-116. https://doi.org/10.11648/j.acm.20140303.16

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ACS Style

Shams Forruque Ahmed. Conversion of Energy Equation for Turbulent Motion and its Applications. Appl. Comput. Math. 2014, 3(3), 110-116. doi: 10.11648/j.acm.20140303.16

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AMA Style

Shams Forruque Ahmed. Conversion of Energy Equation for Turbulent Motion and its Applications. Appl Comput Math. 2014;3(3):110-116. doi: 10.11648/j.acm.20140303.16

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@article{10.11648/j.acm.20140303.16,
  author = {Shams Forruque Ahmed},
  title = {Conversion of Energy Equation for Turbulent Motion and its Applications},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {3},
  pages = {110-116},
  doi = {10.11648/j.acm.20140303.16},
  url = {https://doi.org/10.11648/j.acm.20140303.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140303.16},
  abstract = {Turbulent energy has developed revolutionary technology in the form of a portfolio of devices for the mixing, separation and the homogenization of liquids with liquids, liquids with gasses and gasses with gasses. The mixing technology may be applied to a wide variety including chemicals, pharmaceuticals, cosmetics, foods, agricultural, water treatment with purification and hybrid fuels. The paper reports the transformation of energy equation for turbulent flow in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between two points, one point has been taken as the origin of the coordinate system. Correlation between pressure fluctuations and velocity fluctuations at the two points of flow field is applied to the turbulent energy equation. The applications of turbulent energy are discussed for the source of oceanic turbulence by means of Richardson number. A multiplication factor in terms of kinetic energy and potential energy is considered for finding the correlation between the multiplication factor and critical flux Richardson number and to signify the relative efficiency of mixing by Kelvin-Helmholtz billows and the critical flux Richardson number.},
 year = {2014}
}

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TY  - JOUR
T1  - Conversion of Energy Equation for Turbulent Motion and its Applications
AU  - Shams Forruque Ahmed
Y1  - 2014/07/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140303.16
DO  - 10.11648/j.acm.20140303.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 110
EP  - 116
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140303.16
AB  - Turbulent energy has developed revolutionary technology in the form of a portfolio of devices for the mixing, separation and the homogenization of liquids with liquids, liquids with gasses and gasses with gasses. The mixing technology may be applied to a wide variety including chemicals, pharmaceuticals, cosmetics, foods, agricultural, water treatment with purification and hybrid fuels. The paper reports the transformation of energy equation for turbulent flow in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between two points, one point has been taken as the origin of the coordinate system. Correlation between pressure fluctuations and velocity fluctuations at the two points of flow field is applied to the turbulent energy equation. The applications of turbulent energy are discussed for the source of oceanic turbulence by means of Richardson number. A multiplication factor in terms of kinetic energy and potential energy is considered for finding the correlation between the multiplication factor and critical flux Richardson number and to signify the relative efficiency of mixing by Kelvin-Helmholtz billows and the critical flux Richardson number.
VL  - 3
IS  - 3
ER  -

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Author Information

Shams Forruque Ahmed

Senior Lecturer in Mathematics, Prime University, Dhaka, Bangladesh

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APA Style

Shams Forruque Ahmed. (2014). Conversion of Energy Equation for Turbulent Motion and its Applications. Applied and Computational Mathematics, 3(3), 110-116. https://doi.org/10.11648/j.acm.20140303.16

Copy | Download

ACS Style

Shams Forruque Ahmed. Conversion of Energy Equation for Turbulent Motion and its Applications. Appl. Comput. Math. 2014, 3(3), 110-116. doi: 10.11648/j.acm.20140303.16

Copy | Download

AMA Style

Shams Forruque Ahmed. Conversion of Energy Equation for Turbulent Motion and its Applications. Appl Comput Math. 2014;3(3):110-116. doi: 10.11648/j.acm.20140303.16

Copy | Download

@article{10.11648/j.acm.20140303.16,
  author = {Shams Forruque Ahmed},
  title = {Conversion of Energy Equation for Turbulent Motion and its Applications},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {3},
  pages = {110-116},
  doi = {10.11648/j.acm.20140303.16},
  url = {https://doi.org/10.11648/j.acm.20140303.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140303.16},
  abstract = {Turbulent energy has developed revolutionary technology in the form of a portfolio of devices for the mixing, separation and the homogenization of liquids with liquids, liquids with gasses and gasses with gasses. The mixing technology may be applied to a wide variety including chemicals, pharmaceuticals, cosmetics, foods, agricultural, water treatment with purification and hybrid fuels. The paper reports the transformation of energy equation for turbulent flow in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between two points, one point has been taken as the origin of the coordinate system. Correlation between pressure fluctuations and velocity fluctuations at the two points of flow field is applied to the turbulent energy equation. The applications of turbulent energy are discussed for the source of oceanic turbulence by means of Richardson number. A multiplication factor in terms of kinetic energy and potential energy is considered for finding the correlation between the multiplication factor and critical flux Richardson number and to signify the relative efficiency of mixing by Kelvin-Helmholtz billows and the critical flux Richardson number.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Conversion of Energy Equation for Turbulent Motion and its Applications
AU  - Shams Forruque Ahmed
Y1  - 2014/07/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140303.16
DO  - 10.11648/j.acm.20140303.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 110
EP  - 116
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140303.16
AB  - Turbulent energy has developed revolutionary technology in the form of a portfolio of devices for the mixing, separation and the homogenization of liquids with liquids, liquids with gasses and gasses with gasses. The mixing technology may be applied to a wide variety including chemicals, pharmaceuticals, cosmetics, foods, agricultural, water treatment with purification and hybrid fuels. The paper reports the transformation of energy equation for turbulent flow in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between two points, one point has been taken as the origin of the coordinate system. Correlation between pressure fluctuations and velocity fluctuations at the two points of flow field is applied to the turbulent energy equation. The applications of turbulent energy are discussed for the source of oceanic turbulence by means of Richardson number. A multiplication factor in terms of kinetic energy and potential energy is considered for finding the correlation between the multiplication factor and critical flux Richardson number and to signify the relative efficiency of mixing by Kelvin-Helmholtz billows and the critical flux Richardson number.
VL  - 3
IS  - 3
ER  -

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