Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation

Shams Forruque Ahmed

doi:doi:10.11648/j.pamj.20130206.15

| Peer-Reviewed

Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation

Shams Forruque Ahmed

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 6)

Received: 8 December 2013 Accepted: Published: 30 January 2014

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The energy equation for turbulent flow has been derived in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. An independent variable has been introduced in order to differentiate between the effects of distance and location. 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.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 6)
DOI	10.11648/j.pamj.20130206.15
Page(s)	197-200
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

Energy Equation, Turbulent Flow, Two-Point Correlation, Correlation Tensor

References

[1]	C.T. Crowe, T.R. Troutt and J.N. Chung, "Numerical models for two-phase turbulent flows", Annual Review of Fluid Mechanics, vol. 28, pp.11-43, 1996.
[2]	N.S. Oakey, "Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements", J. Phys. Oceanogr., Vol. 12, pp. 256-271, 1982.
[3]	M.B. Saito and M.J.S. de Lemos, "A macroscopic two-energy equation model for turbulent flow and heat transfer in highly porous media", vol. 35, pp. 2424-2433, 2010.
[4]	R.V. Ozmidov, "On the turbulent exchange in a stably stratified ocean, Atmos", Ocean Phys., vol. 8, pp. 853-860, 1965.
[5]	D.K. Lilly, D.E. Wacoand and S.I. Adelfang, "Stratospheric mixing estimated from high-altitude turbulence measurements", J. Appl. Meteor., vol. 131, pp. 488-493, 1974.
[6]	J.D. Nash and J. N. Moum, "Microstructure Estimates of Turbulent Salinity Flux and the Dissipation Spectrum of Salinity", J. Phys. Oceanogr., vol. 32, pp. 2312-2333, 2002.
[7]	R.B. Williams and C.H. Gibson, "Direct measurements of turbulence in the pacific equatorial undercurrent", J. Phys. Oceanogr., vol. 4, pp. 104-108, 1974.
[8]	A.E. Gargett, "An investigation of the occurrence of oceanic turbulence with respect to fine structure", J. Phys. Oceanogr., vol. 6, pp. 139-156, 1976.
[9]	T.R. Osborn, "Estimates of the Local Rate of Vertical Diffusion from Dissipation Measurements", J. Phys. Oceanogr., vol. 10, pp. 83-89, 1980.
[10]	J. Weinstock, "Vertical turbulent diffusion in a stably stratified fluid", J. Atmos. Sci., vol. 35, pp. 1022-1027, 1978.
[11]	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", J. Atmos. Oceanic Technol., vol. 12, pp. 346-366, 1995.
[12]	T.M. Dillon and D.R. Caldwell, "The Batchelor Spectrum and Dissipation in the Upper Ocean", J. Geophys. Res., vol. 85, no. C4, pp. 1910-1916, 1980.
[13]	D.A. Luketina and J. Imberger, "Determining turbulent kinetic energy dissipation from batchelor curve fitting", J. Atmos. Oceanic Technol., vol. 18, pp. 100-113, 2001.
[14]	J.N. Moum, Energy-containing scales of turbulence in the ocean thermo cline. J. Geophys. Res., vol. 101, no. C6, pp.14095-14109, 1996b.
[15]	M.S.A. Sarker and S.F. Ahmed, "Motion of Fibers in Turbulent Flow in a Rotating System", Rajshahi University Studies Part-B, Journal of Science, vol. 37, pp. 107-117, 2009.
[16]	T.R. Osborn, Measurements of energy dissipation adjacent to an island, J.Geophys. Res., vol. 83, pp. 2939-2957, 1978.
[17]	J. O. Hinze, Turbulence, McGraw-Hill Book Co., New York, 1959.
[18]	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.
[19]	M.S.A. Sarker and S.F. Ahmed, "Fiber motion in dusty fluid turbulent flow with two-point correlation", Journal of Scientific Research, vol. 3, no. 2, pp. 283-290, 2011.

Cite This Article

Plain Text BibTeX RIS

APA Style

Shams Forruque Ahmed. (2014). Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation. Pure and Applied Mathematics Journal, 2(6), 197-200. https://doi.org/10.11648/j.pamj.20130206.15

Copy | Download

ACS Style

Shams Forruque Ahmed. Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation. Pure Appl. Math. J. 2014, 2(6), 197-200. doi: 10.11648/j.pamj.20130206.15

Copy | Download

AMA Style

Shams Forruque Ahmed. Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation. Pure Appl Math J. 2014;2(6):197-200. doi: 10.11648/j.pamj.20130206.15

Copy | Download

@article{10.11648/j.pamj.20130206.15,
  author = {Shams Forruque Ahmed},
  title = {Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {6},
  pages = {197-200},
  doi = {10.11648/j.pamj.20130206.15},
  url = {https://doi.org/10.11648/j.pamj.20130206.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130206.15},
  abstract = {The energy equation for turbulent flow has been derived in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. An independent variable has been introduced in order to differentiate between the effects of distance and location. 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.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation
AU  - Shams Forruque Ahmed
Y1  - 2014/01/30
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20130206.15
DO  - 10.11648/j.pamj.20130206.15
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 197
EP  - 200
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130206.15
AB  - The energy equation for turbulent flow has been derived in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. An independent variable has been introduced in order to differentiate between the effects of distance and location. 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.
VL  - 2
IS  - 6
ER  -

Copy | Download

Author Information

Shams Forruque Ahmed

Senior Lecturer in Mathematics, Prime University, Dhaka, Bangladesh

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Shams Forruque Ahmed. (2014). Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation. Pure and Applied Mathematics Journal, 2(6), 197-200. https://doi.org/10.11648/j.pamj.20130206.15

Copy | Download

ACS Style

Shams Forruque Ahmed. Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation. Pure Appl. Math. J. 2014, 2(6), 197-200. doi: 10.11648/j.pamj.20130206.15

Copy | Download

AMA Style

Shams Forruque Ahmed. Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation. Pure Appl Math J. 2014;2(6):197-200. doi: 10.11648/j.pamj.20130206.15

Copy | Download

@article{10.11648/j.pamj.20130206.15,
  author = {Shams Forruque Ahmed},
  title = {Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {6},
  pages = {197-200},
  doi = {10.11648/j.pamj.20130206.15},
  url = {https://doi.org/10.11648/j.pamj.20130206.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130206.15},
  abstract = {The energy equation for turbulent flow has been derived in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. An independent variable has been introduced in order to differentiate between the effects of distance and location. 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.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Derivation of Energy Equation for Turbulent Flow with Two-Point Correlation
AU  - Shams Forruque Ahmed
Y1  - 2014/01/30
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20130206.15
DO  - 10.11648/j.pamj.20130206.15
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 197
EP  - 200
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130206.15
AB  - The energy equation for turbulent flow has been derived in terms of correlation tensors of second order, where the correlation tensors are the functions of space coordinates, distance between two points and time. An independent variable has been introduced in order to differentiate between the effects of distance and location. 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.
VL  - 2
IS  - 6
ER  -

Copy | Download