Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity

Mohammed Anwar Batal; Sawsan Othman

doi:doi:10.11648/j.ajmse.20170206.16

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Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity

Mohammed Anwar Batal, Sawsan Othman

Published in American Journal of Management Science and Engineering (Volume 2, Issue 6)

Received: 30 March 2017 Accepted: 11 May 2017 Published: 30 January 2018

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Abstract

Using Rossby wave equations, the dispersion equation is developed. The wave normal diagram for Rossby waves on a beta plane is a circle in wave number (k, l) space whose center is displaced along the negative X axis, and whose radius is less than this displacement, which means that phase propagation is entirely westward. The phase velocity diagram is a circle whose center is displaced along the negative X axis, the group velocity diagram is an ellipse whose center is displaced westward and whose major and minor axes give the maximum all the directions group speeds as function of the frequency and parameter Q.

Published in	American Journal of Management Science and Engineering (Volume 2, Issue 6)
DOI	10.11648/j.ajmse.20170206.16
Page(s)	199-204
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), 2018. Published by Science Publishing Group

Keywords

Rossby Waves, Planetary Waves, Phase Velocity, Group Velocity, Barotropic Fluid, Baroclinic Fluid

References

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[2]	VALLIS G. K., 2006- Atmospheric Oceanic Fluid Dynamics, Fundamentals and Large-scale Circulation, p. 745. (Cambridge University Press: Cambridge).
[3]	PEDLOSKY J., 1987- Geophysical Fluid Dynamics, p. 710, (Springer-Verlag: New York).
[4]	DIAMOND P. H, GURCAN D. D, HAHN, T. S, MIKI K and GARBET X., Momentum theorems and the structure of atmospheric jets and zonal flows in plasmas. Plasma Phys. Control. Fusion 2008, 50, 124018. doi:10.1088/0741-3335/50/12/124018.
[5]	KIDSTON J. and VALLIS G. K., 2012- The relationship between the speed and the latitude of an eddy-driven jet in a stirred barotropic model. J. Atmos. Sci, 69, 3251–3263.
[6]	BHAGAVATHIAMMAL G., 2012-Studies on mean winds and planetary waves in the middle atmosphere. Equatorial geophysical research laboratory, India, 8-11.
[7]	DAVIS R., 2014-Wave Dynamics of the Middle Atmosphere. University of Bath, 26-29.
[8]	RHINES P., 2009-Rossby waves. J. Atmos. Sci, 1-3.
[9]	RHINES P., 2003- Rossby waves. In Encyclopedia of Atmospheric Sciences. Academic Press: Oxford, 22-30.
[10]	ANDREWS D., 2010-An Introduction to Atmospheric Physics. Cambridge University Press, 2nd ed, New York, 249.
[11]	MCKENZIE, J., 2014- The group velocity and radiation pattern of Rossby waves. Geophysical and Astrophysical Fluid Dynamics. 1-5.
[12]	DIAMOND P. H, GURCAN D. D, HAHN T. S, MIKI K., and GARBET X., 2008- Momentum theorems and the structure of atmospheric jets and zonal flows in plasmas. Plasma Phys, Control. Fusion, 50,124018, doi:10.1088/0741-3335/50/12/124018.

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APA Style

Mohammed Anwar Batal, Sawsan Othman. (2018). Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity. American Journal of Management Science and Engineering, 2(6), 199-204. https://doi.org/10.11648/j.ajmse.20170206.16

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ACS Style

Mohammed Anwar Batal; Sawsan Othman. Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity. Am. J. Manag. Sci. Eng. 2018, 2(6), 199-204. doi: 10.11648/j.ajmse.20170206.16

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AMA Style

Mohammed Anwar Batal, Sawsan Othman. Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity. Am J Manag Sci Eng. 2018;2(6):199-204. doi: 10.11648/j.ajmse.20170206.16

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@article{10.11648/j.ajmse.20170206.16,
  author = {Mohammed Anwar Batal and Sawsan Othman},
  title = {Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity},
  journal = {American Journal of Management Science and Engineering},
  volume = {2},
  number = {6},
  pages = {199-204},
  doi = {10.11648/j.ajmse.20170206.16},
  url = {https://doi.org/10.11648/j.ajmse.20170206.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmse.20170206.16},
  abstract = {Using Rossby wave equations, the dispersion equation is developed. The wave normal diagram for Rossby waves on a beta plane is a circle in wave number (k, l) space whose center is displaced along the negative X axis, and whose radius is less than this displacement, which means that phase propagation is entirely westward. The phase velocity diagram is a circle whose center is displaced along the negative X axis, the group velocity diagram is an ellipse whose center is displaced westward and whose major and minor axes give the maximum all the directions group speeds as function of the frequency and parameter Q.},
 year = {2018}
}

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TY  - JOUR
T1  - Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity
AU  - Mohammed Anwar Batal
AU  - Sawsan Othman
Y1  - 2018/01/30
PY  - 2018
N1  - https://doi.org/10.11648/j.ajmse.20170206.16
DO  - 10.11648/j.ajmse.20170206.16
T2  - American Journal of Management Science and Engineering
JF  - American Journal of Management Science and Engineering
JO  - American Journal of Management Science and Engineering
SP  - 199
EP  - 204
PB  - Science Publishing Group
SN  - 2575-1379
UR  - https://doi.org/10.11648/j.ajmse.20170206.16
AB  - Using Rossby wave equations, the dispersion equation is developed. The wave normal diagram for Rossby waves on a beta plane is a circle in wave number (k, l) space whose center is displaced along the negative X axis, and whose radius is less than this displacement, which means that phase propagation is entirely westward. The phase velocity diagram is a circle whose center is displaced along the negative X axis, the group velocity diagram is an ellipse whose center is displaced westward and whose major and minor axes give the maximum all the directions group speeds as function of the frequency and parameter Q.
VL  - 2
IS  - 6
ER  -

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Author Information

Mohammed Anwar Batal

Department of Physic, Aleppo University, Aleppo City, Syria
Sawsan Othman

Department of Physic, Aleppo University, Aleppo City, Syria

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APA Style

Mohammed Anwar Batal, Sawsan Othman. (2018). Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity. American Journal of Management Science and Engineering, 2(6), 199-204. https://doi.org/10.11648/j.ajmse.20170206.16

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ACS Style

Mohammed Anwar Batal; Sawsan Othman. Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity. Am. J. Manag. Sci. Eng. 2018, 2(6), 199-204. doi: 10.11648/j.ajmse.20170206.16

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AMA Style

Mohammed Anwar Batal, Sawsan Othman. Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity. Am J Manag Sci Eng. 2018;2(6):199-204. doi: 10.11648/j.ajmse.20170206.16

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@article{10.11648/j.ajmse.20170206.16,
  author = {Mohammed Anwar Batal and Sawsan Othman},
  title = {Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity},
  journal = {American Journal of Management Science and Engineering},
  volume = {2},
  number = {6},
  pages = {199-204},
  doi = {10.11648/j.ajmse.20170206.16},
  url = {https://doi.org/10.11648/j.ajmse.20170206.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmse.20170206.16},
  abstract = {Using Rossby wave equations, the dispersion equation is developed. The wave normal diagram for Rossby waves on a beta plane is a circle in wave number (k, l) space whose center is displaced along the negative X axis, and whose radius is less than this displacement, which means that phase propagation is entirely westward. The phase velocity diagram is a circle whose center is displaced along the negative X axis, the group velocity diagram is an ellipse whose center is displaced westward and whose major and minor axes give the maximum all the directions group speeds as function of the frequency and parameter Q.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Study of Propagation Properties of Rossby Waves in the Atmosphere and Relationship Between the Phase Velocity and the Group Velocity
AU  - Mohammed Anwar Batal
AU  - Sawsan Othman
Y1  - 2018/01/30
PY  - 2018
N1  - https://doi.org/10.11648/j.ajmse.20170206.16
DO  - 10.11648/j.ajmse.20170206.16
T2  - American Journal of Management Science and Engineering
JF  - American Journal of Management Science and Engineering
JO  - American Journal of Management Science and Engineering
SP  - 199
EP  - 204
PB  - Science Publishing Group
SN  - 2575-1379
UR  - https://doi.org/10.11648/j.ajmse.20170206.16
AB  - Using Rossby wave equations, the dispersion equation is developed. The wave normal diagram for Rossby waves on a beta plane is a circle in wave number (k, l) space whose center is displaced along the negative X axis, and whose radius is less than this displacement, which means that phase propagation is entirely westward. The phase velocity diagram is a circle whose center is displaced along the negative X axis, the group velocity diagram is an ellipse whose center is displaced westward and whose major and minor axes give the maximum all the directions group speeds as function of the frequency and parameter Q.
VL  - 2
IS  - 6
ER  -

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