On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation

M. Z. Rahman; A.B.M. Shamim. Ul Hasan

doi:doi:10.11648/j.pamj.20130203.11

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On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation

M. Z. Rahman, A.B.M. Shamim. Ul Hasan

Received: 24 April 2013 Accepted: Published: 30 May 2013

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Abstract

In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the applied wind stress. The equation involves the gradient of the Coriolis parameter and has particular relevance to the equatorial region, such as the North Indian Ocean. Some interesting physical properties of the solutions are considered. In this paper we find some more complicated but similar exact and explicit solutions. Some properties for these solutions are derived which are in some sense complementary to the kind of properties of the simpler solutions considered in advance.

DOI	10.11648/j.pamj.20130203.11
Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 3, June 2013)
Page(s)	110-118
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

Rossby Equation, Velocity, Coriolis Parameter, Gradient

References

[1]	Anderson, D.L.T., and Rowlands, P.B. 1979 ‘The Somali current response to the S. W. Monsoon: The relative importance of local and remote forcing’, J. Mar. Res. 34, 395-417.
[2]	Bryan, k. 1963 ‘A numerical investigation of a non-linear model of wind-driven ocean’, J. Atmos. Sci., 20, 594-606.
[3]	Davies, A. M. 1991 International Journal for Numerical Methods in fluids, 12, 101Gill, A.E 1982 Atmosphere Ocean Dynamics. Academic Press (U. S. A).
[4]	Gill, A.E. 1982 Atmosphere-Ocean Dynamics, Academic Press, New York.
[5]	Islam, J.N. and Rahman, M.Z. 1998 "On the Dynamic Response of an Ocean to wind stress in an Equatorial Region: Exact Solutions of the Rossby Equation" national conference on applicable mathematics-2001, India.
[6]	James, I. D. 1990 Modelling Marine Systems, 2, 345.
[7]	Lighthill, M.J. 1969a ‘Unsteady wind-driven ocean currents’, Quart. J. Met. Soc. 95, 675-688.
[8]	Lighthill, M.J. 1969b ‘Dynamic response of the Indian Ocean to the onset of Southwest Monsoon’: Philos. Trans. R. Soc. London Ser. A 265, 45-92.
[9]	Richtmyer, R.D. 1978 Principles of Advanced Mathematical Physics, Vol. 1 Springer-Verlag, New York, Heidelberg and Berlin.
[10]	Veronis, G. 1966 ‘Wind-driven Ocean circulation – Part-2. Numerical solution of the non-linear problem’. Deep-Sea Res. 13, 31-55.

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APA Style

M. Z. Rahman, A.B.M. Shamim. Ul Hasan. (2013). On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation. Pure and Applied Mathematics Journal, 2(3), 110-118. https://doi.org/10.11648/j.pamj.20130203.11

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ACS Style

M. Z. Rahman; A.B.M. Shamim. Ul Hasan. On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation. Pure Appl. Math. J. 2013, 2(3), 110-118. doi: 10.11648/j.pamj.20130203.11

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AMA Style

M. Z. Rahman, A.B.M. Shamim. Ul Hasan. On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation. Pure Appl Math J. 2013;2(3):110-118. doi: 10.11648/j.pamj.20130203.11

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@article{10.11648/j.pamj.20130203.11,
  author = {M. Z. Rahman and A.B.M. Shamim. Ul Hasan},
  title = {On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {3},
  pages = {110-118},
  doi = {10.11648/j.pamj.20130203.11},
  url = {https://doi.org/10.11648/j.pamj.20130203.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130203.11},
  abstract = {In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the applied wind stress. The equation involves the gradient of the Coriolis parameter and has particular relevance to the equatorial region, such as the North Indian Ocean. Some interesting physical properties of the solutions are considered. In this paper we find some more complicated but similar exact and explicit solutions. Some properties for these solutions are derived which are in some sense complementary to the kind of properties of the simpler solutions considered in advance.},
 year = {2013}
}

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TY  - JOUR
T1  - On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation
AU  - M. Z. Rahman
AU  - A.B.M. Shamim. Ul Hasan
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PY  - 2013
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DO  - 10.11648/j.pamj.20130203.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.pamj.20130203.11
AB  - In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the applied wind stress. The equation involves the gradient of the Coriolis parameter and has particular relevance to the equatorial region, such as the North Indian Ocean. Some interesting physical properties of the solutions are considered. In this paper we find some more complicated but similar exact and explicit solutions. Some properties for these solutions are derived which are in some sense complementary to the kind of properties of the simpler solutions considered in advance.
VL  - 2
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Author Information

M. Z. Rahman

Department of Applied Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh
A.B.M. Shamim. Ul Hasan

Department of Applied Mathematics, University of Rajshahi, Rajshahi-6206, Bangladesh

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APA Style

M. Z. Rahman, A.B.M. Shamim. Ul Hasan. (2013). On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation. Pure and Applied Mathematics Journal, 2(3), 110-118. https://doi.org/10.11648/j.pamj.20130203.11

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ACS Style

M. Z. Rahman; A.B.M. Shamim. Ul Hasan. On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation. Pure Appl. Math. J. 2013, 2(3), 110-118. doi: 10.11648/j.pamj.20130203.11

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AMA Style

M. Z. Rahman, A.B.M. Shamim. Ul Hasan. On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation. Pure Appl Math J. 2013;2(3):110-118. doi: 10.11648/j.pamj.20130203.11

Copy | Download

@article{10.11648/j.pamj.20130203.11,
  author = {M. Z. Rahman and A.B.M. Shamim. Ul Hasan},
  title = {On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {3},
  pages = {110-118},
  doi = {10.11648/j.pamj.20130203.11},
  url = {https://doi.org/10.11648/j.pamj.20130203.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130203.11},
  abstract = {In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the applied wind stress. The equation involves the gradient of the Coriolis parameter and has particular relevance to the equatorial region, such as the North Indian Ocean. Some interesting physical properties of the solutions are considered. In this paper we find some more complicated but similar exact and explicit solutions. Some properties for these solutions are derived which are in some sense complementary to the kind of properties of the simpler solutions considered in advance.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation
AU  - M. Z. Rahman
AU  - A.B.M. Shamim. Ul Hasan
Y1  - 2013/05/30
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130203.11
DO  - 10.11648/j.pamj.20130203.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 110
EP  - 118
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130203.11
AB  - In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the applied wind stress. The equation involves the gradient of the Coriolis parameter and has particular relevance to the equatorial region, such as the North Indian Ocean. Some interesting physical properties of the solutions are considered. In this paper we find some more complicated but similar exact and explicit solutions. Some properties for these solutions are derived which are in some sense complementary to the kind of properties of the simpler solutions considered in advance.
VL  - 2
IS  - 3
ER  -

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