Baroclinic Kelvin Waves in a Rotating Circular Basin

R. N. Ibragimov

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 2, page 38-51
  • ISSN: 0973-5348

Abstract

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A linear, uniformly stratified ocean model is used to investigate propagation of baroclinic Kelvin waves in a cylindrical basin. It is found that smaller wave amplitudes are inherent to higher mode individual terms of the obtained solutions that are also evanescent away of a costal line toward the center of the circular basin. It is also shown that the individual terms if the obtained solutions can be visualized as spinning patterns in rotating stratified fluid confined in a circular basin. Moreover, the fluid patterns look rotating in an anticlockwise sense looking above the North Pole and that spinning is more intensive for smaller mode numbers. Finally, we observe the existence of the oceanic region where the pressure increases relatively rapidly with the depth.

How to cite

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Ibragimov, R. N.. "Baroclinic Kelvin Waves in a Rotating Circular Basin." Mathematical Modelling of Natural Phenomena 7.2 (2012): 38-51. <http://eudml.org/doc/222421>.

@article{Ibragimov2012,
abstract = {A linear, uniformly stratified ocean model is used to investigate propagation of baroclinic Kelvin waves in a cylindrical basin. It is found that smaller wave amplitudes are inherent to higher mode individual terms of the obtained solutions that are also evanescent away of a costal line toward the center of the circular basin. It is also shown that the individual terms if the obtained solutions can be visualized as spinning patterns in rotating stratified fluid confined in a circular basin. Moreover, the fluid patterns look rotating in an anticlockwise sense looking above the North Pole and that spinning is more intensive for smaller mode numbers. Finally, we observe the existence of the oceanic region where the pressure increases relatively rapidly with the depth.},
author = {Ibragimov, R. N.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {internal gravity waves; group analysis of differential equations; Earth's rotation; Coriolis forces; Boussinesq approximation},
language = {eng},
month = {2},
number = {2},
pages = {38-51},
publisher = {EDP Sciences},
title = {Baroclinic Kelvin Waves in a Rotating Circular Basin},
url = {http://eudml.org/doc/222421},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Ibragimov, R. N.
TI - Baroclinic Kelvin Waves in a Rotating Circular Basin
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/2//
PB - EDP Sciences
VL - 7
IS - 2
SP - 38
EP - 51
AB - A linear, uniformly stratified ocean model is used to investigate propagation of baroclinic Kelvin waves in a cylindrical basin. It is found that smaller wave amplitudes are inherent to higher mode individual terms of the obtained solutions that are also evanescent away of a costal line toward the center of the circular basin. It is also shown that the individual terms if the obtained solutions can be visualized as spinning patterns in rotating stratified fluid confined in a circular basin. Moreover, the fluid patterns look rotating in an anticlockwise sense looking above the North Pole and that spinning is more intensive for smaller mode numbers. Finally, we observe the existence of the oceanic region where the pressure increases relatively rapidly with the depth.
LA - eng
KW - internal gravity waves; group analysis of differential equations; Earth's rotation; Coriolis forces; Boussinesq approximation
UR - http://eudml.org/doc/222421
ER -

References

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  1. S. Balasuriya. Vanishing viscosity in the barotropic β–plane. J. Math.Anal. Appl., (1997), 214, 128-150.  Zbl0906.35072
  2. E. Dewan, R. Picard, R. O’Neil, H. Gardiner, J. Gibson. MSX satellite observations of thunderstorm-generated gravity waves in mid-wave infrared images of the upper stratosphere. Geophys. Res. Lett., (1998), 25, 939-942.  
  3. A. Gill. Atmosphere-Ocean Dynamics. New York, etc., Academic Press, 1983.  
  4. G. Haltiner, R. Williams. Numerical prediction and dynamic meteorology, 1980.  
  5. P. Hsieh. Application of modflow for oil reservoir simulation during the Deepwater Horizon crisis. Ground Water, (2011), 49 (3), 319-323.  
  6. J. Lions, R. Teman, S. Wang. On the equations of the large-scale ocean. Nonlinearity, (1992), 5, 1007-1053.  Zbl0766.35039
  7. J. Lions, R. Teman, S. Wang. New formulations of the primitive equations of atmosphere and applications. Nonlinearity, (1992), 5, 237-288.  Zbl0746.76019
  8. J. McCreary. Easern tropical ocean response to changing wind systems with applications to El Niño. J. Phys, Oceanogr., (1976), 6, 632-645.  
  9. J. McCreary. A linear stratified ocean model of the equatorial undercurrent. Phil. Trans. Roy. Soc. London., (1981), 302, 385-413.  
  10. J. McCreary. E quatorial beams. J. Mar. Res., (1984), 42, 395-430.  
  11. P. Müller, G. Holloway, F. Henyey, N. Pomphrey. Nonlinear interactions among internal gravity waves. Rev. Geophys., (1986), 24, 3, 493-536.  
  12. D. Nethery, D. Shankar. Vertical propagation of baroclinic Kelvin waves along the west coast of India. J. Earth. Syst. Sci., (2007), 116 (4), 331-339.  
  13. R. Romea, J. Allen. On vertically propagating coastal Kelvin waves at low latitudes. J. Phys. Oceanogr., (1983), 13 (1), 241-1, 254.  
  14. D. Shindell, G. Schmidt. Southern Hemisphere climate response to ozone changes and greenhouse gas increases. Res. Lett., (2004), 31, L18209.  
  15. C. Staquet, J. Sommeria. Internal Gravity Waves : From instabilities to turbulence. Annu. Rev. Fluid Mech., (2002), 34, 559-593.  Zbl1047.76014
  16. C. Summerhayes, S. Thorpe. Oceanography, An Illustrative Guide, New York : John Willey & Sons, (1996).  
  17. R. Szoeke, R. Samelson. The duality between the Boussinesq and non-Boussinesq hydrostatic equations of motion. J. Phys. Oceanogr., (2002), 32, 2194-2203.  
  18. A. Timmermann, M. Latif, A. Grotzner, R. Voss, R., Modes of climate variability as simulated by a copled general circulation model. Part I : ENSO-like climate variability and its low-frequency modulation. Climate Dynamics., (1999), 15 (8), 605-618.  
  19. G. Watson. A Treatise on the Theory of Bessel Functions, Second edition, Cambridge University Press, (1996)(ISBN-13 : 9780521483919 — ISBN-10 : 0521483913) . 

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