Start Submission Become a Reviewer

Reading: Normal modes of an incompressible and stratified fluid model including the vertical and hori...

Download

A- A+
Alt. Display

Original Research Papers

Normal modes of an incompressible and stratified fluid model including the vertical and horizontal components of coriolis force

Authors:

Akira Kasahara ,

National Center for Atmospheric Research, Boulder, Colorado, US
X close

John M. Gary

National Center for Atmospheric Research, Boulder, Colorado, US
X close

Abstract

Numerical solutions of the normal modes of a linearized Boussinesq fluid model are studied with respect to the variable static stability in height z, the Brunt-Väisälä frequency N(z). The model includes both the vertical and horizontal components of Coriolis force. Our aim is to explore the characteristics of the little-known class of normal modes, referred to as the ‘boundary-induced inertial (BII)’ modes, in addition to the traditional inertio-gravity (IG) modes. Two kinds of finite-difference schemes are used to set up the eigenvalue-eigenvector matrix problem for crosscheck.

Numerical results of the characteristics of IG and BII modes are presented for the case of an exponential form of N(z), together with the cases of constant N, whose exact solutions are used to check the performance of the numerical models. Because the frequencies of BII modes are close to the inertial frequency, which is a singular point of the model, the eigenfunctions of BII modes become highly oscillatory in z for a large value of N. It is shown that, under a realistic profile of N(z) in the oceans, the BII modes can appear complementary to the IG modes throughout the domain, suggesting that the joint consideration of both the IG and BII modes is necessary to understand the near-inertial oscillations in the seas.

How to Cite: Kasahara, A. and Gary, J.M., 2006. Normal modes of an incompressible and stratified fluid model including the vertical and horizontal components of coriolis force. Tellus A: Dynamic Meteorology and Oceanography, 58(3), pp.368–384. DOI: http://doi.org/10.1111/j.1600-0870.2006.00182.x
  Published on 01 Jan 2006
 Accepted on 26 Oct 2005            Submitted on 28 Jul 2005

References

  1. Anderson , E. , Bai , Z. , Bischof , C. , Blackford , L. S. , Demmel , J. and co-authors . 1999 . LAPACK User’s Guide . 3rd Edition , SIAM, Philadelphia, PA .  

  2. D’Asaro , E. A. , Ericksen , C. C. , Levine , M. D. , Niiler , P. , Paulson , C. A. and Van Meurs , P. 1995 . Upper-ocean inertial currents forced by a strong storm. Part I: Data and comparisons with linear theory . J. Phys. Oceanogr . 25 , 2909 – 2936 .  

  3. Durran , D. R. and Bretherton , C. 2004 . Comments on “the roles of the horizontal component of the earth’s angular velocity in nonhydrostatic linear models . ” J. Atmos. Sci . 61 , 1982 – 1986 .  

  4. Eckart , C. 1960 . Hydrodynamics of Oceans and Atmospheres . Pergamon Press , 290 pp .  

  5. Fu , L.-L. 1981 . Observations and models of inertial waves in the deep ocean . Rev. Geophys. Space Phys . 19 , 141 – 170 .  

  6. Garrett , C. and Munk , W. 1972 . Space-time scales of internal waves . Geophys. Fluid Dyn . 3 , 225 – 264 .  

  7. Gill , A. E. 1982 . Atmosphere-Ocean Dynamics . Academic Press , New York . 662 pp .  

  8. Gill , A. E. 1984 . On the behavior of internal waves in the wakes of storms . J. Phys. Oceanogr 14 , 1129 – 1151 .  

  9. Kamenkovich , V. M. and Kulakov , A. V. 1977 . Influence of rotation on waves in a stratified ocean . Oceanology 17 , 260 – 266 .  

  10. Kasahara , A. 2003a . The roles of the horizontal component of the Earth’s angular velocity in nonhydrostatic linear models . J. Atmos. Sci . 60 , 1085 – 1095 .  

  11. Kasahara , A. 2003b . On the nonhydrostatic atmospheric models with inclusion of the horizontal component of the Earth’s angular velocity . J. MeteoroL Soc. Japan 81 , 935 – 950 .  

  12. Kasahara , A. 2004 . Reply . J. Atmos. Sci . 61 , 1987 – 1991 .  

  13. Klein , P. and Smith , S. L. 2001 . Horizontal dispersion of near-inertial oscillations in a turbulent mesoscale eddy field . J. Marine Res . 59 , 697 – 723 .  

  14. Kroll , J. 1975 . The propagation of wind-generated inertial oscillations from the surface into the deep ocean . J. Mar Res . 33 , 15 – 51 .  

  15. Kundu , P. K. and Thomson , R. E. 1985 . Inertial oscillations due to a moving front . J. Phys. Oceanogr . 15 , 1076 – 1084 .  

  16. Miropol’sky , Yu Z. 2001 . Dynamics of internal gravity waves in the ocean . Kluwer Academic Pub ., Boston . 406 pp .  

  17. Munk , W. and Phillips , N. A. 1968 . Coherence and band structure of inertial motions in the sea . Rev. Geophys . 6 , 447 – 472 .  

  18. Pollard , R. T. 1970 . On the generation by winds of inertial waves in the ocean . Deep-Sea Res . 17 , 795 – 812 .  

  19. Simmons , A. J. and Temperton , C. 1997 . Stability of a two-time-level semi-implicit integration scheme for gravity wave motion . Mon. Wea. Rev . 125 , 600 – 615 .  

  20. Stern , M. E. 1975 . Ocean circulation physics . Academic Press , New York . 246 pp .  

  21. Thuburn , J. , Wood , N. and Staniforth , A. 2002 . Normal modes of deep atmospheres. II: f - F-plane geometry . Quart. J. Roy. Meteor Soc . 128 , 1793 – 1806 .  

  22. Tolstoy , I. 1973 . Wave Propagation . McGraw-Hill , 466 pp .  

  23. Webster , F. 1968 . Observations of inertial-period motions in the deep sea . Rev. Geophys . 6 , 473 – 490 .  

  24. Zervakis , V. and Levine , M. D. 1995 . Near-inertial energy propagation from the mixed layer: Theoretical considerations . J. Phys. Oceanogr 25 , 2872 – 2889 .  

comments powered by Disqus