Japanese

Eigen modes of a linear shear flow in shallow water on an equatorial β-plane

Hiroshi Taniguchi (Disaster Prevention Research Institute, Kyoto University)
Masaki Ishiwatari (Faculty of Science, Hokkaido University)

(Received 14 March 2008; in revised form 27 June 2008)

Eigen modes of a linear shear flow in shallow water on an equatorial β-plane are obtained over a wide parameter range. High-order unstable modes, neutral modes, and continuous modes are examined based on the results of Taniguchi and Ishiwatari (2006) that investigates mainly the lowest order most unstable modes. The results are summarized as follows:

  1. With detailed examinations of mode structures, it is shown that some continuous modes have equatorial Rossby wave like structures. This result confirms the discussion of Taniguchi and Ishiwatari (2006) that all equatorial Rossby modes assimilate into continuous modes.
  2. High-order zonally symmetric unstable modes obtained by Stevens (1983) are described in terms of resonance between neutral waves. The high-order modes are caused by resonance between eastward mixed Rossby-gravity modes and continuous modes or by resonance between eastward inertial gravity modes and continuous modes.
  3. Neutral modes whose dispersion curves intersect with nearby dispersion curves of other neutral modes are examined. These neutral modes do not resonate with contiuous modes having pseudomomenta with opposite sign in spite of intersection of dispersion curves of the neutral modes and contiuous modes. Such neutral modes appear when there exist regions outside inertially unstable region, and have large amplitudes outside inertially unstable region.
  4. The behaviors of dispersion curves of equatorial Kelvin modes and westward mixed Rossby-gravity modes are examined in cases that the two curves come closer. With narrowing calculational domains, it is observed that dispersion curves of equatorial Kelvin modes kink, when equatorial Kelvin modes and westward mixed Rossby-gravity modes resonate.

Contents

  1. Introduction
  2. Governing equations
  3. Search for equatorial Rossby modes
  4. Interpretaion of high-order symmetric modes
  5. Characteristic of neutral modes whose dispersion curves have intersection with other neutral modes
  6. Identification of dispersion curves of equatorial Kelvin modes and mixed Rossby-gravity modes
  7. Summary

Appendix

  1. Structural change of continuous modes
  2. The change of the number of crossing modes with the change of meridional width of computational domain
  3. Resolution dependence of dispersion curves for the cases with the inertially unstable region as calculational domain
  4. Horizontal structures of crossing modes
  5. References
  6. Acknowledgements
  7. Authors' address

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