Abstract
It is demonstrated that nonlinear Rossby modes, such as modons and IG eddies, can be excited in planetary fluids by a sufficiently strong forcing of potential vorticity. When a weak forcing is balanced with a weak dissipation, two (linear and nonlinear) equilibrium states can be produced, depending on the initial condition. When the fluid is inviscid, a sufficiently strong steady forcing may generate a sequence of propagating nonlinear eddies. A weak forcing, by contrast, only generates linear Rossby waves. The criterion which divides the high amplitude nonlinear state and the low amplitude linear state may be interpreted in terms of a ratio of a time necessary to force the eddy to a time for a fluid particle to circulate about the nonlinear eddy once.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arakawa, A. (1966),Computational Design for Long-term Numerical Integration of the Equations of Fluid Motion: Two-dimensional Incompressible Flow. Part I, J. Comput. Phys.1, 119–143.
Davey, M. K., andKillworth, P. D. (1989),Flows Produced by Discrete Sources of Buoyancy, J. Phys. Oceanogr.19, 1279–1290.
Flierl, G. R., Larichev, V. D., McWilliams, J. C., andReznik, G. M. (1980),The Dynamics of Baroclinic and Barotropic Solitary Eddies, Dyn. Atmos. Oceans5, 1–44.
Hoskins, B. J., McIntyre, M. E., andRobertson, A. W. (1985),On the Use and Significance of Isentropic Potential-vorticity Maps, Quart. J. Roy. Meteor. Soc.111, 877–946.
Larichev, V. D., andReznik, G. M. (1976),Two-dimensional Rossby Soliton: An Exact Solution, Rep. U.S.S.R. Acad. Sci.,231, 1077–79.
Malanotte-Rizzoli, P.,Planetary waves in geophysical flows, InAdvances in Geophysics, vol. 24 (Academic Press 1982) pp. 147–224.
Matsuura, T., andYamagata, T. (1982),On the Evolution of Nonlinear Planetary Eddies Larger than the Radius of Deformation, J. Phys. Oceanogr.12, 440–456.
McWilliams, J. C. (1980),An Application of Equivalent Modons to Atmospheric Blocking, Dyn. Atmos. Oceans5, 43–66.
McWilliams, J. C., Flierl, G. R., Larichev, V. D., andReznik, G. M. (1981),Numerical Studies of Barotropic Modons, Dyn. Atmos. Oceans5, 219–238.
Pierrehumbert, R. T., andMalguzzi, P. (1984),Forced Coherent Structures and Local Multiple Equilibria in a Barotropic Atmosphere, J. Atmos. Sci.41, 246–257.
Rhines, P. B. (1983),Lectures in Geophysical Fluid Dynamics, Lec. Appl. Math.20, 3–58.
Rhines, P. B. (1986),Vorticity Dynamics of the Oceanic General Circulation, Ann. Rev. Fluid Mech.18, 433–497.
Scott-Russell, J. (1844),Report on Waves, Proc. Roy. Soc. Edinb., 319–320.
Stern, M. E. (1975),Minimal Properties of Planetary Eddies, J. Mar. Res.33, 1–13.
Stommel, H. (1948),The Westward Intensification of Wind-driven Ocean Currents, Trans. Am. Geophys. Union29, 202–206.
Umatani, S., andYamagata, T. (1989),The Response of the Eastern Tropical Pacific to Meridional Migration of the ITCZ: The Generation of the Costa Rica Dome, submitted to J. Phys. Oceanogr.
Williams, G. P., andYamagata, T. (1985),Geostrophic Regimes, Intermediate Solitary Vortices and Jovian Eddies, J. Atmos. Sci.41, 453–478.
Yamagata, T. (1976),A Note on Boundary Layers and Wakes in Rotating Fluids, J. Oceanogr. Soc. Japan32, 155–161.
Yamagata, T. (1982),On Nonlinear Planetary Waves: A Class of Solutions Missed by the Traditional Quasi-geostrophic Approximation, J. Oceanogr. Soc. Japan38, 236–244.
Yamagata, T., andUmatani, S. (1987),The Capture of Current Meander by Coastal Geometry with Possible Application to the Kuroshio Current, Tellus39A, 161–169.
Yamagata, T., andUmatani, S. (1989),Geometry-forced Coherent Structures as a Model of the Kuroshio Meander, J. Phys. Oceanogr.19, 130–138.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yamagata, T., Sakamoto, K. & Arai, M. Locally-induced nonlinear modes and multiple equilibria in planetary fluids. PAGEOPH 133, 733–748 (1990). https://doi.org/10.1007/BF00876230
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00876230