Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-03T05:16:46.220Z Has data issue: false hasContentIssue false
  • English
  • Français

Almost symmetric solitary eddies in a two-layer ocean

Published online by Cambridge University Press:  26 April 2006

G. G. Sutyrin  and
W. K. Dewar
G. G. Sutyrin
Affiliation:
P. P. Shirshov Institute of Oceanology, USSR Academy of Sciences, Krasikova 23, 117218, Moscow, USSR
W. K. Dewar
Affiliation:
Department of Oceanography, Florida State University, Tallahasee, FL 32306, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

An asymptotic theory of two-dimensional planetary solitary eddies is presented. Previous studies in one-and-a-half layer models have discovered special classes of radially symmetric structure which are associated with eddies of permanent form. We generalize these studies by including an active lower layer and by considering the effects of azimuthal structure. Accordingly, we stress two main results; namely, (i) permanent-form two-layer eddies with essentially arbitrary radial structure exist, provided that the eddy includes a weak imbedded dipolar asymmetry and an appropriate counter-rotating deep flow, and (ii) fluid trapped under an eddy in Taylor columns can significantly affect eddy properties if the trapped fluid possesses non-trivial potential vorticity.

The structural permanency in our solutions arises from a balance between nonlinear steepening, driven by the continuity equation, and planetary dispersion. The structural asymmetries affect eddy propagation, either by dipole interaction within the layer (as occurs in modons) or by pressure forces acting between layers. The primary role of the deep counter-rotating flow is to balance the net upper-layer transport. The interesting layer-layer interaction, however, involves higher-order dynamics and is sensitive to the continuity of the potential-vorticity field. In general, these eddies trap fluid both in the upper thermocline and in the lower layer.

The dominance of oceanic anticyclones over cyclones is relatively well known. A main conclusion of this study is that the class of long-lived anticyclones is considerably broader than previously realized. This may help explain the observed bias toward anticyclonic eddies. A second conclusion is that estimates of material transport by eddies may need to account for the movement of fluid outside the main bowl of the eddies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 238 , May 1992 , pp. 633 - 656
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bender, C. & Orszag, S. 1978 Advanced Mathematics Methods for Scientists and Engineers. McGraw-Hill, pp. 593.
Berestov, A. L. 1981 Some new solutions for the Rossby solitons. Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 17, 60–64.Google Scholar
Charney, J. C. & Flierl, G. R. 1981 Oceanic analogues of large scale atmospheric motions. In Evolution of Physical Oceanography (ed. B. A. Warren & C. Wunsch), pp. 504–548. MIT Press.
Chassignet, E. & Cushman-Roisin, B. 1991 On the influence of the lower layer on an upper layer isolated ocean ring in a two-layer system. J. Phys. Oceanogr. 21, 939–957.Google Scholar
Cushman-Roisin, B. 1986 Frontal geostrophic dynamics. J. Phys. Oceanogr. 16, 132–143.Google Scholar
Cushman-Roisin, B., Chassignet, E. & Tang, B. 1990 Westward motion of mesoscale eddies. J. Phys. Oceanogr. 20, 758–768.Google Scholar
Cushman-Roisin, B., Sutyrin, G. G. & Tang, B. 1992 Two-layer geostrophic dynamics. Part I: Governing equations. J. Phys. Oceanogr. (in press).Google Scholar
Ebbesmeyer, C., Taft, B. A., McWilliams, J. C., Shen, C. Y., Riser, S. C., Rossby, H. T., Biscayne, P. E. & Ostlund, H. G. 1986 Detection, structure and origin of extreme anomalies in a western Atlantic oceanographic section. J. Phys. Oceanogr. 16, 591–612.Google Scholar
Flierl, G. 1979 Baroclinic solitary waves with radial symmetry. Dyn. Atmos. Oceans 3, 15–38.Google Scholar
Flierl, G. 1984a Model of the structure and motion of a warm-core ring. Austral. J. Mar. Freshwat. Res. 35, 9–23.Google Scholar
Flierl, G. 1984b Rossby wave radiation from a strongly nonlinear warm eddy. J. Phys. Oceanogr. 14, 47–58.Google Scholar
Flierl, G. 1987 Isolated eddy models in geophysics. Ann. Rev. Fluid Mech. 19, 493–530.Google Scholar
Flierl, G., Larichev, V. D., McWilliams, J. C. & Reznick, G. M. 1980 The dynamics of baroclinic and barotropic solitary eddies. Dyn. Atmos. Oceans 5, 1–41.Google Scholar
Flierl, G., Stern, M. & Whitehead, J. A. 1983 The physical significance of modons: laboratory experiments and general integral constraints. Dyn. Atmos. Oceans 7, 233–263.Google Scholar
Joyce, T. M. & McDougall, T. J. 1991 Physical structure and temporal evolution of Gulf Stream warm-core ring 82B. Deep-Sea Res. (in press).Google Scholar
Larichev, V. D. & Reznik, G. M. 1976 Two-dimensional Rossby soliton: an exact solution. Rep. USSR Acad. Sci. 231, 1077–1079.Google Scholar
Makino, M., Kamimura, T. & Taniuti, T. 1981 Dynamics of two-dimensional solitary vortices in a low-β plasma with convective mode. J. Phys. Soc. Japan 50, 980–989.Google Scholar
Malanotte-Rizzoli, P. 1982 Planetary solitary waves in geophysical flows. Adv. Geophys. 24, 147–224.Google Scholar
Matsuura, T. & Yamagata, T. 1982 On the evolution of nonlinear planetary eddies larger than the radius of deformation. J. Phys. Oceanogr. 12, 440–456.Google Scholar
McWilliams, J. C. 1984 The emergence of isolated, coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
McWilliams, J. C. 1985 Submesoscale, coherent vortices in the ocean. Rev. Geophys. 23, 165–182.Google Scholar
McWilliams, J. C., Gent, P. R. & Norton, N. J. 1986 The evolution of balanced, low-mode vortices on the β-plane. J. Phys. Oceanogr. 16, 838–855.Google Scholar
Mikhailova, E. I. & Shapiro, N. B. 1980 Two-dimensional model of synoptic disturbances evolution in the ocean. Izv. Akad. Nauk SSSR. Fiz. Atmos. Okeana 16, 823–833.Google Scholar
Nezlin, M. V. & Sutyrin, G. G. 1989 Long-lived solitary anticyclones in the planetary atmospheres and oceans, in laboratory experiments and in theory. In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. J. C. J. Nihoul & B. M. Jamart), pp. 701–720. Elsevier.
Nof, D. 1981 On the β-induced movement of isolated baroclinic eddies. J. Phys. Oceanogr. 11, 1662–1672.Google Scholar
Nycander, J. & Sutyrin, G. G. 1991 Stationary translating anticyclones on the beta-plane. Dyn. Atmos. Ocean. (in press).Google Scholar
Petviashvili, V. I. 1980 Red spot of Jupiter and the drift soliton in a plasma. JETP Lett. 32, 632–635.Google Scholar
Petviashvili, V. I. & Yan'kov, V. V. 1982 Two-layer vortices in a rotating stratified fluid. Dokl. Akad. Nauk SSSR 267, 825–828.Google Scholar
Phillips, N. A. 1954 Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level, quasi-geostrophic model. Tellus 6, 273–286.Google Scholar
Stern, M. E. 1975 Minimal properties of planetary eddies. J. Mar. Res. 33, 1–13.Google Scholar
Sutyrin, G. G. 1985 On the theory of solitary anticyclones in a rotating fluid. Dokl. Akad. Nauk SSSR 280, 1101–1105 (Transl: Earth Sci. pp. 38–41).Google Scholar
Sutyrin, G. G. & Yushina, I. G. 1986 On the evolution of isolated eddies in a rotating fluid. Izv. Akad. Nauk SSSR. Mekh. Zhid. i Gaza 4, 52–59 (Transl: Fluid Dyn. pp. 550–556).Google Scholar
Sutyrin, G. G. & Yushina, I. G. 1988 Formation of a vortical soliton. Dokl. Akad. Nauk SSSR 299, 580–584 (Transl: Sov. Phys. Dokl. 33(3), 179–181).Google Scholar
Swenson, M. 1987 Instability of equivalent barotropic riders. J. Phys. Oceanogr. 17, 492–506.Google Scholar
Tang, B. & Cushman-Roisin, B. 1992 Two-layer geostrophic dynamics. Part II: Geostrophic turbulence. J. Phys. Oceanogr. (in press).Google Scholar
Yamagata, T. 1982 On nonlinear planetary waves: a class of solutions missed by the quasigeostrophic approximation. J. Oceanogr. Soc. Japan 38, 236–244.Google Scholar