A skewed eddy of Batchelor-modon type

  • Akira Masuda
Article

Abstract

A Batchelor-modon eddy is a highly specialized nonlinear vortex pair, whose potential vorticity depends linearly on the stream function viewed from the coordinates moving with the translation velocity of the eddy. To generalize it, a skewed model is developed by introducing a cubic nonlinearity in addition to the linear term.

A perturbation analysis shows that the eddy region is no longer a circle but is elongated longitudinally or transversely according as the sign of the cubic term. Moreover, the eddy is slightly flattened or steepened. The cubic term increases or decreases the translation velocity, if the average radius and the amplitude are fixed.

A numerical experiment on anf-plane is carried out to show that these skewed eddies retain their initial forms even after they turn a corner of the basin; they are as stable as (first-mode) standard Batchelor-modon eddies. The present skewed model gives a reasonable qualitative interpretation of deformed eddies which result from merging of two eddies or from initially Gaussian eddies near the boundary.

Keywords

Vortex Vorticity Numerical Experiment Stream Function Linear Term 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Batchelor, G.K. (1967): An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge, 615 pp.Google Scholar
  2. Flierl, G.R. (1987): Isolated eddy models in Geophysics. Ann. Rev. Fluid Mech.,19, 493–530.CrossRefGoogle Scholar
  3. Flierl, G.R., V.D. Larichev, J.C. McWilliams and G.M. Reznik (1980): The dynamics of baroclinic and barotropic solitary eddies. Dyn. Atmos. Oceans,5, 1–41.CrossRefGoogle Scholar
  4. Hasegawa, A. and K. Mima (1978): Pseudo-three-dimensional turbulence in magnetized nonuniform plasma. Phys. Fluids,21, 87–92.CrossRefGoogle Scholar
  5. Laedke, E.W. and K.H. Spatschek (1985): Dynamical properties of drift vortices. Phys. Fluids,28, 1008–1010.Google Scholar
  6. Lamb, H. (1932): Hydrodynamics. Cambridge Univ. Press, Cambridge, 738 pp.Google Scholar
  7. Larichev, V.D. and G.M. Reznik (1976): Two-dimensional Rossby soliton: an exact solution. Rep. USSR Acad. Sci.,231, 1077–1079.Google Scholar
  8. Masuda, A., K. Marubayashi and M. Ishibashi (1987a): An approximation by a Batchelor-modon eddy to an initially Gaussian warm eddy translating along a solid wall on anf-plane. Rep. Res. Inst. Appl. Mech., Kyushu Univ.,65, 57–65 (in Japanese).Google Scholar
  9. Masuda, A., K. Marubayashi and M. Ishibashi (1987b): Batchelor-modon eddies and isolated eddies near the coast. J. Oceanogr. Soc. Japan,43, 383–394.Google Scholar
  10. McWilliams, J.C. (1983): Interactions of Isolated Vortices. II. Modon Generation by Monopole Vortices. Geophys. Astrophys. Fluid Dyn.,24, 1–22.Google Scholar
  11. McWilliams, J.C. and N.J. Zabusky (1982): Interactions of Isolated Vortices. I: Modons Colliding with Modons. Geophys. Astrophys. Fluid Dyn.,19, 207–227.Google Scholar
  12. Moore, D.W. and D.I. Pullin (1987): The compressible vortex pair. J. Fluid Mech.,185, 171–204.Google Scholar
  13. Pedlosky, J. (1979): Geophysical Fluid Dynamics. Springer-Verlag, New York, 624 pp.Google Scholar
  14. Phillips, O.M. (1977): The Dynamics of the Upper Ocean. Cambridge University Press, Cambridge, 366 pp.Google Scholar
  15. Pierrehumbert, R.T. (1980): A family of steady, translating vortex pairs with distributed vorticity. J. Fluid Mech.,99, 129–144.Google Scholar
  16. Swenson, M. (1982): Isolated 2D vortices in the presence of shear. Summer Study Program in Geophysical Fluid Dynamics, Woods Hole Oceanographic Institution, 324–336.Google Scholar
  17. Stern, M.E. (1975): Minimal properties of planetary eddies. J. Mar. Res.33, 1–13.Google Scholar
  18. Yasuda, I., K. Okuda and K. Mizuno (1986): Numerical study on the vortices near boundaries—considerations on warm core rings in the vicinity of east coast of Japan—. Bulletin of Tohoku Regional Fisheries Research Laboratory,48, 67–86.Google Scholar
  19. Wu, H.M., E.A. Overman and N.J. Zabusky (1984): Steady-state solutions of the Euler equations in two dimensions: rotating and translating V-states with limiting cases. I. Numerical algorithms and results. J. Comp. Phys.,53, 42–71.Google Scholar

Copyright information

© the Oceanographical Society of Japan 1988

Authors and Affiliations

  • Akira Masuda
    • 1
  1. 1.Research Institute for Applied MechanicsKyushu UniversityKasugaJapan

Personalised recommendations