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.
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References
Batchelor, G.K. (1967): An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge, 615 pp.
Flierl, G.R. (1987): Isolated eddy models in Geophysics. Ann. Rev. Fluid Mech.,19, 493–530.
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.
Hasegawa, A. and K. Mima (1978): Pseudo-three-dimensional turbulence in magnetized nonuniform plasma. Phys. Fluids,21, 87–92.
Laedke, E.W. and K.H. Spatschek (1985): Dynamical properties of drift vortices. Phys. Fluids,28, 1008–1010.
Lamb, H. (1932): Hydrodynamics. Cambridge Univ. Press, Cambridge, 738 pp.
Larichev, V.D. and G.M. Reznik (1976): Two-dimensional Rossby soliton: an exact solution. Rep. USSR Acad. Sci.,231, 1077–1079.
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).
Masuda, A., K. Marubayashi and M. Ishibashi (1987b): Batchelor-modon eddies and isolated eddies near the coast. J. Oceanogr. Soc. Japan,43, 383–394.
McWilliams, J.C. (1983): Interactions of Isolated Vortices. II. Modon Generation by Monopole Vortices. Geophys. Astrophys. Fluid Dyn.,24, 1–22.
McWilliams, J.C. and N.J. Zabusky (1982): Interactions of Isolated Vortices. I: Modons Colliding with Modons. Geophys. Astrophys. Fluid Dyn.,19, 207–227.
Moore, D.W. and D.I. Pullin (1987): The compressible vortex pair. J. Fluid Mech.,185, 171–204.
Pedlosky, J. (1979): Geophysical Fluid Dynamics. Springer-Verlag, New York, 624 pp.
Phillips, O.M. (1977): The Dynamics of the Upper Ocean. Cambridge University Press, Cambridge, 366 pp.
Pierrehumbert, R.T. (1980): A family of steady, translating vortex pairs with distributed vorticity. J. Fluid Mech.,99, 129–144.
Swenson, M. (1982): Isolated 2D vortices in the presence of shear. Summer Study Program in Geophysical Fluid Dynamics, Woods Hole Oceanographic Institution, 324–336.
Stern, M.E. (1975): Minimal properties of planetary eddies. J. Mar. Res.33, 1–13.
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.
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.
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Masuda, A. A skewed eddy of Batchelor-modon type. Journal of the Oceanographical Society of Japan 44, 189–199 (1988). https://doi.org/10.1007/BF02302642
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DOI: https://doi.org/10.1007/BF02302642