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Singular front formation in a model for quasigeostrophic flow. (English) Zbl 0826.76014
Summary: A two-dimensional model for quasigeostrophic flow which exhibits an analogy with the three-dimensional incompressible Euler equations is considered. Numerical experiments show that this model develops sharp fronts without the need to explicitly incorporate any ageostrophic effect. Furthermore, these fronts appear to become singular in finite time. The numerical evidence for singular behavior survives the tests of rigorous mathematical criteria.

MSC:
76B99 Incompressible inviscid fluids
86A05 Hydrology, hydrography, oceanography
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[1] J. Pedlosky, Geophysical Fluid Dynamics (Springer-Verlag, New York, 1987), pp. 345–368 and 653–670. · Zbl 0713.76005
[2] R. T. Pierrehumbert, I. M. Held, and K. L. Swanson, ”Spectra of local and nonlocal two dimensional turbulence,” Preprint, December 1992. · Zbl 0823.76034
[3] P. Constantin, ”Regularity results for incompressible fluids,” Proceedings of the Workshop on The Earth Climate as a Dynamical System, Argonne National Laboratory, 25–26 September, 1992, ANL/MCS-TM-170. Also ”Geometric statistics in turbulence” submitted to SIAM Rev., May 1993.
[4] A. Chorin, ”The evolution of a turbulent vortex,” Commun. Math. Phys. 83, 517 (1982).CMPHAY0010-3616
[5] A. Majda, ”Vorticity, turbulence and acoustics in fluid flow,” SIAM Rev. 33, 349 (1991).SIREAD0036-1445 · Zbl 0850.76278
[6] R. Kerr, ”Evidence for a singularity of the three-dimensional, incompressible Euler equations,” Phys. Fluids A 5, 1725 (1993).PFADEB0899-8213 · Zbl 0800.76083
[7] P. Constantin, P. D. Lax, and A. Majda, ”A simple one-dimensional model for the three-dimensional vorticity equation,” Commun. Pure Appl. Math., 38, 715 (1985).CPMAMV0010-3640 · Zbl 0615.76029 · doi:10.1002/cpa.3160380605
[8] P. Constantin, A. Majda, and E. G. Tabak, ”Singular front formation in a two-dimensional model for quasigeostrophic flow,” in preparation. · Zbl 0826.76014
[9] T. Beale, T. Kato, and A. Majda, ”Remarks on breakdown of smooth solutions for the three-dimensional Euler equations,” Commun. Math. Phys. 94, 61 (1984).CMPHAY0010-3616 · Zbl 0573.76029
[10] W. E and C. Shu, ”Effective equations and inverse cascade theory for Kolmogorov flows,” Phys. Fluids A 5, 998 (1993).PFADEB0899-8213 · Zbl 0779.76032
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