Abstract
By employing Arnol’d’s method (energy-Casimir), this paper has studied the nonlinear stability of the two-layer generalized Phillips’ model for which the top and bottom surfaces are either rigid or free, and obtained some nonlinear stability criteria. In addition, some linear stability criteria are obtained by normal mode method. The results reveal the influences of the free surface parameter on the stability of atmospheric and oceanic motions.
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References
Arnol’d, V. I. (1965), Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid,Dokl. Akad. Nauk. USSR.,162: 975–978, English Transl:Soviet Math.,6: 773–777.
Arnol’d, V. I. (1966), On a priori estimate in the theory of hydrodynamic stability,lzv. Uyssh. Uchebn. Zaved, Matematika,54(5): 3–5, English Transl:Am. Math. Soc. Transl. Series 2,79: 267–269, (1969).
Charney, J. G., and M. E. Stern (1962), On the stability of internal baroclinic jets in a rotating atmosphere,J. Atmos. Sci.,19: 159–172.
Kuo, H. L. (1949), Dynamical instability of two-dimensional non-divergent flow in a barotropic atmosphere,J. Me-teor.,6: 105–122.
Lindzen, R. S., E. S. Batten, and J. W. Kim (1968), Oscillations in atmospheres with tops,Mon. Wea. Rev.,96: 133–140.
Liu, Y. M. and Mu Mu (1994), Arnol’d’s second nonlinear stability theorem for general multilayer quasi-geostrophic model,Adv. Atmos. Sci.,11: 36–42.
Mclntyre, M. E. and T. G. Shepherd (1987), An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Aronl’d’s stability theorems,J. Fluid Mech,181: 527–565.
Mu and T.G. Shepherd (1994), Nonlinear stability of Eady’s model,J. Atmos. Sci.,51: 3427–3436.
Mu Mu, Q. C. Zeng, T. G. Shepherd and Y. M. Liu (1994), Nonlinear stability of multilayer quasi-geostrophic flow,J. Fluid Mech.,264: 165–184.
Pedlosky, P. (1963), Baroclinic instability in two layer systems,Tellus,15: 20–25.
Pedlosky, P. (1979), Geophysical Fluid Dynamis, Springer, 624pp.
Phillips, N. A. (1954), Energy transformations and meridional circulation associated with baroclinic waves in a two-level, quasi-geostrophic model,Tellus,6: 273–286.
Rayleigh, Lord (1880), On the stability or instability of certain fluid motions,Proc. Lond. Math. Soc.,11: 57–70.
Ripa, P. (1992), Wave energy-momentum and pseudoenrgy-momentum conservation for the layered quasi-geostrophic instability problem,J. Fluid Mech.,235: 379–398.
Shepherd, T. G. (1988), Nonlinear saturation of baroclinic instability, Part I: The two-layer model,J. Atmos. Sci.,45: 2014–2025.
Zeng, Q. C. (1989), Uariational principle of instability of atmospheric motion,Adv. Atmos. Sci.,6: 137–172.
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Yang, L., Mu, M. Baroclinic instability in the generalized Phillips’ model Part I: Two-layer model. Adv. Atmos. Sci. 13, 33–42 (1996). https://doi.org/10.1007/BF02657026
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DOI: https://doi.org/10.1007/BF02657026