LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
WARN, T.; GAUTHIER, P. (2011)
Publisher: Co-Action Publishing
Journal: Tellus A
Languages: English
Types: Article
Subjects:
The weakly nonlinear dynamics of a baroclinic wave in a two-layer model near minimum critical shear is described in terms of a nonlinear critical layer problem which is completely integrable in the absence of dissipation. Sufficiently small amplitude supercritical inviscid disturbances are found to equilibrate to leading order, even though the absolute potential enstrophy of the lowest layer is always transient and transferred irreversibly to smaller and smaller scales. The inviscid equilibrium amplitude of the fundamental is found to be larger by a factor of 2 than the weakly dissipative value found by Pedlosky, implying that the limits t → ∞ and vanishing dissipation are not interchangeable. The fundamental equilibrates when the mixing in the lowest layer results in the streamwise homogenization of the coarse-grained potential vorticity. It is also noted that coarse-grain homogenization can be established on faster time scales than the fine-grain versions discussed by Rhines and Young. With weak or vanishing supercriticality or larger initial disturbance amplitudes, the fundamental may either equilibrate or oscillate periodically, depending on the form and strength of the initial disturbance. In the oscillating case, the baroclinic vortex reversibly wraps up and un-wraps and there is no tendency to mix potential vorticity. Finally, the possibility of further instabilities similar to those discussed by Killworth and McIntyre, and Haynes for the Rossby wave critical layer problem is also noted.DOI: 10.1111/j.1600-0870.1989.tb00370.x
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • Abramowitz, M. and Stegun, I. 1972. Handbook of mathematicalfunctions. New York : Dover, 1046 pp.
    • Akylas, T. and Benney, D. 1980. Direct resonance in nonlinear wave systems. Stud. Appl. Math. 63, 209- 226.
    • Akylas, T. and Benney, D. 1982. The evolution of waves near direct resonance conditions. Stud. Appl. Math. 67, 107-123.
    • Batchelor, G. 1956. Steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 5, 113-133.
    • Benney D. and Bergeron, R. 1969. A new class of nonlinear waves in parallel flows. Stud. Appl. Math. 48, 181-204.
    • Boville, B. 1981. Amplitude vacillation on a /?-plane. J. Armos. Sci. 38, 609418.
    • Davis, R. 1969. On the high Reynolds number flow over a wavy boundary. J. Fluid Mech. 36, 337-346.
    • Haynes, P. 1985. Nonlinear instability of a Rossby wave critical layer. J . Fluid Mech. 161, 493-51 I .
    • Holopainen, E. 1961. On the effect of friction in baroclinic waves. Tellus 13, 363-367.
    • Killworth, P. and Mclntyre, M. 1985. Do Rossby wave critical layers absorb, reflect, or overreflect? J . Fluid Mech. 161, 449492.
    • Maslowe, S . 1986. Critical layers in shear flows. Ann. Rev. Fluid Mech. 18, 405432.
    • Newell, A. 1972. The post-bifurcation stage of baroclinic instability. J. Atmos. Sci. 29, 64-76.
    • Pedlosky, I . 1970.Finite-amplitude baroclinic waves. J. Atmos. Sci. 27, 15-30.
    • Pedlosky, J . 1979. Geophysical fluid dynamics. New York: Springer-Verlag, 624 pp.
    • Pedlosky, J . 1981. The effect of 0 on the chaotic behaviour of unstable baroclinic waves. J. Atmos. Sci. 38, 717-731.
    • Pedlosky, J. 1982a. Finite-amplitude baroclinic waves at minimum critical shear. J. Atmos. Sci. 39, 555-562.
    • Pedlosky, J . 1982b. A simple model for nonlinear critical layers in an unstable baroclinic wave. J . Atmos. Sci.39, 21 19-2127.
    • Pedlosky, J . and Polvani, L. 1987. Wave-wave interaction of unstable baroclinic waves. J. Armos. Sci. 44, 631-647.
    • Phillips, N. 1954. Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level, quasi-geostrophic model. Tellus 6, 273-286.
    • Rhines, P. and Young, W. 1983. How rapidly is a passive scalar mixed within closed streamlines? J . Fluid Mech. 133. 133-145.
    • Salmon, R. 1980. Baroclinic instability and geostrophic turbulence. Geophys. Astrophys. Fluid Dyn. 15, 167- 211.
    • Shepherd, T. 1988. On the nonlinear saturation of baroclinic instability. Part I : The two-layer model. J. Amos. Sci., in press.
    • Stewartson, K . 1978. The evolution of the critical layer of a Rossby wave. Geophys. Astrophys. Fluid D y n . 9, 185-200.
    • Stone, P. 1978. Baroclinic adjustment. J. A m o s . Sci.35, 561-571,
    • Vallis, G. 1988. Numerical studies of eddy transport properties in eddy-resolving and parameterized models. Q.J. R . Meteorol. Soc. 114, 183-204.
    • Warn, T. and Warn, H . 1976. On the development of a Rossby wave critical level. J. Afmos. Sci. 33, 2021- 2024.
    • Warn, T. and Warn, H. 1978. The evolution of a nonlinear critical level. Stud. Appl. Math. 59, 37-71, Welander, P. 1955. Studies on the general development of motion in a two-dimensional, ideal fluid. Tellus 7, 141-1 56.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article

Collected from