Frontiers in Nonlinear Waves
in honor of Vladimir Zakharov's 70th birthday
March 26–29, 2010
University of Arizona, Tucson, AZ, USA

About Conference Program and Speakers Lodging Local Attractions Organizing Committee

Conference Program

Mar 26 Mar 27 Mar 28 Mar 29 Speakers

Sunday March 28, 10:55–11:20

Extra Invariant and Zonal Jets
Alexander Balk
Department of Mathematics, University of Utah, Salt Lake City, UT
We show that rotating shallow water dynamics possesses an approximate (adiabatic type) positive quadratic invariant. The extra conservation holds to leading orders with respect to two small parameters, the first characterizing the strength of the nonlinearity and the second the degree of spatial inhomogeneity. We show that this invariant exists not only away from the equator, where its analogue in the quasigeostrophic equation has been previously investigated, but throughout the equatorial region as well, where the quasigeostrophic equation is not applicable. The extra invariant is important because its constraints on the dynamics lead to the generation of zonal jets. We find that this tendency should be especially pronounced near the equator.

Joint work with F. van Heerden and P.B. Weichman.

 presentation file (PPT, 1.11 MiB)