English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

An initial zonally symmetric quasigeostrophic potential-vorticity (PV)distribution q_i(y) is subjected to complete or partial mixing within somefinite zone |y| < L, where y is latitude. The change in M, the total absoluteangular momentum, between the initial and any later time is considered. Forstandard quasigeostrophic shallow-water beta-channel dynamics it is provedthat, for any q_i(y) such that dq_i/dy > 0 throughout |y| < L, the change in Mis always negative. This theorem holds even when "mixing" is understood in themost general possible sense. Arbitrary stirring or advective rearrangement isincluded, combined to an arbitrary extent with spatially inhomogeneousdiffusion. The theorem holds whether or not the PV distribution is zonallysymmetric at the later time. The same theorem governs Boussinesqpotential-energy changes due to buoyancy mixing in the vertical. For thestandard quasigeostrophic beta-channel dynamics to be valid the Rossbydeformation length L_D >> \epsilon L where \epsilon is the Rossby number; whenL_D = \infty the theorem applies not only to the beta-channel, but also to asingle barotropic layer on the full sphere, as considered in the recent work ofDunkerton and Scott on "PV staircases". It follows that the M-conserving PVreconfigurations studied by those authors must involve processes describable asPV unmixing, or anti-diffusion, in the sense of time-reversed diffusion.Ordinary jet self-sharpening and jet-core acceleration do not, by contrast,require unmixing, as is shown here by detailed analysis. Mixing in the jetflanks suffices. The theorem extends to multiple layers and continuousstratification. A corollary is a new nonlinear stability theorem for shearflows.

A general theorem on angular-momentum changes due to potential vorticity mixing and on potential-energy changes due to buoyancy mixing