2009/11/08 by John Gibbon, J. D. Gibbon, Darryl D. Holm +3
Earth and Planetary Sciences · Environmental Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Climate variability and models #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Oceanographic and Atmospheric Processes #Solar and Space Plasma Dynamics #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.0911.1476
8 pages, 1 figure. Comments welcome! Accepted at J Phys A
openalex publication_date 2009/11/08 · arxiv created 2010/03/19 · arxiv updated 2010/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The transport of the potential vorticity gradient \bnablaq along surfaces of constant temperature θ is investigated for the stratified Euler, Navier-Stokes and hydrostatic primitive equations of the oceans and atmosphere using the divergenceless flux vector \bdB = \bnabla Q(q)×\bnablaθ, for any smooth function Q(q). The flux \bdB is shown to satisfy ∂t\bdB - curl (\bU×\bdB) = - \bnabla[qQ'(q) div \bU]×\bnablaθ, where \bU is a formal transport velocity of PV flux. While the left hand side of this expression is reminiscent of the frozen-in magnetic field flux in magnetohydrodynamics, the non-zero right hand side means that \bdB is not frozen into the flow of \bU when div \bU ≠ 0. The result may apply to measurements of potential vorticity and potential temperature at the tropopause.