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- W2952099654 abstract "The transport of the potential vorticity gradient $bnabla{q}$ along surfaces of constant temperature $theta$ is investigated for the stratified Euler, Navier-Stokes and hydrostatic primitive equations of the oceans and atmosphere using the divergenceless flux vector $bdB = bnabla Q(q)timesbnablatheta$, for any smooth function $Q(q)$. The flux $bdB$ is shown to satisfy $$ partial_tbdB - {curl} (bUtimesbdB) = - bnablabig[qQ'(q) {div} bUbig]timesbnablatheta, $$ 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 ${div} bU neq 0$. The result may apply to measurements of potential vorticity and potential temperature at the tropopause." @default.
- W2952099654 created "2019-06-27" @default.
- W2952099654 creator A5059930044 @default.
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- W2952099654 date "2009-11-07" @default.
- W2952099654 modified "2023-09-23" @default.
- W2952099654 title "The dynamics of the gradient of potential vorticity" @default.
- W2952099654 cites W2126345454 @default.
- W2952099654 doi "https://doi.org/10.48550/arxiv.0911.1476" @default.
- W2952099654 hasPublicationYear "2009" @default.
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