A local diagnostic energy to study diabatic effects on a class of degenerate Hamiltonian systems with application to mixing in stratified flows
Abstract
In Hamiltonian systems characterized by a degenerate Poisson algebra, we show how to construct a local energylike quantity that can be used to study diabatic effects on the evolution of the Available Energy of the system, the latter concept formalizing the original idea of Margules'. We calculate the local diagnostic energy for geophysically relevant flows. For the particular case of stratified Boussinesq flows, we show that under moderately general conditions, in inertial frames where the initial distribution of potential vorticity is even around the origin, our framework recovers the Available Potential Energy introduced by Holliday and McIntyre \cite{HollidayM81}, and as such depends only on the mass distribution of the flow. In noninertial frames, we show that the local diagnostic energy of flows which are, in an appropriate sense, characterized by a lowRossby number ${\rm Ro}$ ground state, has to lowest order in ${\rm Ro}$, a universal character.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.08093
 Bibcode:
 2017arXiv170108093S
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 Under consideration in Proc. Royal Soc. A