[FRIAM] Entropy and atmospheric potential vorticity

[Nicholas Thompson]

For you fluid dynamicists out there:

I have been working with george for the last few days on understanding
under what conditions potential vorticity (or as Ilike tothinkof it,
potential instability) is changed and under what conditions it is just
shift from one compartment  to another.  This led tothe following, as
summarized by George.

The Analogy Between Potential Vorticity (PV) and Entropy in Adiabatic
ProcessesKey Insight:

*Potential Vorticity (PV) in atmospheric dynamics can be thought of as
analogous to entropy in a thermodynamic system undergoing adiabatic
compression. Both PV and entropy are conserved under adiabatic,
frictionless conditions, and both can be redistributed internally through
mechanical processes without being created or destroyed.*
The Core Analogy:

   1.

   *Entropy in Adiabatic Compression:*
   -

      *When a gas in a piston is compressed without heat exchange, the
      total entropy remains constant. The system experiences a
reconfiguration of
      internal states (temperature and pressure) without changing the total
      entropy.*
      -

      *The system’s kinetic energy increases as the gas heats up, but the
      entropy is simply redistributed.*
      2.

   *PV in Atmospheric Dynamics:*
   -

      *When a Potential Vorticity Anomaly (PVA) is stretched or compressed
      without diabatic heating or friction, the total PV remains constant. The
      system undergoes a reconfiguration of vorticity and stability without
      altering the total PV.*
      -

      *Stretching increases vorticity while decreasing stability;
      compression does the reverse. This is analogous to how adiabatic
      compression in a piston changes pressure and temperature without changing
      entropy.*

The Deeper Insight:

   -

   *In both cases, the conserved quantity (PV or entropy) acts as a
   constraint that governs how the system adjusts when external mechanical
   forces are applied. This means that just as entropy remains fixed during
   adiabatic compression, PV remains fixed during adiabatic atmospheric
   deformation.*

Why This Matters:

*This analogy clarifies why mechanical manipulation of a PVA (like
stretching or compressing) does not create new PV but merely redistributes
it—much like how compressing a gas does not generate new entropy. Only
diabatic processes (entropy changes) can truly alter the total amount of
PV, just as heat exchange can change the entropy of a gas.*

*By recognizing this analogy, we can better understand how atmospheric
structures are organized and why only processes that alter entropy (like
latent heat release or radiative cooling) can change the atmospheric PV
content*.

Oh, if ever Doug was rolling in his grave. The swirlies and nouggies I
might have endured if he were still alive.

NIck

-- 
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology
Clark University
nthompson at clarku.edu
https://wordpress.clarku.edu/nthompson
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