[FRIAM] Entropy and atmospheric potential vorticity

[Frank Wimberly]

Doug Roberts?

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Thu, May 15, 2025, 9:32 PM Nicholas Thompson <thompnickson2 at gmail.com>
wrote:

> 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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