<div dir="auto"><div><br></div><div>Dan GuPTa had this response when asked to relate your .PDF to Bernard cells and other prompting:</div><div dir="auto"><br></div><div dir="auto"><div dir="auto"><div dir="auto">Here’s a integration of potential vorticity (PV), atmospheric stability, and their relationship to Bénard cells, emphasizing isentropic layering in both meteorological and experimental fluid dynamics contexts.</div><div dir="auto"><br></div><div dir="auto">### Connecting Bénard Cells and Atmospheric Dynamics</div><div dir="auto"><br></div><div dir="auto">In Bénard cells, fluid heated from below shows a critical transition from conductive to convective heat transfer, forming cellular patterns. Similarly, in the atmosphere, when the vertical temperature gradient becomes unstable—akin to the Bénard cell transition—convection can initiate, influenced by factors like the earth's rotation and potential vorticity.</div><div dir="auto"><br></div><div dir="auto">### Potential Vorticity and Stability</div><div dir="auto"><br></div><div dir="auto">- **PV on Isentropic Surfaces:** Potential vorticity combines fluid rotation and atmospheric stratification. In meteorology, PV is mapped on isentropic surfaces (constant potential temperature layers), where it highlights regions prone to atmospheric instability and potential convection, akin to early instability in Bénard cells.</div><div dir="auto"> </div><div dir="auto">- **Dynamic Tropopause:** Acting like the fluid surface in a Bénard cell, the dynamic tropopause is flexible, responding to distortions from jet streams. These distortions can lead to convective activity by modifying local stability and vorticity, driving weather patterns similarly to temperature gradients in Bénard convection.</div><div dir="auto"><br></div><div dir="auto">### PV Anomalies and Convective Cells</div><div dir="auto"><br></div><div dir="auto">- **Weather Forecasting:** Monitoring PV anomalies helps predict convective weather events, similar to observing Bénard cells to anticipate pattern formation. For example, sharp PV changes can indicate regions ripe for convective storms if conditions like moisture and surface temperature align.</div><div dir="auto"><br></div><div dir="auto">- **Role of Isentropic Layering:** Both in Bénard cells and weather systems, the spacing between isentropic layers indicates stability. Closer layers suggest a steep gradient and instability, potentially leading to convective movements. In the atmosphere, this translates to dynamic interactions where lower stability near the surface can trigger or enhance convective processes.</div><div dir="auto"><br></div><div dir="auto">### Conclusion</div><div dir="auto"><br></div><div dir="auto">Understanding the parallels between Bénard cell dynamics and atmospheric conditions through potential vorticity and isentropic surfaces not only illustrates universal fluid dynamics principles but also enhances meteorological predictions of convective weather events, demonstrating how small-scale changes in stability can lead to significant atmospheric phenomena.</div></div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Apr 11, 2024, 2:04 PM Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><br></div><div><br></div>
<p class="MsoNormal" style="line-height:6pt;margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif">Hi, Phellow Phriammers,<span> </span>Nick, here. <span></span></span></p>
<p class="MsoNormal" style="line-height:6pt;margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><span><br></span></span></p><p class="MsoNormal" style="line-height:6pt;margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><span> </span></span></p><p class="MsoNormal" style="line-height:6pt;margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><span><br></span></span></p><p class="MsoNormal" style="line-height:6pt;margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><span><br></span></span></p>
<p class="MsoNormal" style="line-height:6pt;margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif">I have been lost in the
weather.<span> </span>This publication,<span></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><br></span></p><p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><a href="https://acrobat.adobe.com/id/urn:aaid:sc:us:d481610b-e5d5-4a03-879c-6db6ec1d5e4a" style="color:rgb(70,120,134);text-decoration:underline" target="_blank" rel="noreferrer">https://acrobat.adobe.com/id/urn:aaid:sc:us:d481610b-e5d5-4a03-879c-6db6ec1d5e4a</a><br></span></p><p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><span><br></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif">with its
glorious eye-candy, is an example of what seems to be a new perspective in
meteorology, the DT-PV perspective.<span> </span>PV
refers to a parameter, potential vorticity, which seems to be a measure of how
liable the atmosphere is to churn; DT refers to the DYNAMIC
tropopause.<span> </span>The tropopause is the
transition zone between the stratosphere and our own layer, the troposphere, through
which gas exchange is limited because the lapse rate of the troposphere<span> </span>-- its decline in temperature with fall of
pressure -- is reversed in the stratosphere.<span>
</span>In the Bad Old Days, we were taught that the tropopause was like a
ceiling, tilted upward from the poles to the tropics.<span> </span>Now we have begun to think of it as more like
a tent fly, still tilted up equator-ward, but loose and floppy and buffeted up
and down by the jetstreams’ winds. These floppings up and down have the power
to destabilize the lower atmosphere and lead to bad weather, if conditions there are
ripe. <span></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><span> </span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif">This is
not one of my usual cries for help.<span> </span>I have
some good tutors. However, I would love to hear from others whom this paper
interests. In particular I am struggling with the notion of potential vorticity, whose formula seems to take many odd forms.<span></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><span> </span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif">Best, <span></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><span> </span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif">Nick<span></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><a name="m_-7348361263660409556_m_7024090818089540325__MailAutoSig" rel="noreferrer"><span style="font-family:"Times New Roman",serif"><span> </span></span></a></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span><span style="font-family:"Times New Roman",serif"><span> </span></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span><span style="font-family:"Times New Roman",serif">Nicholas S. Thompson<span></span></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span><span style="font-family:"Times New Roman",serif">Emeritus Professor of Psychology
and Ethology<span></span></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span><span style="font-family:"Times New Roman",serif">Clark University,<span></span></span></span></p>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span><span style="font-family:"Times New Roman",serif"><a href="mailto:nthompson@clarku.edu" target="_blank" rel="noreferrer">nthompson@clarku.edu</a> <span></span></span></span></p>
<span></span>
<p class="MsoNormal" style="margin:0in;font-size:11pt;font-family:"Aptos",sans-serif"><span style="font-family:"Times New Roman",serif"><span> </span></span></p>
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