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CLIMATE/EARTH 401�Geophysical Fluid Dynamics�Dynamical Meteorology

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/

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Potential Vorticity: Introduction

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Scaled vorticity equation (terms of 10-10 s-2)

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Potential vorticity

  • Potential Vorticity is a variable that combines the absolute vorticity and some measure of the thickness of a column of air.
  • It links dynamic and thermodynamic properties.
  • In a generalized definition, it is conserved in adiabatic motion.

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A simple version of potential vorticity

returned relative vorticity to equation

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A simple version of potential vorticity

Horizontal divergence

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A simple version of potential vorticity

Assume constant density and temperature.

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A simple version of potential vorticity

Integrate with height,z1 🡪 z2 over a layer of depth H.

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A simple version of potential vorticity

Integrate with height,z1 🡪 z2 over a layer of depth H.

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A simple version of potential vorticity

  • This is the potential vorticity under the set of assumptions that we used to derive the equation.
    • Constant density, constant temperature 🡪 so this is only relevant to the atmosphere in a shallow layer.

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  • But the key is…
    • Potential vorticity is a measure of absolute vorticity relative to the depth of the vortex.

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Relative vorticity with change of depth

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What happens when the vortex meets the mountain?

Surface with a hill.

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Vorticity and depth

  • We can see that there is a relationship between depth and vorticity.
  • As the depth of the vortex changes, the relative vorticity has to change in order to conserve the potential vorticity.
  • We have now linked the rotational and irrotational components of the wind.
    • divergence and curl
    • vorticity and divergence
  • Potential vorticity indicates an interplay between relative and planetary vorticity through conservation of absolute angular momentum.

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End: Potential Vorticity: Introduction

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/