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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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Vorticity 4: Divergence Term

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Vorticity and Divergence

  • Related to shear �of the velocity field.

∂v/∂x-∂u/∂y

  • Related to stretching �of the velocity field.

∂u/∂x+∂v/∂y

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Let’s go through this term by term

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Divergence Term

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Divergence

  • Divergence is related to vertical motion

Divergence

Absolute Vorticity

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Vertical motion and horizontal divergence

  • Vertical wind is related to divergence of the horizontal wind.
    • Through mass continuity equation
    • Requires an ageostrophic part of the wind
    • Related to D( )/Dt of surface pressure

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  • Changes in vorticity are related to divergence of the horizontal wind

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Pure constant vorticity flow.

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Pure divergent flow

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Divergence influence on vorticity

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Divergence influence on vorticity

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Let's consider a spinning skater

Motion is in the (x,y) plane

Axis of rotation is in the vertical plane

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End: Vorticity 4: Divergence Term

Richard B. Rood

rbrood@umich.edu

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

https://openclimate.org/