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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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Lagrangian & Eulerian Visuals & Examples

  • Link to Mount Pinatubo trajectories at end.

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Advection examples

  • Advection of sand in TX and near the Saharan desert

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Using temperature, T, as an example): �Local Changes & Material Derivative

Local change�at a fixed location

(Eulerian(

Total change along�a trajectory (Lagrangian)

Advection term

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Meteorology: Temperature Advection & Convection

Advection: Heat transport by the wind in the horizontal direction

Convection: Heat transport by the mass movement of the air� in the vertical direction

Source: University of Wisconsin AOS

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An Eulerian Map

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Another Perspective

Eulerian view: �Anchored (fixed) buoys that �measure the ocean temper.

Lagrangian view: �Drifting buoys that�measure T during their drift

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Consider some parameter, like temperature, T

x

y

Material derivative, T change following the parcel

(Lagrangian)

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Consider some parameter, like temperature, T

x

y

Local T change at a fixed point (Eulerian)

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Consider some parameter, like temperature, T

x

y

Advection (Eulerian)

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Consider some parameter, like temperature, T

x

y

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Temperature advection term

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Temperature advection term

http://ww2010.atmos.uiuc.edu/%28Gh%29/guides/mtr/af/adv/adv.rxml

���http://ww2010.atmos.uiuc.edu/%28Gh%29/wwhlpr/fcst_temps_advection.rxml?hret=/guides/mtr/af/adv/adv.rxml

​

Advection:

Temperature advection:

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Advection of cold or warm air

  • Temperature advection:
  • Imagine the isotherms are oriented in the E-W direction���
  • ���
  • Draw the horizontal temperature gradient vector
  • pure west wind u > 0, v=0, w=0:
    • Is there temperature advection?
    • If yes, is it cold or warm air advection?

cold

warm

u

X

y

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Advection of cold or warm air

  • Temperature advection:
  • Imagine the isotherms are oriented in the E-W direction������

​

  • Draw the gradient of the temperature (vector)
  • pure south wind v > 0, u=0, w=0:
    • Is there temperature advection?
    • If yes, is it cold or warm air advection?

cold

warm

v

X

y

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Advection of cold or warm air

  • Temperature advection:
  • Imagine the isotherms are oriented as�������
  • Draw the horizontal temperature gradient
  • pure west wind u > 0, v=0, w=0:
    • Is there temperature advection?
    • If yes, is it cold or warm air advection?

cold

warm

u

X

y

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Identify warm/cold air advection on a map

In NH:�Air rotates�clockwise�around H

In NH:�Air rotates�counter-�clockwise�around L

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Lagrangian point of view: Eruption of Mount Pinatubo

  • Trajectories trace the motion of individual fluid � parcels over a finite time interval
  • Volcanic eruption in 1991 injected particles into � the tropical stratosphere (at 15.13 N, 120.35 E)
  • The particles got transported by the atmospheric � flow, we can follow their trajectories
  • Mt. Pinatubo, NASA animation :
  • Colors in animation reflect the atmospheric height of � the particles. Red is higher, blue closer to the surface.
  • This is a Lagrangian view of transport processes.

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End: Lagrangian & Eulerian Visuals & Examples

Richard B. Rood

rbrood@umich.edu

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

https://openclimate.org/