1.%20The%20thermodynamic%20energy%20equation

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ATOC 4720 class35

• 1. The thermodynamic energy equation
• 2. The continuity equation

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Previous classes
Horizontal vector form
Components
Vertical equation of motion
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Brief Review of previous a few classes
Geostrophic wind value
T- days Mid-latitude
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Cross-isobar flow due to friction
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The gradient wind
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• Smaller-scale convection GEOSTROPHY BREAKS
• 
  DOWN

z
y
x
Observations for small-scale convection Velocity
U-V 20 m/s Time T (100-1000s)
S
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Hydrostatic balance
Hydrostatic balance is well satisfied even by
mesoscale convection.
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Thermal wind relation
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1. Thermodynamic energy equation
Rewrite hydrostatic equation (show math on
blackboard)
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Obviously, we have 3 equations, 4 unknowns We
need an equation for T. Prompt
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The first law of thermodynamics says
Denote as the heating rate
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Since
So,
Substituting into the above equation and denote
Where,
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Physics Temperature change is
determined by
1 the rate of adiabatic heating or cooling due
to compression or expansion 2 the rate
of diabetic heating.
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Scale analysis estimating the relative important
of adiabatic and diabetic heating
1 Adiabatic heating
Typical pressure change over the course of a day
following an air parcel
In mid latitude mid-troposphere,
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2 Diabetic heating absorption of solar
radiation, absorption and emission of
infrared radiation, latent heat release,
in upper atmosphere,heat absorbed or
liberated in chemical photochemical reactions.
Diabetic mixing with environment (latent
sensible). In lower atmosphere, sources
and sinks tend to balance each other. As a
result,
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Note that all time-dependent term we introduced
so far is
Time change following an individual air parcel.
(Lagrangian)
In most cases, we wish to know time change at a
Specific location, say T change over Boulder.
Local change Eularian change.
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Since
We obtain
Because,
We have
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3-d advection
Local change
Individual change
Cold T
Warm T
Tb
Ta
Boulder
Mountain in the west