Forces (gravity, pressure gradient force)

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Lecture 7

• Forces (gravity, pressure gradient force)
• Imaginary forces (Coriolis, centrifugal)
• Force balance and resulting horiz. wind
• Geostrophic wind
• Gradient wind
• Adjustment to balance
• The thermal wind (change in geostrophic wind in
  the vertical)

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Wind direction is the direction from which the
wind is blowing. Wind direction is expressed in
degrees
Units m/s or knots 1 knot 0.5 m/s 1knot 1
mile/hr
Wind speed is expressed in terms of the
flagpole
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Newtons law of motion

• A body at rest tends to stay at rest a body in
  motion tends to stay in motion, traveling at a
  constant speed in a straight line.
• A force exerted on a body of mass m causes the
  body to accelerate in the direction of the
  applied force.
• Force mass x acceleration

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A force has direction and magnitude (it is a
vector). Adding two forces is vector addition.
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Forces that move the air

• Gravitational force (g9.8 m/s2)
• Pressure gradient force (-1/rho x dp/dx or
  --1/rho x dp/dy). It points toward lower p. The
  pressure gradients causing the wind are
  horizontal.
• Coriolis force
• Centrifugal force
• Frictional force

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Pressure gradient force pushes from higher to
lower pressures
PGF
Magnitude depends on value of pressure gradient
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Isobaric chart (height contours on a constant
pressure surface)
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Pressure (p) as a function of height
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Vertical structure in the atmosphere

• What about pressure?
• Hydrostatic equation balance between pressure
  gradient force and gravity.
• dp/dz - rho g
• Ideal gas law
• p rho R T

Lets go to the board!
z - H ln (p/p0), where H is scale height and
is only constant if T is constant. In other
words, p p0 exp(- z/H)
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Next Coriolis forceEarths rotational speed is
greatest at the equator and exactly zero at the
poles
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Coriolis deflection
Coriolis force deflects moving air to the right
in the Northern Hemisp.
Coriolis force deflects moving air to the left
in the S. Hemisphere
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The magnitude of the Coriolis force (CF) is
proportional to the wind speed and sine of
latitude
CF f x V, Where f is 2xEarths rotation rate
xsin(latitude)
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Centrifugal force arises because the trajectory
is curved. CENTF V2/R, where R (radius of
curvature) is positive for cyclones, negative for
anticyclones
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Frictional force is proportional to the wind-
speed and directed opposite to the wind dir.
FF -k V (where k describes the roughness)
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Summary The Forces

• Gravity the strong silent type
• PGF arises from pressure gradients generated by
  differential solar heating leads to wind. Only
  then do the other forces start acting.
• CF, CENTF, FF all depend of V, wind speed.

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Atmospheric force balancesSum of forces mass x
accelerationBalance when the forces add up to
zero

• Hydrostatic balance in the vertical (gravity does
  not cause wind).
• Strong horizontal PGF means strong wind
• CF changes wind direction not speed
• CENTF only acts on curved flow
• FF slows down the wind (regardless of direction).

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Geostrophic wind, geostrophic balancePGF CF 0
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Wind blows counterclockwise around lows (cyclonic
wind in cyclones), clockwise around highs
(anticyclones)
Force balance not quite right since we have
curved flows
Add centrifugal force
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Gradient balance and the gradient wind
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Gradient balance results in gradient wind

• Represents balance of three forces
• It is an excellent approximation to free
  atmospheric flow.
• Around highs it is supergeostrophic
• Around lows it is subgeostrophic

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Adjustment to balance

• The atmosphere tries hard to stay in balance, but
  it is constantly being pushed away from it.
• The atmosphere adjusts very quickly (in a matter
  of minutes) to imbalance.

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Adjustment to balance with 3 forces