Download AirForces

PHSC 3033: Meteorology
Air Forces
Pressure Gradient
∆P/∆d = Pressure Gradient (Change in Pressure/Distance)
Horizontal Pressure Gradient Force (PGF):
Force due to pressure differences, and the cause of
air movement (winds) on the surface of the Earth.
Horizontal Pressure Gradient Force (PGF)
Air moves from High
pressure to Low
pressure.
The force provided by
the pressure difference
is the pressure gradient
force. Force is directed
perpendicular to the
isobars from Highs to
Lows.
Isobars
Isobars = Contours of Constant Pressure
Topographical Analogy: Just as close topographic lines
indicate steep terrain, close isobars mean steep pressure
gradient, large pressure force and therefore strong winds.
SURFACE MAP
Standard Isobaric Levels
Each isobaric level picks
out a general altitude to
study. These are constant
altitude charts, similar to
the surface map.
Bernoulli’s Principle
Pressure is lower for faster steady flow than for slower
Higher v, Lower P
Airplane Wings
Lower v, Higher P
Bernoulli’s Equation
Recall that WORK = change in both Potential Energy
and Kinetic Energy.
W = Force * Distance
=PAx
=PV
Finally, P2, v2, x2, h2, A2
h2
Initially, P1, v1, x1, h1, A1
Bernoulli’s Equation
∆ KE = 1/2 m (v2-v1)2
∆ PE = mg (h2-h1)
Finally, P2, v2, x2, h2, A2
h2
Initially, P1, v1, x1, h1, A1
Bernoulli’s Equation
∆ KE = 1/2 m (v2-v1)2
∆ PE = mg (h2-h1)
∆W = ∆KE + ∆PE
Leads to the equation of continuity...
P + 1/2 ρ v2 + ρ g h = constant
The sum of pressure, kinetic energy per volume and
potential energy per volume have the same value
along all points in a streamline.
Wind Speed Vectors
Vectors are arrows representing wind direction and
speed.
Coriolis
Coriolis FORCE
A. Force: due to a rotating frame of reference.
B. Objects moving in a straight line with respect to the stars,
will experience an apparent deflection to the RIGHT in
the N.Hemisphere and an apparent deflection to the LEFT
in the S. Hemisphere.
C. The Coriolis force is strongest at the poles and zero at the
equator.
D. The Coriolis force is proportional to the speed.
E. The "force" affects the direction NOT the speed.
But since velocity is a vector, with both direction and
speed, the velocity change is the same as acceleration and
the Coriolis force is the culprit.
Coriolis Force Equation
Relative to a carousel, someone walking on a carousel
moves in a straight line with respect to the fixtures.
Relative to others and equipment on the ground,
the person moves in an arc as if affected by a force.
The Coriolis Force
Fc = 2Ω v sin φ
v = wind speed
Ω = angular velocity (Earth rotation, 360 degrees/24 hours)
φ = latitude
(sin 0 = 0.0 equator, sin 90 = 1.0 poles)
Coriolis Deflection
Fc = 2Ω v sin φ
Increase of the
Coriolis Force with
wind speed.
Density and Pressure
• The warmer air column is less dense.
• At the same height, the pressure is higher in the
warmer air column.
Latitude Pressure Gradient
• At the same altitude, the pressure is higher on average in the
warmer latitudes.
Temperature PGF versus Altitude
Global Circulation
• In the absence of rotation, air would tend to flow
from the equator toward the poles.
Hot, less dense air
rising at the equator,
becomes denser as
it cools and descends
at the poles, traveling
back to tropical areas
to heat up again.
Pressure Gradient Force
• Air flows from high pressure to low pressure, so on average,
from the equators to the poles.
Geostrophic Flow
PGF = Coriolis
1/ρ*∆P/∆d = 2 Ω v sin φ
The wind velocity is v = (1/ρ 2 Ω sin φ)*∆P/∆d
This is known as the geostrophic wind equation.
Geostrophic flow
• Remember that the coriolis force depends upon
velocity.
As air is accelerated by
the PGF its speed
increases and the
coriolis deflection
grows. Equilibrium is reached when the PGF and
coriolis effect are equal.
Geostrophic flow
• With the inclusion of the Coriolis Force, air flows
parallel to isobars of constant pressure.
Westerlies
• At mid latitudes, air moving from S. to N. in the
northern hemisphere flows from west to east.
Bernoulli Winds
Friction Effect
Friction retards
wind speed near
the surface due
to topography,
lowering the
coriolis force.
Therefore, wind
direction is
altered from
parallel to isobars.
Cyclonic Flow
Low Pressure Cyclonic Winds
High Pressure Cyclonic Winds
Isobar Surface Map
Table 7.2: Summary of the properties of forces acting on air in the Earth’s atmosphere
Force
Direction in which
force acts
Strength depends
on
Effect on air
Balances
Vertical Pressure Gradient
Force
Upward, from higher to
lower pressure
Magnitude of the
vertical pressure
gradient
Accelerates air
vertically toward lower
pressure
Hydrostatic balance
when equal and
opposite to
gravitational force
Horizontal Pressure gradient
force
Horizontally, from
higher to lower pressure
Magnitude of the
horizontal pressure
gradient
Accelerates air
horizontally
Geostrophic balance
when equal and
opposite to Coriolis
force
Coriolis Force
To the right (left) of the
wind direction in the
Northern (Southern)
Hemisphere
Wind speed and
latitude
Affects wind direction,
but no effect on wind
speed
Geostrophic balance
when equal and
opposite to
horizontal pressure
gradient force
Frictional force
Gravitational force
Opposite the direction
of the flow
The roughness of the
underlying surface
Reduces air velocity,
important primarily in
boundary layer
Toward the center of the
earth
Essentially constant
in the troposphere
Accelerates air
downward
_________
Hydrostatic balance
when equal and
opposite to vertical
pressure gradient
force.