Transcript Surface Winds, Vertical Air Motions

NATS 101
Lecture 13
Curved Flow and Friction
Local Diurnal Winds
QuickTime™ and a
decompressor
are needed to see this picture.
Mullen’s 1st Law of NATS 101
Clicker=Points
RUC surface analysis for 1800 UTC Mar 01, 2010
that shows winds blowing from high to low pressure
Last time we talked about two of the force
terms in the simplified equation for
horizontal air motion
Geostrophic Balance:
PRESSURE GRADIENT = CORIOLIS
Geostrophic Wind and Upper Level Charts
CORIOLIS
FORCE
PRESSURE
GRADIENT
FORCE
GEOSTROPHIC
WIND
Winds at upper
levels are pretty
close to being
geostrophic:
Wind is parallel to
isobars
Wind strength
dependents on
how close together
isobars are
Simplified equation of horizontal atmospheric
motion
1 p
V2
Total Force 
 2V sin  
 Fr
 d
r
(1)
(2)
(3)
(4)
Term
Force
Cause
1
Pressure gradient force
Spatial differences in pressure
2
FOCUS
Coriolis
force
3
Centripetal force
4
ON LAST TWO
TODAY…
Rotation
of the Earth
Curvature of the flow
Friction force
Acts against
direction
of motion
GEOSTROHIC
BALANCE
LAST
TIME…
due to interaction with surface
The centripetal force and friction force are
typically much smaller, but they are very
important for two reasons:
1. Cause mass divergence and convergence
2. Can be relatively large in special cases that
are meteorologically important (i.e. cool)
MASS DIVERGENCE
MASS CONVERGENCE
AIR RISING
ABOVE
AIR SINKING
ABOVE
INITIAL
WIND
FASTER
WIND
AIR RISING
BELOW
MASS LOST
INITIAL
WIND
SLOWER
WIND
AIR SINKING
BELOW
MASS GAINED
To begin a discussion of centripetal force,
let’s address the popular belief about how
water goes down the drain…
Popular belief: The way the toilet flushes or
the sink drains depends on which hemisphere
you’re in.
Bart vs. Australia Simpson’s episode: Bart calls an
Australian boy to see if his toilet really does flush
clockwise…We’ll see what the surprising answer is later.
Centripetal Force =
V2
r
Arises from a change in wind direction with a constant speed (v)
due to the curvature of the flow around a radius (r)
Centripetal acceleration (a)
(towards the center of circle)
Center of circle
-V1
V2
Final velocity
V1
Initial velocity
a
a
v 2  v1
t
V2
The centripetal acceleration is always directed toward the center of
the axis of rotation.
Note to be physically correct, the expression should have a
negative sign, so +V2/r is actually the centrifugal acceleration.
Centripetal Force
CENTRIFUGAL
FORCE
CENTRIPETAL
FORCE
You experience acceleration
without a change in speed, for
example, on a tilt-a-whirl
carnival ride.
The force is directed toward
the center of the wheel.
An equal an opposite
(fictitious) centrifugal force is
exerted by the inertia of your
body on the wheel—so you
stay put and don’t fall off even
when upside down.
CENTRIPETAL
ACCELERATION
NEEDED ACCOUNT FOR
THE CURVATURE OF
THE FLOW
WINDS IN
GEOSTROPIC
BALANCE FOR
STRAIGHT FLOW
Recall: Uniform Circular Motion
Requires Acceleration/Force
Circle
Center
Circular
Path
Initial
Velocity
Final
Velocity
Final
Velocity
Initial
Velocity
Acceleration
directed toward
center of circle
Centripetal (center seeking) acceleration is required for
curved flow, i.e. to change the direction of the velocity vector!
Flow Around Curved Contours
Assume PGF constant size
along entire channel
L
H
Centripetal
Acceleration
is Required
for Air Parcel
to Curve
Flow Around Curved Contours
Assume PGF constant size
along entire channel
L
H
Centripetal
Acceleration
How does atmosphere produce the necessary centripetal force?
Forces for Curved Flow
Assume PGF constant size
along entire channel
PGF
Wind
PGF
PGF
CF
CF
Wind
Centripetal = PGF + CF
CF
Centripetal << PGF or CF
Gradient Wind Balance
Simplified equation of atmospheric motion
Gradient Wind Balance


1 p
V2
Total Force 
 2V sin  
 Fr
 d
r
(1)
(2)
(3)
(4)
Term
Force
Cause
1
Pressure gradient force
Spatial differences in pressure
2
Coriolis force
Rotation of the Earth
3
Centripetal force
Curvature of the flow
4
Friction force
Acts against direction of motion
GRADIENT WIND BALANCE…
due to interaction with surface
Gradient Wind Balance: End Result
Assume PGF constant size
along entire channel
Slower than
Geo Wind
Faster than
Geo Wind
Wind speeds are
Slower at trough
Faster at ridge
Therefore, wind speeds
Increase downwind of trough
Decrease downwind of ridge
Gradient Wind Balance
Assume PGF constant size
along entire channel
2
1
1
Speeds and Areas:
Increase downwind of trough
Decrease downwind of ridge
2
Divergence and Convergence
Assume PGF constant size
along entire channel
Divergence: Horizontal
Area Increases with Time
Convergence: Horizontal
Area Decreases with Time
Parcel Shapes:
Stretch Downwind of
Trough so Area Increases
Compress Downwind of
Ridge so Area Decreases
Divergence and Convergence
Assume PGF constant size
along entire channel
Large
Small
Mass transport
across channel
THERE MUST BE COMPENSATING VERTICAL MOTION DUE TO
CHANGES IN WIND SPEED AHEAD OF THE TROUGH AND RIDGE.
MASS DIVERGENCE AND COVERGENCE AT UPPER LEVELS
(DUE TO CURVATURE OF THE FLOW)
MASS DIVERGENCE
Stratosphere (acts as a lid)
INITIAL
WIND
FASTER
WIND
AIR
RISING
DOWNWIND OF A TROUGH
UPWIND OF A RIDGE
MASS CONVERGENCE
Stratosphere (acts as a lid)
INITIAL
WIND
SLOWER
WIND
AIR
SINKING
UPWIND OF A TROUGH
DOWNWIND OF A RIDGE
Relationship between upper-level
troughs-ridges and vertical motion
Ridge
Trough
Ridge
JET LEVEL
~300 mb
SURFACE
Surface
High
SINKING MOTION
TYPICALLY STABLE
(clear skies likely)
Surface Low
Gedzelman, p249
RISING MOTION
MAY BE CONDITIONALLY UNSTABLE
(if clouds form and air is saturated)
Faster than geostrophic
Ridge
Slower than geostrophic
Trough
Divergence
Trough
Trough
Convergence
Divergence
Convergence
Gradient balance and flow around lows
and highs (Northern Hemisphere)
Cent. force
Cent. force
Counterclockwise flow
around lows
Clockwise flow
Around highs
Flow around low pressure
NORTHERN HEMISPHERE
Counterclockwise flow
SOUTHERN HEMISPHERE
Clockwise flow
(because Coriolis force reverses
with respect to wind direction)
There is another force balance possible
if the Coriolis
force is very small or zero,
so it’s negligible.
In that case,
the pressure gradient force would
balance the centripetal force.
Simplified equation of atmospheric motion
Cyclostrophic Balance



1 p
V2
Total Force 
 2V sin  
 Fr
 d
r
(1)
(2)
(3)
(4)
Term
Force
Cause
1
Pressure gradient force
Spatial differences in pressure
2
Coriolis force
Rotation of the Earth
3
Centripetal force
Curvature of the flow
4
Friction force
Acts against direction of motion
CYCLOSTROPHIC BALANCE…
due to interaction with surface
Cyclostrophic Balance
PGF + Centripetal Force = 0
OR
PGF = Centrifugal Force
L
Pressure
Gradient
Force
Centrifugal
Force
Pressure gradient balances
the centrifugal force.
Occurs where flow is on a
small enough scale where
the Coriolis force becomes
negligible.
Important for understanding (really cool) meteorological phenomena
that have extremely strong winds and tight pressure gradients!
TORNADOES
Examples of
Cyclostrophic Flow
HURRICANES
And
flushing
toilets,
too!!
The Unsolved Mystery
of the
Flushing Toilet Solved!
Centrifugal
force
PGF
To Bart and Lisa: “A swirling, flushing toilet is in cyclostrophic
balance, so the way it flushes depends more on the shape of the
drain—and nothing to do with whether you’re in Australia or not!”
One last force to consider…
Friction
Friction
Pressure Gradient Force
1004 mb
Friction
Geostrophic Wind
1008 mb
Coriolis Force
Frictional Force is directed opposite to velocity.
It acts to slow down (decelerate) the wind.
Once the wind speed becomes slower than the
geostrophic value, geostrophic balance is
destroyed because the Coriolis Force decreases.
Friction
Pressure Gradient Force
1004 mb
Friction
Wind
1008 mb
Coriolis Force
Because PGF becomes larger than CF, air
parcel will turn toward lower pressure.
Friction Turns Wind Toward Lower Pressure.
Friction
1004 mb
Wind
1008 mb PGF
CF
Fr
Eventually, a balance among the PGF, Coriolis
and Frictional Force is achieved.
PGF + CF + Friction = 0
Net force is zero, so parcel does not accelerate.
Friction
1004 mb
Mtns
30o-50o
Water
10o-30o
1008 mb
The decrease in wind speed and deviation to
lower pressure depends on surface roughness.
Smooth surfaces (water) show the least slowing
and turning (typically 10o-30o from geostrophic).
Rough surfaces (mtns) show the most slowing
and turning (typically 30o-50o from geostrophic).
Friction
1004 mb
SFC 0.3 km
0.6 km
~1 km
1008 mb
Friction is important in the lowest km above surface.
Its impact gradually decreases with height.
By 1-2 km, the wind is close to geostrophic balance,
gradient wind balance, or cyclostrophic.
www.met.tamu.edu
Flow in Surface Lows and Highs
Gedzelman, p249
Spirals Outward
Divergence
Spirals Inward
Convergence
MASS DIVERGENCE AND CONVERGENCE AT SURFACE
(DUE TO THE FORCE OF FRICTION)
MASS DIVERGENCE
MASS CONVERGENCE
AIR
RISING
AIR
SINKING
INITIAL
WIND
L
FASTER
WIND
INITIAL
WIND
H
SLOWER
WIND
Ground is a solid barrier
Ground is a solid barrier
Flow into Lows
Flow out of Highs
Friction Induced Vertical Motion
Ahrens, Fig 6.22
Air curves inward toward
surface low pressure.
Air curves outward away
from surface high pressure
Mass convergence and
rising motion
Mass divergence and
sinking motion.
Divergence
Convergence
Divergence
Surface Convergence and Divergence
Summary of Force Balances
Why the Wind Blows
Force Balance
Forces Involved
Where it happens
Geostrophic
Pressure gradient, Coriolis
Winds at upper levels
(with no curvature)
Gradient
Pressure gradient, Coriolis,
Centripetal (or Centrifugal)
Winds at upper levels
with curvature
Cyclostrophic
Pressure Gradient, Centrifugal
Smaller-scale, tight
rotations like tornadoes
and hurricanes (sinks too)
Gradient +
Friction
Pressure Gradient, Coriolis,
Centripetal, Friction
Surface winds
Assignment for Next Lecture
Local Winds, Monsoons
• Reading - Ahrens
3rd: Pg 165-178
4th: Pg 167-181
5th: Pg 169-184
• Homework06 - D2L (Due Monday Mar. 22)
3rd-Pg 194: 7.3, 4, 5
4th-Pg 198: 7.3, 4, 5
5th-Pg 200: 7.3, 4, 5
Do Not Hand in 7.3
Assignment for Next Lecture
• QUIZ 2 this Thursday
D2L only
Similar format as before
7 am -12 pm time period for the exam
70 minutes to finish test