Transcript curved-flow_atmo170_lecture-12_2015

ATMO 170A1
Curved Flow
Centripetal Force
Vertical Velocity
DrM’s 1st Law of ATMO 170A1
RUC surface analysis for 1800 UTC Mar 01, 2010
Surface winds directed from high to low pressure
Simplified equation of horizontal atmospheric
motion
1 Dp
V2
0 =
+ 2WV sin f +
+ Fr
r Dx
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
GEOSTROHIC
BALANCE
LAST
TIME…
due to interaction with surface
Geostrophic Balance and Upper Level Winds
Winds aloft are very
close to geostrophic
CORIOLIS
FORCE
PRESSURE
GRADIENT
FORCE
Explains why…
1) Wind is parallel to
isobars… within
10°-15°
2) Wind speed
depends on
isobar spacing
GEOSTROPHIC
WIND
Geostrophic balance
can only exist where
flow is straight!
CURVED FLOW
CENTRIPETAL
ACCELERATION
NEEDED TO CHANGE
WIND DIRECTION
STRAIGHT FLOW
WINDS NEAR
GEOSTROPIC
BALANCE
Simplified equation of horizontal atmospheric
motion
1 Dp
V2
0 =
+ 2WV sin f +
+ Fr
r Dx
r
(1)
(2)
(3)
(4)
Term
Force
Cause
1
Pressure
gradient
force
FOCUS
ON
LAST
2
Coriolis force
Rotation of the Earth
3
Centripetal force
Curvature of the flow
4
Friction force
Acts against direction of motion
due to interaction with surface
Spatial
differences in pressure
TWO
TODAY…
Centripetal (3) and friction (4) forces are
typically much smaller than the PGF (1) or the
Coriolis (2) forces, but they are important for two
reasons
1. Can be relatively large in special cases that
are meteorologically important
1. Cause mass divergence and convergence,
which forces vertical motion
What is the Centripetal Force?
Circular Motion Requires
Acceleration or Force
Circle
Center
Circular
r
Path
Initial
Velocity
Radius r
of
Curvature
Final
Velocity
Final
Velocity
Initial
Velocity
V2
r
Acceleration
directed toward
center of circle
Centripetal force (center seeking force)
is required for a moving air parcel
to change its direction.
V2
r
r2
r4
r1
r3
Examples of r radius of curvature on a 500 mb map.
By convention, r is positive for flow about a trough.
r1 and r3 would be positive, and r2 and r4 negative.
As we will learn soon, upward motion is
needed to produce clouds and precipitation.
Hence, meteorologists want to know whether
the air is moving upward or downward.
Curved flow produces vertical motion through
the process of divergence and convergence,
but what are divergence and convergence?
http://www.richhoffmanclass.com/chapter6.html
Why does the upward motion
stop at a centain level?
Vertical motion tends to be dampened or
inhibited in areas of high static stability.
http://lukemweather.blogspot.com/
HORIZONTAL
DIVERGENCE
Fast
HORIZONTAL
CONVERGENCE
Slow
Note different speeds
into/out of sides
Fast
Slow
Note different speeds
into/out of sides
HORIZONTAL
DIVERGENCE
HORIZONTAL
CONVERGENCE
SINKING
ABOVE
RISING
ABOVE
RISING
BELOW
SINKING
BELOW
Top/Bottom Areas Expand
Column Shrinks
Top/Bottom Areas Shrink
Column Stretches
Area Expansion is called
Divergence
Area Expansion is called
Convergence
Flow Around Curved Contours
Assume PGF constant size
along entire channel
L
H
Centripetal
Acceleration
Required for
Parcel to Turn
But how does the atmosphere produce
the necessary centripetal force V2/r?
Forces for Curved Flow
By producing winds that
deviate by ~10% from
geostrophic winds
PGF
Slower
< |PGF| CF
yields a force to the
left of air motion
PGF
Faster
CF
|PGF|
yields a force to the
right of the air motion
Gradient Wind Balance
Centripetal = PGF +
Simplified equation of atmospheric motion
Gradient Wind Balance
×
1 Dp
V2
Total Force = 0 =
+ 2WV sinf +
+ Fr
r Dx
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
Assume size of PGF constant
along entire channel
Slower than
Geo Wind
Faster than
Geo Wind
Winds are
Slower than Geo at trough
Faster than Geo at ridge
So wind speeds tend to
Increase downwind of trough
Decrease downwind of ridge
But Something Else Happens Too
Assume size of PGF constant
along entire channel
2
1
1
2
Speeds and Areas:
Increase downwind of trough
Decrease downwind of ridge
Box stretches
Area expands
from 1 to 2
Mass Divergence and Convergence
Assume size of PGF constant
along entire channel
Large
Small
More mass goes
out than in
AS SHOWN ON THE NEXT SLIDES, THERE MUST BE COMPENSATING
VERTICAL MOTION DUE TO CHANGE IN WIND SPEED DOWNWIND OF
THE TROUGH.
MASS DIVERGENCE-COVERGENCE AT UPPER LEVELS
(DUE TO THE CHANGE IN WIND SPEED)
DIVERGENCE
Tropopause (acts as a lid)
INITIAL
WIND
FASTER
WIND
AIR
RISING
DOWNWIND OF A TROUGH
CONVERGENCE
Tropopause (acts as a lid)
INITIAL
WIND
SLOWER
WIND
AIR
SINKING
DOWNWIND OF A RIDGE
MASS DIVERGENCE-COVERGENCE AT UPPER LEVELS
(DUE TO THE CHANGE IN WIND SPEED)
DIVERGENCE
Tropopause (acts as a lid)
CONVERGENCE
Tropopause (acts as a lid)
Downwind
Trough
INITIAL
WIND
Downwind
Ridge
FASTER
WIND
AIR
RISING
DOWNWIND OF A TROUGH
INITIAL
WIND
SLOWER
WIND
AIR
SINKING
DOWNWIND OF A RIDGE
Storms form beneath areas of upper-level divergence
Lutgens and Tarbuck
Faster than geostrophic
Ridge
Slower than geostrophic
Trough
RED Grad Wind
CYAN Geo Wind
Divergence
Trough
Trough
Convergence
Divergence
Trough
Trough
Convergence
Summary: Curved Flow & Friction
• Curved Flow
Requires Centripetal Acceleration
Difference between PGF and Coriolis Force
Speed Changes => Convergence-Divergence
• Curvature
Leads to Vertical Motions…and Weather!
Assignment for Next Lecture
Friction; Air Masses and Fronts
• Reading - Ahrens
Pgs: 174-182; 223-234
• Questions for Review – Ahrens
Pg 182-183: 23, 24
Pg 254-255: 1, 11, 12, 13