NATS 101-05
Lecture 12
Curved Flow and Friction
Local winds
Supplemental References for
Today’s Lecture
Gedzelman, S. D., 1980: The Science and Wonders of the Atmosphere.
535 pp. John-Wiley & Sons. (ISBN 0-471-02972-6)
Danielson, E. W., J. Levin and E. Abrams, 1998: Meteorology. 462 pp.
McGraw-Hill. (ISBN 0-697-21711-6)
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
Required
Centripetal
Acceleration
Forces for Curved Flow
Assume PGF constant size
along entire channel
PGF
Wind
PGF
PGF
CF
CF
Wind
Centripetal = CF + PGF
CF
Centripetal << CF or PGF
Gradient Wind Balance
Gradient Wind Balance
Assume PGF constant size
along entire channel
Slower than
Geo Wind
Faster than
Geo Wind
Wind speeds are
Slowest at trough
Fastest 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
Speeds and Areas:
Increase downwind of trough
Decrease downwind of ridge
Divergence and Convergence
Assume PGF constant size
along entire channel
Parcel Shapes:
Stretch downwind of trough
Compress downwind of ridge
Divergence and Convergence
Assume PGF constant size
along entire channel
Large
Small
Mass transport
across channel
Vertical Motion
Ridge
Trough
Ridge
Gedzelman, p249
Mass Conservation leads to
Upward motion beneath regions of divergence
Downward motion beneath regions of convergence
Convergence
Divergence
Divergence
500mb WV Animation (Java applet)
Super-geostrophic
Sub-geostrophic
Divergence
Convergence
Divergence
Convergence
Now
Add Friction near the surface…
This changes the force balance
Force of Friction 1
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.
Force of Friction 2
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.
Force of Friction 3
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.
Force of Friction 4
1004 mb
Mtns
30o-40o
Water
20o-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 20o-30o from geostrophic).
Rough surfaces (mtns) show the most slowing
and turning (typically 30o-40o from geostrophic).
Force of Friction 5
1004 mb
SFC 0.3 km
0.6 km
~1 km
1008 mb
Friction is important in the lowest km above sfc.
Its impact gradually decreases with height.
By 1-2 km, the wind is close to geostrophic or
gradient wind balance.
Flow at Surface Lows and Highs
Gedzelman, p249
Spirals Outward
Divergence
Spirals Inward
Convergence
www.met.tamu.edu
Friction Induced Vertical Motion
downward motion
upward motion
Ahrens, Fig 6.21
Summary
• Curved Flow
Requires Centripetal Acceleration
Difference between PGF and Coriolis Force
Speed Changes => Convergence-Divergence
• Frictional Force
Causes Winds to Turn toward Low Pressure
Important in the lowest 1 km above the Surface
Leads to Convergence-Divergence
• Curvature and Friction
Leads to Vertical Motions
Atmospheric Scales of Motion
Ahrens, Fig 7.1
Review:
Thermally Direct Circulation
DIV
CON
Heat
Heat
Warm Rising
Sinking Cold
CON
DIV
Heat
Heat
Sea Breeze Development
(Courtesy of Mohan Ramamurthy, WW2010)
1
2
3
4
Sea Breeze Development
(Courtesy of Mohan Ramamurthy, WW2010)
5
7
6
DIV
CON
Rising
Sinking
CON
DIV
Heat
Heat
PM
Sea Breeze versus Land Breeze
(Courtesy of Mohan Ramamurthy, WW2010)
AM
Stronger Temperature
contrast during PM
than during AM
Sea breezes are stronger
than land breezes
LAX Airport
4 PM upper
7 AM lower
Sea Breeze
• Regular feature of many coastal areas
California, Florida, Gulf Coast
• Occurs along large lakes-Great Lakes
• Typically strongest during Spring-Summer
• Can penetrate inland 50 km or more
• Temperatures can drop ~10oC
• Nose of cool air can trigger thunderstorms
Florida Satellite Loop
Mountain-Valley Breeze
DIV
Sun warms slopes
Density decreases
Air rises
CON
Rising
Sinking
CON
DIV
Heat
Heat
IR cools slopes
Density increases
Air drains
Ahrens, Older Ed.
Mountain-Valley circulation important to Tucson
Convection over Catalinas during PM summer.
SE drainage flows during early AM all year.
AM
TUS
PM
TUS
Phoenix-Tucson Diurnal Winds
5 AM
AM
5 PM
5 AM
PHX
PM heating
AM cooling
5 PM
PM
PM heating
AM cooling
PHX
Assignment for Next Lecture
• Reading - Ahrens pg 167-181
• Problems - 7.3, 7.4, 7.5