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 Final Velocity Circular Path Acceleration directed toward center of circle Final Velocity Initial Velocity Initial Velocity 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 5700 m 5640 m L H Zero Required Centripetal Acceleration

Assume PGF constant size along entire channel Forces for Curved Flow Assume PGF constant size along entire channel PGF 5700 m 5640 m Wind PGF Geo Wind PGF CF CF Wind Centripetal = CF + PGF Centripetal << CF or PGF Gradient Wind Balance CF

Assume PGF constant size along entire channel Gradient Wind Balance Assume PGF constant size along entire channel Faster than Geo Wind 5700 m 5640 m Wind Speed Decreases Wind Speed Increases Geo Wind Wind speeds are Slowest at trough Fastest at ridge Therefore, wind speeds Increase downwind of trough Decrease downwind of ridge Slower than Geo Wind

Assume PGF constant size along entire channel Gradient Wind Balance Assume PGF constant size along entire channel Wind Speed Decreases Wind Speed Increases 5700 m 5640 m Wind Speed Decreases Area Increases 2 Area Decreases 1 Speeds and Areas: Increase downwind of trough Decrease downwind of ridge

Divergence and Convergence Assume PGF constant size along entire channel Area Increases Divergence Area Decreases Convergence Parcel Shapes: Stretch downwind of trough Compress downwind of ridge

Divergence and Convergence Assume PGF constant size along entire channel Divergence Net Mass Loss Convergence Net Mass Gain Large Mass transport across channel Small

Vertical Motion Ridge Ridge Trough Gedzelman, p249 Mass Conservation leads to Upward motion beneath regions of divergence Downward motion beneath regions of convergence

500mb WV Animation (Java applet) Convergence Divergence Divergence 500mb WV Animation (Java applet)

Super-geostrophic Sub-geostrophic

Divergence Convergence

Convergence Divergence

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.

Friction Turns Wind Toward Lower Pressure. Force of Friction 2 Pressure Gradient Force 1004 mb Wind Friction 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 CF PGF 1008 mb 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 SFC 0.3 km 1004 mb 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 Heat Warm Cold Rising Sinking DIV CON

Sea Breeze Development (Courtesy of Mohan Ramamurthy, WW2010) 3 4

Sea Breeze Development (Courtesy of Mohan Ramamurthy, WW2010) 5 6 Rising Sinking DIV CON Heat 7

Sea Breeze versus Land Breeze (Courtesy of Mohan Ramamurthy, WW2010) PM Stronger Temperature contrast during PM than during AM Sea breezes are stronger than land breezes AM LAX Airport 4 PM upper 7 AM lower

Florida Satellite Loop 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 Rising Sinking DIV CON Heat Sun warms slopes Density decreases Air rises 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.

Phoenix-Tucson Diurnal Winds AM TUS Phoenix-Tucson Diurnal Winds PM TUS 5 PM 5 AM PM heating AM cooling 5 PM 5 AM PM heating AM cooling AM PHX PM PHX

Assignment for Next Lecture Reading - Ahrens pg 167-181 Problems - 7.3, 7.4, 7.5