NATS 101

Lecture 17Curved Flow and Friction

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)

Recall: Uniform Circular Motion Requires Acceleration/Force

Initial Velocity

Final Velocity

Acceleration directed toward center of circleInitial

Velocity

Final Velocity

Circular Path

Circle Center

Centripetal (center seeking) acceleration is required for Centripetal (center seeking) acceleration is required for curved flow, i.e. to change the direction of the velocity vector! curved flow, i.e. to change the direction of the velocity vector!

Flow Around Curved Contours

5700 m5640 m

Required Centripetal Acceleration

LL HHZero

Zero

Assume PGF constant size along entire channel

Forces for Curved Flow

5700 m5640 m

Centripetal = CF + PGF

Centripetal << CF or PGF

Gradient Wind Balance

Wind

Wind

Geo W

indPGF

PGF

PGF

CF

CF

CF

Assume PGF constant size along entire channel

Gradient Wind Balance

5700 m5640 m

Wind speeds are Slowest at trough Fastest at ridge

Therefore, wind speeds Increase downwind of trough Decrease downwind of ridge

Slower than Geo Wind

Faster than Geo Wind

Geo W

ind

Wind Sp

eed

Incr

eases

Wind Speed

Decreases

Assume PGF constant size along entire channel

Gradient Wind Balance

Speeds and Areas: Increase downwind of trough Decrease downwind of ridge

Wind Sp

eed

Incr

eases

Wind Speed

Decreases

Wind Speed

Decreases

5700 m5640 m

Area

Incr

eases

1

2

Assume PGF constant size along entire channel

Area

Decreases

Divergence and Convergence

Parcel Shapes: Stretch downwind of trough Compress downwind of ridge

Area I

ncrea

ses

Diverg

ence

Area Decreases

Convergence

Assume PGF constant size along entire channel

Divergence and Convergence

Diverg

ence

Net M

ass L

oss

Convergence

Net Mass Gain

Mass transport across channel

Large

Small

Assume PGF constant size along entire channel

Gedzelman, p249

Vertical Motion

Mass Conservation leads to Mass Conservation leads to Upward motion beneath regions of divergence Upward motion beneath regions of divergence Downward motion beneath regions of convergenceDownward motion beneath regions of convergence

ConvergenceConvergenceDivergenceDivergenceDivergenceDivergence

500mb WV Animation (Java applet)

Force of Friction 1

Pressure Gradient Force

Coriolis Force

Geostrophic Wind

1004 mb

1008 mb

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

Force of Friction 2

Pressure Gradient Force

Coriolis Force

Wind1004 mb

1008 mb

Because PGF becomes larger than CF, air parcel will turn toward lower pressure.

Friction Turns Wind Toward Lower Pressure.

Friction

Force of Friction 3

PGFCF

Wind1004 mb

1008 mb

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.

Fr

Force of Friction 4

1004 mb

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).

Mtns Water20o-30o

30o-40o

Force of Friction 5

1004 mb

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.

SFC

~1 km0.6 km

0.3 km

Gedzelman, p249

Flow at Surface LowsLows and HighsHighs

Spirals OutwardDivergence

Spirals InwardConvergence

upward motiondownward motion

Ahrens, Fig 6.21

Friction Induced Vertical MotionFriction Induced Vertical Motion

Summary • Curved Flow

Requires Centripetal AccelerationDifference between PGF and Coriolis ForceSpeed Changes => Convergence-Divergence

• Frictional ForceCauses Winds to Turn toward Low Pressure Important in the lowest 1 km above the Surface Leads to Convergence-Divergence

• Curvature and FrictionLeads to Vertical Motions

Next Lecture • Local Winds with Diurnal or Shorter Times

Land-Sea BreezeMountain-Valley Breeze

• Charles Darwin was RightDarwin “Natural Selection” Award

Assignment for Next LectureAssignment for Next Lecture • Reading - Reading - Ahrens pg Ahrens pg 167-181167-181• Problems - Problems - 7.3, 7.47.3, 7.4