Air in Motion. Anthes, Chapter 4, pp

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1 Air in Motion Anthes, Chapter 4, pp

2 Newtonʼs Laws of Motion 1. Law of Inertia. A body at rest remains at rest, a body in motion remains in motion, unless acted upon by an outside force. 2. F = ma. (or a = F/m) Acceleration is directly proportional to the force applied and inversely proportional to the mass. (4.1 in Anthes) 3. For every action, there is an equal and opposite reaction.

3 Speed, Velocity, Acceleration, Force Speed = distance / time Velocity = Speed in a particular direction Acceleration = change of velocity with time Change of speed Change of direction Change of both speed and direction Acceleration indicates that a force is being applied to a body. a = F/m (Newtonʼs 2nd law).

4 Gravity Primary Forces (vertical) Downward directed force, F g = - mg (4.2) Vertical Pressure Gradient Upward directed force, F pg = ΔPA Hydrostatic Balance F pg = - F g ΔPA = - mg (4.3) Substitute m = ρv = ρaδz ΔPA = - ρaδz g Hydrostatic Equation ΔP/Δz = -ρg (4.4)

5 Pressure Gradient Force: The primary horizontal force Horizontal pressure gradient force. Fpg = P/d This force is not balanced by gravity. Winds blow from areas of high pressure toward areas of low pressure. Winds cut across isobars. Example of Sea breeze

6 Thermal wind

7 Coriolis Force: A horizontal force caused by motion Coriolis force -- an effect of the Earthʼs rotation. Acts on a moving air mass. Acts perpendicular to the wind direction. Changes wind direction, but not speed. Deflection of the wind to the right in the Northern Hemisphere. Determined by the rate of rotation around vertical axis -- 0 at the Equator, maximum at the poles. Fc = 2mVω sin φ

8 Forces arising from rotation

9

10 Geostrophic Wind (or Balance) Valid for large scale, upper air winds. Straight-line wind flows that are unaccelerated. Assume Ff = 0 Pressure gradient force is balanced by Coriolis force Fpg = Fc Result: In N. Hemisphere wind blows parallel to the height contours with lower pressure to the left. The closer the spacing of the height contours, the faster the wind speed.

11 Geostrophic Wind (frictionless)

12 Gradient Wind: Circulation around an upper-level Low Circular flow around a Low is parallel to curved height contours. Counterclockwise in N. Hemisphere. Accelerated motion because there is a continual change in direction of the wind. Closer spacing of contours means greater wind speeds. Fpg > Fc

13 Gradient Wind: Circulation around an upper-level High Circular flow around a High is parallel to curved height contours. Clockwise in N. Hemisphere. Accelerated motion because there is a continual change in direction of the wind. Closer spacing of contours means greater wind speeds. Fpg < Fc

14 Gradient wind (frictionless)

15 Friction A horizontal force caused by motion Friction -- retarding force caused by surface irregularities and adhesion. Viscosity -- retarding force in a fluid. Molecular viscosity -- high for syrup, low for air. Eddy Viscosity or Turbulence -- transfer of momentum away from a flow. Caused by surface roughness and lack of thermal stability. Net effect -- Ff slows down the wind.

16 Veering of winds near the surface The effect of friction near the surface slows the wind. As V decreases, Fc also decreases. Winds veer to the left. Winds cross isobars from H --> L pressure.

17

18 Surface Highs and Lows In a High, as V decreases and Fc decreases, the winds circulate outward from the center -- DIVERGENCE. Since Fpg is inwardly directed in a Low, winds then circulate in toward the center, crossing the isobars -- CONVERGENCE.

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