Science 123
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Spring 2026
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Forces and Winds
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Newton`s Laws of Motion
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Pressure Gradient Force
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Coriolis Effect
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our perspective is from a rotating frame
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the resultant effective force has a magnitude given as $F_{co}=2\Omega v \sin \phi$ where
- $\Omega$ = rotation rate of the Earth
- $v$ = the object's speed
- $\phi$ = latitude
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Geostrophic Wind
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balance of pressure gradient force and the coriolis effect
$2\Omega v_g \sin \phi = \frac{1}{\rho}\frac{\Delta P}{\Delta x}$
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contours (pressure or height) are parallel and straight
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the closer the contour lines, the greater the wind speed
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example (pdf)
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Gradient Wind
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pressure and height contours are curved and parallel
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cyclonic flow - subgeostrophic flow
$2\Omega \cdot v \cdot \sin \phi + \frac{v^2}{r_0} = \frac{1}{\rho}\frac{\Delta P}{\Delta r}$
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anticyclonic flow - supergeostrophic flow
$2\Omega \cdot v \cdot \sin \phi = \frac{1}{\rho}\frac{\Delta P}{\Delta r} + \frac{v^2}{r_0}$
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Planetary Boundary Layer (Friction Layer) Wind
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Hydrostatic Equation
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balance of vertical pressure gradient and the force of gravity
$\frac{1}{\rho}\frac{\Delta P}{\Delta z} = -g$
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no vertical wind?
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buoyant force - Archimedes' Principle
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pressure contours are parallel to height contours
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examples
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Upper Air (UA) Charts
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Three-dimensional Circulation between high and low pressure