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##### Lecture 7

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**Lecture 7**• Forces (gravity, pressure gradient force) • Imaginary forces (Coriolis, centrifugal) • Force balance and resulting horiz. wind • Geostrophic wind • Gradient wind • Adjustment to balance • The thermal “wind” (change in geostrophic wind in the vertical)**Wind direction is the direction from which the wind is**blowing. Wind direction is expressed in degrees Units: m/s or knots 1 knot = 0.5 m/s 1knot ~ 1 mile/hr Wind speed is expressed in terms of the flagpole**Newton’s law of motion**• A body at rest tends to stay at rest; a body in motion tends to stay in motion, traveling at a constant speed in a straight line. • A force exerted on a body of mass m causes the body to accelerate in the direction of the applied force. Force = mass x acceleration**A force has direction and magnitude (it is a vector).**Adding two forces is vector addition.**Forces that move the air**• Gravitational force (g=9.8 m/s2) • Pressure gradient force (-1/rho x dp/dx or --1/rho x dp/dy). It points toward lower p. The pressure gradients causing the wind are horizontal. • Coriolis force • Centrifugal force • Frictional force**Pressure gradient force pushes from higher to lower**pressures PGF Magnitude depends on value of pressure gradient**Isobaric chart (height contours on a constant pressure**surface)**Vertical structure in the atmosphere**• What about pressure? • Hydrostatic equation: balance between pressure gradient force and gravity. • dp/dz = - rho g • Ideal gas law: • p = rho R T Let’s go to the board! z = - H ln (p/p0), where H is scale height and is only constant if T is constant. In other words, p = p0 exp(- z/H)**Next: Coriolis forceEarth’s rotational speed is greatest**at the equator and exactly zero at the poles**Coriolis deflection**Coriolis force deflects moving air to the right in the Northern Hemisp. Coriolis force deflects moving air to the left in the S. Hemisphere**The magnitude of the Coriolis force (CF) is proportional to**the wind speed and sine of latitude CF= f x V, Where f is 2xEarth’s rotation rate xsin(latitude)**Centrifugal force: arises because the trajectory is curved.**CENTF= V^2/R, where R (radius of curvature) is positive for cyclones, negative for anticyclones**Frictional force is proportional to the wind- speed and**directed opposite to the wind dir. FF = -k V (where k describes the roughness)**Summary: The Forces**• Gravity – the strong silent type • PGF arises from pressure gradients generated by differential solar heating –leads to wind. Only then do the other forces start acting. • CF, CENTF, FF all depend of V, wind speed.**Atmospheric force balancesSum of forces = mass x**accelerationBalance when the forces add up to zero • Hydrostatic balance in the vertical (gravity does not cause wind). • Strong horizontal PGF means strong wind • CF changes wind direction not speed • CENTF only acts on curved flow • FF slows down the wind (regardless of direction).**Wind blows counterclockwise around lows (cyclonic wind in**cyclones), clockwise around highs (anticyclones) Force balance not quite right since we have curved flows Add centrifugal force**Gradient balance results in gradient wind**• Represents balance of three forces • It is an excellent approximation to free atmospheric flow. • Around highs it is supergeostrophic • Around lows it is subgeostrophic**Adjustment to balance**• The atmosphere tries hard to stay in balance, but it is constantly being pushed away from it. • The atmosphere adjusts very quickly (in a matter of minutes) to imbalance.