Force Balance (Chap. 6) ATM100

Topics of the Day ◦ Review Test 1 ◦ Newton’s Laws of Motion ◦ Review of vectors and forces ◦ Forces that act to move the air ◦ Force balances and Winds ◦ Local winds ◦ Scales of Motion

Centrifugal / Centripetal Acceleration (CENTF) Another apparent force, generated by a turning motion. Centripetal Acceleration pulls an object toward the center. The apparent centrifugal force pushes the object perpendicularly to the curvature of the wind.

Centrifugal / Centripetal Acceleration (2) CENTF = V 2 / R ◦ Where Where V is the velocity of the wind ◦ R is the radius of curvature of the wind

Friction (FF) Is a dissipative force – it always acts in the opposite direction to the motion of the object In the case of the atmosphere, it is directly related to the “roughness” of the surface. As such it is a major factor near the Earth’s surface, but plays a more minor role above the surface. FF = -kV

Hydrostatic Balance The vertical pressure gradient is larger than any horizontal gradient, including hurricanes! However, the vertical motions that results from the pressure gradient are balanced by the gravitational force. PGF (vertical) + GF = 0

Geostrophic Balance and Wind The PGF may get the wind to blow, but as soon as it starting moving, the CF force starts to deflect it. Eventually the PGF and CF reach equilibrium, so PGF +CF = 0. This keeps the winds blowing in a direction parallel to the isobars.

Buys Ballot Law and Pressure Systems Buys Ballot law says that as a result of Geostrophic balance the low pressure has to be the left of the direction the wind is blowing. This implies that the wind blows counter-clockwise (clockwise) around low (high) pressure in the Northern Hemisphere. The opposite is true in the Southern Hemisphere

Gradient Balance and Wind Geostrophic Balance requires that the wind blows in a straight line parallel to the isobars. Well that is rarely the case, the atmosphere is rarely that orderly, so it is going to have some twists and turns. As soon as the wind makes a turn, the Centrifugal Force (CENTF) is added to the mix.

Gradient Balance and Wind (2) When moving counter-clockwise around a low pressure system, the CENTF pulls in the same direction as the CF. So it aids the Coriolis effect. When moving Clockwise around a high pressure system, the CENTF pulls in opposite direction as the CF. So it tends to counteract the Coriolis effect.

Gradient Balance and Wind (3) Subgeostrophic flow - around the low pressure system with CF and CENTF co- operating, balance is maintained with a wind that is moving slower than the geostrophic case.

Gradient Balance and Wind (3) Supergeostrophic flow - around the high pressure system with CF and CENTF working against each other, balance can be maintained only with a wind that is moving faster than the geostrophic case.

Gradient Balance and Wind (5) Therefore, gradient winds will blow stronger around high pressure systems that low pressure for the same size gradient. However, as we’ll see in later on gradients around low pressure systems tend to be steeper than high pressure systems so the winds are plenty strong!

Guldberg-Mohn Balance Near the surface winds encounter significant friction. So the FF has to be added to the mix of forces. The FF acts to slow the speed of the wind which in turns weakens the CF. Now the CF cannot completely balance the PGF. In this case the wind falls out of geostrophic balance and no longer blows along the isobars, but across them at an angle.

The Thermal Wind In the mid-latitudes, vertical pressure heights decrease towards the poles as a result of being colder. Therefore the prevailing wind in the mid- latitudes will be a Westerly (out of the west and heading eastward) wind.

Convergence and Divergence If air is spinning into a low pressure system, what happens when it reaches the center? It has to go someplace. So in addition to horizontal motions there are also corresponding vertical motions. Convergence at the surface implies divergence aloft. (and visa versa)

Sea (Land) Breezes Are caused by the move rapidly heating and cooling of the land as compared with the sea. This causes pressure variations leading to a local circulation of air.

Scales of Motion Microscale – less than 1 km. PGF CENTF and FF are important forces Mesoscale – 1 to few hundred Km. CF becomes increasing important at the larger end of the scale. Synoptic-scale – 1000 km in size. The realm of geostrophic balance between PGF and CF. Planetary-scale – larger than 1000 km in size