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Climate Science 102 Winds go sideways [1]

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Date: 2023-06-22

Air in vents usually travels from high pressure to low pressure, but wind outside is mostly traveling perpendicular to the pressure gradient, or at least at a very high angle. This leads to the persistence of high and low pressure areas, but also controls the affects the weather in other ways.

For those who haven’t guessed or already knew, this is because the earth is a spinning ball. At the equator the surface of the earth is traveling about a 1000 miles per hour to the east. Eight miles from the poles the surface is traveling at about 1 mile per hour. This difference causes the Coriolis force, which is really inertia, which despite the above explanation is stronger at the poles and nonexistent at the equator.

Coriolis Force

The Coriolis force acts perpendicular to the velocity of an air parcel. Wikipedia has a good write up. Important from our point of view is, forces that are perpendicular to the direction of travel result in circles. A rock tied to a string will move in a circle. The string can only pull inwards. Gravity pulls the earth towards the sun.

The strength of the Coriolis force is proportional to the velocity of the air in the moving frame of reference (us). The argument for winds moving perpendicular to the pressure force is that air starts moving down the pressure gradient and is deflected by Coriolis force. As long as there is some component of the velocity in the direction of the pressure the air will accelerate and turn. Once the air is perpendicular to the pressure gradient it won’t speed up and the Coriolis force will balance the pressure force.

From Wiki Commons an open site Inertial Circles the movement of air vs latitude. Because the Coriolis force depends on the velocity. The size also does. It is also supposed to show that they get smaller near the poles, and that there is no Coriolis force at the equator.

At that point the wind travels parallel to the isobars (lines of equal pressure on a weather map, and also the height lines)

Winds that travel along lines of constant pressure reacting to a balance of the pressure gradient and the Coriolis force are call geostrophic. The jet streams are mostly geostrophic as are the winds around high pressure and low pressure areas. They effect the climate and the weather, and are also basic to weather forecasting.

The speed of the winds is linearly related to the pressure gradient with higher wind speeds associated with higher pressure gradients. Since pressure gradients are related to density differences and those are related to temperature differences, the fastest winds are near positions with high temperature changes. Jet streams are therefore associated with borders between big air masses of different temperatures. They are located between polar air and mid latitude air, and tropical air and mid latitude air. The famous polar vortexes are Geostrophic winds.

Meteorologists publish what they call inertial circles which show a completed circle if a unit of fluid starts traveling in one direction and is only operated on by the Coriolis force (inertia). Some of those circles are shown above. They are larger near the equator and smaller near the poles. Real fluids have other forces acting on them and move in traveling spirals. A map of some Baltic sea currents is shown here.

Another force associated with circular fluid flow is the centripetal force. This force acts on a much smaller scale than the Coriolis force. Low pressure in the center of a hurricane is balanced by the centripetal force. Winds which balance the Coriolis centripetal, and frictional forces, and pressure gradients are called gradient winds.

Vorticity

Vorticity is a measure of the circularity of the flow. It is calculated mathematically as the curl of the velocity, but can be visualized as the sum of the tightness of the circle in the flow, and the difference in wind velocity, when you move perpendicular to the wind velocity (often called wind shear). A quantity called “absolute vorticity” includes the Coriolis force, which can add and subtract from the atmospheres spin when parcels move north or south. A term called “potential vorticity,” divides that the absolute vorticity by the thickness of the pressure layer (this matters later). The “potential vorticity” is often included in weather maps, as a predictor.

Weather forecasters look at the 500mb height map to monitor vorticity. High levels of vorticity usually occur to the west of storms. This is one of the places where the winds will deviate from geostrophic because warm air is being pulled upwards into the layer which will can lead to rain. Vorticity or large eddies are also important in the large circulations of the atmosphere moving air, water and energy around. Moving energy north or south is called “meridional” flow while moving east or west is called “zonal” flow.

In the northern hemisphere counter clockwise rotation is positive vorticity and clockwise rotation is negative vorticity. Low pressure is always to the left of the wind direction.

Background about pressures

Height in the atmosphere is measured in Bars. A Bar is equal to 100,000 Pascals, which is the metric pressure measure. Since one standard atmosphere is 1.013 Bars, it is convenient to refer atmospheric pressure in Bars. Atmospheric pressure at a point is the weight of the atmosphere above it, so a 500 millibar height has half the atmosphere above it and half below it. The top of the troposphere is often at about 250 millibar meaning about a fourth of the atmosphere is above it. One thousand Bar is supposed to be at the sea surface, but sometimes it is under the ground or over the ground.

Height lines are the height of the pressure being mapped. They use the language of topographical maps and look like them. In a height map the lines are the altitude of pressure of the map. Only the highest 3 digits of the altitude measurement are used in the maps because the ones digit is assumed. Ridges are areas with warm air underneath then and troughs are areas with cold under them, basically because cold air is denser it reaches the pressure at a lower altitude. Pressure decreases from ridges to troughs, but air flows mostly along the contour lines in the height map. The thing called layer thickness is calculated from these height lines.

An earlier diary Climate science 101 is here

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