# Tropical Cyclogenesis

## Storm Rotation

#### Convection Flow

Convection is the upward rise of a liquid or gas that is warmer than the liquid or gas it is replacing. In the case of tropical weather, convection is warm air rising to replace cooler air above the warm air.

As air at the base of the convection flows upward, air from the side is pulled into the base of the convection. Likewise, at the top of the convection flow, air that had been rising bunches up and flows outward. This is illustrated in the following drawing (side view):

Figure 1:  Side view of atmospheric convection.

At the base of the convection (on the Earth’s surface), air rushes into the convection as surface wind, illustrated in the following plan view drawing (looking downward at the convection):

Figure 2:  Plan view of the base of atmospheric convection, with air flowing into the base of the convection.

At the top of the convection, air flows outward:

Figure 3:  Plan view of the top of atmospheric convection, with air flowing outward.

This is the type of air flow a tropical cyclone (TC) starts with, before spinning due to the Coriolis force.

#### Coriolis Force

The Earth rotates, from West to East, 360 degrees in 24 hours, which is 15 degrees per hour. That is, in one hour, the Earth has rotated 15 degrees.

Dividing the Earth’s surface into longitude and latitude lines, along a given latitude the Earth rotates 15° of longitude per hour.

That distance, which the Earth travels in one hour along a latitude, varies depending on the latitude. At the Equator, 15° of longitude is 1667 km apart. But at other latitudes, 15° of longitude is closer together, becoming closer together as you go north.

Figure 4:  The distance between longitudes along the Equator (red arrow) is longer than at other latitudes (blue arrows). [Reisio]

Following is a list showing the distance between 15° of longitude at different latitudes:

0° Latitude (Equator)  =
5° North or South  =
10°  =
15°  =
20°  =
25°  =
30°  =
35°  =
1667 km
1660 km
1641 km
1610 km
1566 km
1510 km
1442 km
1364 km

At the Equator, the Earth’s surface is rotating at a velocity of 1667 kilometers per hour (km/h), at 5° Latitude it is rotating at 1660 km/h, etc.

Consider Latitudes 0 through 5:

0° (Equator)  =
1° North or South  =
2°  =
3°  =
4°  =
5°  =
1667 km/h
1667 km/h
1666 km/h
1665 km/h
1663 km/h
1660 km/h

Near the Equator, there is little difference from one degree of latitude to the next.

Now consider Latitudes 22 through 27:

22°  =
23°  =
24°  =
25°  =
26°  =
27°  =
1545 km/h
1534 km/h
1522 km/h
1510 km/h
1497 km/h
1484 km/h

At these latitudes, there is much more difference from one latitude to the next. The difference of each one of these is greater than the differences of Latitudes 0 through 5 put together.

Near the Earth surface, air that is “still” is actually moving along with the Earth surface, rotating around the Earth axis of rotation. It is “still” at the Earth surface because it is moving along with the Earth surface. Thus, at the Equator, “still” air is moving along with the Earth surface at 1667 km/h.  At 15°Latitude, “still” air is moving along with the Earth surface at 1610 km/h, etc.

Figure 5:  Atmospheric convection in the Northern Hemisphere. The southern portion is moving to the East faster (more) than the northern portion.

If air is pulled directly poleward, besides moving poleward, it was moving toward the East along with the Earth surface where the air is coming from. Thus, it has a velocity in the poleward direction, and also a velocity in the eastward direction.

As this air moves poleward, it is also moving toward the East faster than the Earth surface where the air is arriving to. In other words, the new land under the air is moving to the East at a slower rate than the air is moving to the East.

Likewise, if the air is flowing toward the Equator, the eastward direction of the air flow is not able to keep up with eastward speed of the land underneath.

This phenomenon, called the Coriolis force, causes the inflow of atmospheric convections to rotate clockwise in the Northern Hemisphere, and counter-clockwise in the Southern Hemisphere.

Due to the same Corilios force, outflow from the convection vortex rotates in the opposite direction than the inflow.

Animation opens in new window
Figure 6:  Hurricane Ian, September 2022, Northern Hemisphere. Inflow near the Earth’s surface is counter-clockwise. High cirrus outflow is clockwise. [NOAA]

#### Angular Momentum

If the convection fluid is spinning, the convection is a vortex. In tropical cyclones, the fluid is moist air.

According to the Law of Conservation of Angular Momentum, if the radius of vortex flow is narrowed, then the fluid will spin faster. This is like a figure skater spinning faster by pulling in closer to the axis of rotation.

Figure 7:  By pulling in during a spin, a skater spins faster. [BCcampus]

Figure 8:  Close to spin axis, spins faster. [Wiki]

#### Tropical Cyclogenesis

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Introduction
Cumulonimbus Clouds
Cirrus Clouds