UNDERSTANDING THE CORIOLIS FORCE

Earth rotates such that the Sun rises in the east and sets in the west (left). Therefore, the northern hemisphere rotates counter-clockwise (top right) and the southern hemisphere rotates clockwise (bottom right). Earth’s rotation affects motion of objects in the two hemispheres differently.

Images: http://www.maps.google.com

It is believed by an alarmingly large number of people, that the Coriolis force affects the water being flushed from your toilet in the same way it affects hurricanes - by determining the spiral direction. Of course the Coriolis force does act on the water in your toilet when you flush it, but the strength of the force is extremely small (on the order of 0.00001 Newtons or smaller). Thus, it is negligible compared to other factors such as the shape of the toilet bowl and any initial disturbances in the water. Simply walking into the bathroom will send vibrations through the water in your toilet. This seemingly small disturbance can result in forces that are orders of magnitude larger than the Coriolis force would be. The effects of the Coriolis force produced by Earth’s rotation are only observable on very large scales (e.g. hurricanes).

Satellite Image of Hurricane Sandy

This photo was taken on October 28, 2012 and shows Hurricane Sandy off the east coast of the United States. You can clearly see the hurricane is rotating CCW.

Image: theverge.com

On its own the Coriols force tends to produce circular motion, because it always points perpendicular to an objects velocity. This is similar to the Lorentz force on a charged particle as it moves through a magnetic field (orthogonally to the field lines). However, the Coriolis force in the atmosphere rarely results in perfect circles because other forces are present. Instead it results in curved motion. Air that is approaching a hurricane is influenced by the pressure gradient force (due to the low pressure of the hurricane) and the Coriolis force, so its trajectory exhibits the presence of both forces. Shown below are the Coriolis and pressure gradient force for a unit air mass on its trajectory toward the hurricane. The Coriolis force always acts to add curvature to the linear motion produced by the pressure gradient. It starts by deflecting the air to the right. Closer to the hurricane its pull is stronger, because the pressure gradient is steeper. This is when the pressure gradient force overwhelms the Coriolis force. However the air is now approaching the hurricane at an angle, which determines the direction of the spiral. In the northern hemisphere deflection of air to the right means it must always approach in a counter-clockwise spiral. The Coriolis force almost directly opposes the pressure gradient throughout the spiral thereby lengthening the air’s trajectory and prolonging the spiral behavior.

Movement of air in the atmosphere is driven primarily by gradients in temperature and pressure. However, once the air is in motion it is strongly influenced by the Coriolis force. In general, warm air rises from the equator and moves poleward (down the temperature and pressure gradients). When it reaches around 30º latitude it has cooled sufficiently to sink to lower altitudes. Some of the air continues poleward and some is diverted back to the equator.

On Earth the Coriolis force is most observable on large scales. Thus wherever we find large volumes of fluid, like in the atmosphere or the oceans we can see the Coriolis force at work. As expected, the Coriolis force also results in curved motion in the oceans. However due to the lack of other major forces in the oceans the Coriolis force can produce circular motion there.

As mentioned earlier, the Coriolis force only begins to act on an object when starts moving. So for the Coriolis force to affect water on observably large scales there must be some net movement independent of the Coriolis force. In the ocean this movement is provided by drag from wind on the water’s surface. Once the water is in motion the Coriolis force begins to deflect it right (left) in the northern hemisphere (southern hemisphere). In addition to surface drag from wind, there is drag between layers in the water column. The friction between layers imparts horizontal velocity to water as deep as 100 meters. The Coriolis force acts on each layer in sequence as energy from the surface is transferred down the water column. This produces a spiral current known as the Ekman Spiral. Ekman Spirals in the ocean have resulted in enormous circular currents called gyres. Unlike hurricanes, they rotate clockwise in the northern hemisphere and counter-clockwise in the southern hemisphere. This is because the spiraling motion in gyres is a direct result of the Coriolis force, whereas in hurricanes the Coriolis force only determines the spin direction.

Major Wind Patterns on Earth Affected by Coriolis Force

All moving air in the atmosphere is affected by the Coriolis force. Equator-ward air masses are deflected to the west and poleward air masses are deflected to the east by the Coriols force. The Coriolis force always pushes right in the northern hemisphere and left in the southern hemisphere.

Image: https://courseware.e-education.psu.edu/courses/earth540/nasa.6-cell-model.jpg

This longitudinal motion of air is constantly affected by the Coriolis force.

Air moving south towards the equator is deflected to its right. Air moving north toward the equator is deflected to its left. These deflected equator-ward air currents in the northern and southern hemispheres are referred to as the Trade Winds. They produce a net westward air current around the equator, which aided early trade routes from Europe to the Americas.

Air moving north from 30º N latitude is deflected right, and air moving south from 30º S latitude is deflected left. These deflected poleward air currents are referred to as the Westerlies.

Both the Trade Winds and the Westerlies are very reliable, and have persisted over extremely long time scales. Without the rotation of the earth (and the Coriols force), these winds’ velocities would have no horizontal component!

Coriolis and Pressure Forces on an Air Mass

Air on the bottom right is drawn toward the low pressure center of the hurricane at left middle (pressure gradient force shown in blue). Once the air begins moving it is deflected by the Coriolis force (brown). The magnitude of each force is roughly proportional to the length of the vector shown.

The distance between the two black points in this diagram represents an extremely large distance (1000s of kilometers).

Ocean Gyres Driven by the Coriolis Force

The five main ocean gyres are shown on the left. They circulate clockwise in the northern hemisphere and counter-clockwise in the southern hemisphere. Ocean gyres give rise to characteristic western and eastern boundary currents where they border continents. These currents, such as the Gulf Stream or Humboldt Current are extremely important for many coastal ecosystems.

Image: https://courseware.e-education.psu.edu/courses/earth540/nasa.6-cell-model.jpg

University of British Columbia

Department of Physics

Tony Battistel

December 2012