The Coriolis Effect

Coriolis effect
Coriolis force
Coriolis frequency
- Rossby parameter
Rossby number
Cyclostrophic and Geostrophic Balance
- Sources

Coriolis effect

The Coriolis effect is the apparent deflection of an object’s trajectory when in a rotating reference frame. The object actually travels in a straight line, but since the reference frame is rotating, it appears to curve.

Illustration of effect on the earth’s rotation:

Coriolis force

Equation for the Coriolis force ( $\omega$ is angular velocity, $v$ is linear velocity):

$F = -2m \omega v$

Coriolis frequency

The Coriolis frequency $f$ (known as Coriolis parameter or Coriolis coefficient) is equal to:

$f = 2 \omega sin \phi$

where $\omega$ is the rotation rate (angular frequency) of the Earth, and $\phi$ is the latitude. The Coriolis force can be written as equal to,

$F = f * v$

where $v$ is the velocity.

Rossby parameter

The Rossby parameter $\beta$ describes the rate of change of the Coriolis parameter $f$ with respect to meridians (y). It is defined as:

$\beta = \frac{\partial f}{\partial y} = \frac{1}{a} \frac{d}{d\phi} (2 \omega sin\phi) = \frac{2\omega cos\phi}{a}$

where $\phi$ is the latitude and $a$ is the radius of the Earth.

Rossby number

The Rossby number is defined as the ratio of intertial to Coriolis force.

$Ro = \frac{F_{\text{inertial}}}{F_{\text{Coriolis}}}$

A system with a low Rossby number is dominated by Coriolis forces.
A system with a high Rossby number is dominated by inertial forces.

Cyclostrophic and Geostrophic Balance

When the Coriolis force is low, inertial forces dominate – the pressure gradient force (from high pressure to low pressure) and the centrifugal force. This is called cyclostrophic balance, which happens in tornadoes and cyclones.

In low-pressure systems, the Coriolis force is significant. Therefore, geostrophic balance occurs – a balance between Coriolis and pressure gradient forces. Ashwin Ramaswami.