The Coriolis Effect: How Earth's Rotation Shapes Weather

simulator intermediate ~10 min
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Deflection ≈ 240 km over 12 hours at 45°N

At 45° latitude with 10 m/s wind speed, the Coriolis parameter is 1.03×10⁻⁴ s⁻¹. Over 12 hours, the trajectory deflects approximately 240 km to the right (in the Northern Hemisphere). The inertial period is about 17 hours.

Formula

f = 2Ω sin(φ) (Coriolis parameter)
a_Cor = -2Ω × v (Coriolis acceleration vector)
T_inertial = 2π/(2Ω sin φ) = π/(Ω sin φ)

The Rotating Frame

Stand at the North Pole and throw a ball southward. As it flies, the Earth rotates underneath it. To you, standing on the rotating Earth, the ball appears to curve to the right — even though it is actually traveling in a straight line through space. This apparent deflection is the Coriolis effect, named after French mathematician Gaspard-Gustave de Coriolis who described it mathematically in 1835. It is not a real force but an artifact of our rotating reference frame.

The Coriolis Parameter

The strength of the Coriolis effect depends on latitude and Earth's rotation rate: f = 2Ω sin(φ), where Ω is Earth's angular velocity (7.292×10⁻⁵ rad/s) and φ is latitude. At the equator (φ=0), f=0 — no deflection. At the poles (φ=90°), f is maximum. This latitude dependence explains why hurricanes form in the tropics (enough heat) but not right at the equator (not enough Coriolis). The Coriolis acceleration is perpendicular to velocity: a = -2Ω × v.

Watching Deflection

This simulation shows a top-down view with an object moving from the center. The dashed line shows its intended straight path; the solid curved line shows its actual trajectory as seen from Earth's rotating surface. In the Northern Hemisphere, deflection is to the right. Increase latitude to see stronger deflection. Set rotation to zero to see the object move straight — confirming this is purely a rotational effect. Multiple trajectories at different launch angles create the characteristic spiral pattern of Coriolis-deflected motion.

Global Weather Patterns

The Coriolis effect shapes Earth's entire atmospheric circulation. Rising hot air at the equator flows poleward at altitude but is deflected east, creating the subtropical jet stream. Sinking air at ~30° latitude flows back toward the equator but deflects west, creating the trade winds — the reliable easterly winds that powered centuries of sailing commerce. At mid-latitudes, the prevailing westerlies blow from west to east. These three circulation cells (Hadley, Ferrel, Polar) in each hemisphere create Earth's climate zones. The Coriolis effect also deflects ocean currents, creating the great gyres that redistribute heat across the planet.

FAQ

What is the Coriolis effect?

The Coriolis effect is an apparent deflection of moving objects on a rotating reference frame. On Earth, moving objects are deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. It is not a real force but an artifact of observing motion from a rotating frame.

Does the Coriolis effect affect toilets and bathtub drains?

No — this is a myth. The Coriolis effect is far too weak to influence small-scale water flows. Bathtub drain rotation is determined by residual currents, basin geometry, and how the water was disturbed. The Coriolis effect only significantly affects flows over hundreds of kilometers.

Why do hurricanes rotate?

Low pressure systems draw in surrounding air. The Coriolis effect deflects this inward-flowing air, causing it to spiral. In the Northern Hemisphere, deflection to the right creates counterclockwise rotation; in the Southern, clockwise. This is why hurricanes never cross the equator — the Coriolis effect reverses direction.

What is the Rossby number?

The Rossby number Ro = v/(fL) compares inertial to Coriolis forces. When Ro << 1, Coriolis dominates (large-scale weather). When Ro >> 1, Coriolis is negligible (tornadoes, bathtub drains). Most weather systems have Ro ≈ 0.1, confirming that the Coriolis effect is essential to their dynamics.

Sources

Embed

<iframe src="https://homo-deus.com/lab/earth-science/coriolis-effect/embed" width="100%" height="400" frameborder="0"></iframe>
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