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The Coriolis Effect and Confusion

The Coriolis Effect is a fictitious force that seems to act on an object moving in a rotating frame of reference. For example, the Earth rotates, so something moving on Earth (on large distance scales) will seem to have a fictitious force acting on it.

The Coriolis Effect does not dictate whether a toilet flushing or a bathtub draining does so with the water circulating clockwise or counterclockwise depending on which hemisphere you are in. That is dictated by the structure of the basin and how the water is moving as it is placed into the basin.

Veritasium and SmarterEveryDay have a video explaining this, and then they experiment with two basins, one in each hemisphere, in controlled settings, showing that actually, indeed, the Coriolis Effect does dictate how water circulates down a drain given that other factors like the shape of the basin and the way the water is moving when placed into the drain are taken out. Water draining from the basin in the northern hemisphere rotates counterclockwise and water draining from the basin in the southern hemisphere rotates clockwise. They explain the physics and then mention that this is also the reason why tropical cyclones in the northern hemisphere rotate counterclockwise

Hurricane Isabel, from 2003, which formed in the northern hemisphere near Cape Verde

and tropical cyclones in the southern hemisphere rotate clockwise.
Cyclone Bansi, from 2015, which formed int he southern hemisphere near Madagascar

Then, let’s take a look at ocean currents (surface ocean currents, to be accurate).

Ignoring the Arctic Ocean and the Southern Ocean, every single ocean-hemisphere in the northern hemisphere has a clockwise current (the northern Atlantic and the northern Pacific) and every single ocean-hemisphere in the southern hemisphere has a counterclockwise current (the southern Atlantic, the Indian, and the southern Pacific). So without digging deeper, extrapolating from a draining basin to Earth-sized phenomena doesn’t seem correct. Why does water in draining basins rotate one way while water in oceans rotate the other way? Without knowing this, knowing that tropical cyclones rotate the same way as draining basis feels valueless.

The Coriolis Effect

Imagine some object at the equator on the surface of Earth. Being stationary at the equator, from the perspective of an inertial reference frame, the object actually already has an angular velocity due to the rotation of the Earth. On the surface of the Earth, this is manifested as tangential velocity. Let’s call the tangential velocity at the equator $$v_{eq}$$.

The pink arrows are the tangential velocities at the equator. Any point stationary on the surface of the Earth at the equator has this tangential velocity. At a higher latitude, while the angular velocity is the same as at the equator, the radius between the higher latitude location and the axis of rotation of the Earth (a line going through the north and south pole) is shorter, and so the tangential velocity here, the orange $$v_{lat1}$$ is less than $$v_{eq}$$. Any position on Earth’s surface with this latitude will have the same $$v_{lat1}$$. Further north and the tangential velocity there, the red $$v_{lat2}$$ is even less. If you go all the way up to the north pole, you would be on the axis of rotation, and so while you would be rotating with the Earth, you would have no tangential velocity.

Now, let’s say the object begins to travel north with velocity $$v_{north}$$. The object moves “freely,” e.g. it moves freely in the air with no air friction. Assume for simplicity, of course, that the object doesn’t move “straight up” above the plane of rotation and into space but stays “within” the Earth’s atmosphere with a constant altitude. (It can also be an object that moves freely in water but in that case assume that it is large enough and that water currents and water friction “even out” over long distances. The most relevant and best case is to imagine a large mass of water that moves within the ocean, i.e. a water current.) So before the object begins to travel, it has tangential velocity $$v_{eq}$$. At the moment it begins to travel north, its tangential velocity is unchanged, so it has longitudinal velocity $$v_{north}$$ and tangential velocity $$v_{eq}$$. The surface of the Earth below it is also moving tangentially at $$v_{eq}$$ so relative to the surface below, the object is only moving north.

Now imagine that it has reached “latitude 1.” Its longitudinal velocity to the north is still $$v_{north}$$ and its tangential velocity is still unchanged at $$v_{eq}$$, while the the surface of the Earth below is moving tangentially at a smaller $$v_{lat1}$$. Thus, relative to the surface of the Earth, the object is moving tangentially (to the east) at $$v_{eq}-v_{lat1}$$. At “latitude 2,” its longitudinal velocity is $$v_{north}$$ and its tangential velocity is an even larger $$v_{eq}-v_{lat2}$$. Thus, when moving north in the northern hemisphere, an object seems to veer to the east. In the southern hemisphere, an object moving south also seems to veer to the east, as its starting tangential velocity to the east will be greater than the tangential velocity to the east of the Earth’s surface further south.

If an object is in the northern hemisphere and moves south towards the equator, its starting tangential velocity to the east will be less than the Earth’s surface’s tangential velocity to the east closer to the equator. Thus, relative to the Earth’s surface closer to the equator, the object is moving to the west. Thus, object moving south in the northern hemisphere seem to veer to the west. Similarly, objects moving north in the southern hemisphere seem to veer to the west.

Putting these results together, objects moving in the northern hemisphere veer to the right (compared to its “main” or intended direction of movement) and objects moving in the southern hemisphere veer to the left. Thus, when thinking about masses of water, we have the same result as the draining basins that drain counterclockwise in the northern hemisphere and drain clockwise in the southern hemisphere. It is also consistent with how tropical cyclones rotate.

Tropical Cyclones

Warm humid air rises from the surface of the ocean upwards. This creates a low pressure area near the surface where this air once was. We effectively have a “basin of draining air” where air near the surface around this low pressure area drains toward the low pressure area. As it drains, the Coriolis Effect causes the draining to be counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. The need for warm air to start the process means that tropical cyclones form in hot areas (in the tropics) but the need for the Coriolis Effect to generate the rotation means that they don’t form at the equator. For example, an area that straddles the equator would have air from the north trying to drain into the low pressure area counterclockwise while air from the south would be trying to drain in clockwise, causing a clash and no overall rotation. Furthermore, the Coriolis Effect depends on the difference between $$v_{eq}$$ and $$v_{lat}$$. Thus, in the northern hemisphere, air from the equator needs to move north enough so that there is enough of a difference between $$v_{eq}$$ and $$v_{lat}$$ for the Coriolis Effect to take effect. Thus, tropical cyclones don’t form at the equator. Instead, they form in the tropics but at a certain distance north or south to it.

Ocean Currents (at the Surface) and Trade Winds

So what causes surface ocean currents to rotate clockwise in the northern hemisphere and counterclockwise in the southern hemisphere? Especially since surface ocean currents are affected by surface winds, this defies the explanations above. The answer lies in the trade winds. Air at the equator at the surface (call this Air 1) is heated the most by the sun. This equator surface air will become hotter than the air above it as well as hotter than the air to the north and south, causing the less dense hot air to rise up relative to the colder, denser air all around it. The colder, denser air to the north and south (call this Air 2) move towards the equator to take the place of where the hot risen air once was. This air that has risen will become cooler as it is further from the surface, and with hot air continuously rising from below, the cooler air is pushed to the sides, i.e. pushed to the north and south. This is part of the Hadley Cell, where hot air rises from the surface at the equator, travels to the north (or south), and then once it has cooled due to being high in the atmosphere and now at a higher latitude, sinks down (at the horse latitudes). Part of that sunken air will travel back towards the equator and in the end will become that relatively colder denser air (Air 2) that took the place of the initial hot equator surface air (Air 1) that rose and started the process. Once Air 2 takes the place of the rising Air 1 at the equator surface, Air 2 will eventually be heated and rise, continuing this Hadley Cell process.

What this means is that near the surface and at the latitudes that sandwich the equator, the main movement of air is from the poles towards the equator. The Coriolis Effect acts on this air movement. Air in the northern hemisphere moving south will veer to the west and air in the southern hemisphere moving north will veer to the west, too.

The result is that near the equator, wind moves from east to west.

In actuality, at the equator surface, also known as the the Intertropical Convergence Zone or the doldrums, the air that comes in from the north and south is heated as it travels to the equator from the north and south, not necessarily after it has arrived at the equator. Thus, the heated air begins to rise before it arrives at the equator. What results is a “triangle” of very little wind at the equator surface, which is the doldrums.

Zooming back out, what we have around the equator (but perhaps not exactly at the equator where the doldrums are dominant) is winds from the north traveling south to the equator and winds from the south traveling north to the equator. But due to the Coriolis Effect, above the equator, north-to-south wind veers to the right or west, i.e. air currents here travel from the northeast to the southwest; and below the equator, south-to-north wind veers to the left or west, i.e. air currents here travel form the southeast to the northwest. These air currents drive surface ocean currents. So above the equator, you have water traveling from the northeast to the southwest. However, the Coriolis Effect affects these water currents, too. So above the equator, these water currents veer to the right. What we have is water moving from the northeast to the southwest, but also then veering right to west, and veering right to the northwest, and so on. Thus, surface ocean currents in the northern hemisphere near the equator tend to rotate clockwise. In the southern hemisphere, you have water that’s driven by wind to travel from the southeast to the northwest, which then veers to the left to the west, and veers left again to the southwest, and so on. Thus, surface ocean currents in the southern hemisphere near the equator tend to rotate counterclockwise.

Why do surface ocean currents rotate but air currents near the equator don’t? This is due to the air currents there being dominated by the Hadley Cells. Hot air near the equator becomes less dense and rises. Air nearby that is colder and denser moves toward the equator to fill that space. This movement of air from the horse latitudes toward the equator is what doesn’t allow a rotating air current in this area. The Coriolis Effect only adds the veering of air currents to the west. This Hadley Cell effect dictates that air must move towards the equator and thus doesn’t allow the Coriolis Effect to bring about air current rotation the way that ocean currents rotate.

A Bit More on Air Currents

The Hadley Cell with the Coriolis Effect tells us that between 30° latitude (the horse latitudes) and the equator, in the northern hemisphere, air near the surface travels southwest. This air rises up at the equator, and then then flows north. The Coriolis Effect then causes this air to veer to the right, i.e. to the east. Thus, air higher in the atmosphere travels form the southwest to the northeast. This air drops down towards the surface at 30° latitude.

The Polar Cells have a similar pattern. In the northern hemisphere, air at 60° latitude is warmed and rises. Risen air flows north and veers to the right, i.e. to the east. It sinks at the north pole, and then flows south near the surface. This cold and dense surface Polar Cell air that flows south veers to the right, i.e. to the west, as it replaces warmer and less dense air at 60° latitude.

This leave the question of why the Ferrel Cell, which lies between the Hadley Cell and Polar Cell, circulates the way it does – the opposite way that the other two cells do. Air near the surface flows north (and east, due to the Coriolis Effect), rises at 60° latitude, and then at high altitude flows south (and west, due to the Coriolis Effect), and sinks at 30° latitude. Explanations on the internet generally say that the Ferrel Cell is due to being an eddy formed from the neighboring Hadley Cell and Polar Cell. The winds of the Ferrel Cell near the surface, which flow from the southwest to the northeast, are called the Westerlies (because they are winds that originate from the west).

Cyclones and Water Currents; Low Pressure Rotation and High Pressure Rotation, and No Pressure Rotation

So we’ve described how cyclones end up rotating the way they do and how ocean currents rotate the way they do, but here’s what’s at the core of why they rotate differently. Cyclones form when there is a local area of low pressure (that starts from warm air that rises, leaving in its wake an area of low pressure. Air around that area is drawn into the low pressure area, and then the Coriolis Effect acts on that inwardly moving air.

The black arrows represent the movement of air inward towards the low pressure. The blue arrows represent the pressure-gradient force, which is the force being applied to air due to the difference in pressure, i.e. the “draining” force of air into the low pressure area. The red arrows represent the Coriolis Effect force, which in the northern hemisphere is to the right of the direction of movement. This results in counterclockwise cyclones in the northern hemisphere.

What about an area of high pressure? “Invert” the image above and imagine black arrows radiating outward due to the pressure gradient. All these arrows veer to the right in the northern hemisphere due to the Coriolis Effect. And what you get is clockwise rotation in the northern hemisphere and counterclockwise rotation in the southern hemisphere.

This is an image of an anticyclone in the southern hemisphere (south of Australia) and you can see in some parts the counterclockwise rotation of the cloud streaks.

Finally, what if there is no pressure gradient? Then, if something happens to move in a direction for some external reason, the Coriolis Effect will continually cause it to veer right in the northern hemisphere, i.e. it will cause clockwise rotation in the northern hemisphere and counterclockwise rotation in the southern hemisphere.

The above is an image of inertial circles of air masses, where the Coriolis Effect at a certain latitude is taken, velocity of wind is assumed to be 50 to 70 m/s, and then the radius is found for there to be stable circular motion. In the oceans currents images from above,

these are clearly not the same thing. But the principle is the same. Assuming no pressure gradient, surface ocean currents begin to move in some direction due to the trade winds (from the northeast to the southwest in the northern hemisphere). The Coriolis Effect, in the northern hemisphere, causes the ocean currents to veer to the right. Thus, we have clockwise ocean currents in the northern hemisphere and counterclockwise ocean currents in the southern hemisphere.

Deep Ocean Currents

Surface wind affects ocean currents down to 400m depth. Deep ocean currents are a different beast that move due to thermohaline circulation. Thermo refers to temperature and haline refers to salt. Both refer to how they affect the density of water. Thus, deep ocean currents move due to differences in water density.

Some surface ocean currents move as fast as 1 m/s while deep ocean currents typically move at 1 cm/s. As can be seen from the images, there is no pattern in deep ocean thermohaline circulation that follows the Coriolis Effect in the hemispheres.


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