Geostrophic wind

Why does the wind follow the lines on a weather map instead of blowing straight from high pressure to low?

Open any weather chart and the isobars — lines of equal pressure — curl around the highs and lows like contours on a map. Now put the observed winds on top. They do not run downhill from high to low, the way water would. They run along the lines, near enough parallel, with the low pressure consistently on one side.

That is a strange thing for a fluid to do. Pressure differences push; the push points squarely across the isobars, from high toward low, and there is nothing pushing along them. So how does a fluid end up travelling at right angles to the only force that started it moving?

Take the phrase "the only force" seriously, because it is true at the first instant and false a moment later. Consider a parcel of air initially at rest in a pressure gradient. The pressure gradient force acts on it, across the isobars toward the low, and it accelerates that way. So far, exactly what intuition predicts.

But it is now moving, and moving on a rotating planet. In the frame we actually use — the ground, which turns with the Earth — a moving parcel's track curves: to the right in the northern hemisphere, to the left in the southern. We account for that by writing down an apparent force, the Coriolis force, whose crucial property is that its size is proportional to the speed. At rest it is exactly zero.

So watch the sequence. As the parcel gains speed the Coriolis term grows from nothing and swings its track to the right. Turning right means the pressure gradient force is no longer pushing straight along its path, so the acceleration slackens — but the deflection continues. Where does this end?

It ends when the track has swung far enough that the Coriolis force points exactly opposite the pressure gradient force. That happens when the parcel is moving at right angles to both — which is to say, along the isobars. At that moment the two forces cancel, the net force is zero, and there is no more acceleration in any direction. The parcel keeps going, at constant speed, parallel to the lines. Nothing pushed it along them; it simply stopped being pushed anywhere else.

Which side is the low on? In the northern hemisphere, Coriolis acts to the right of the motion, so it must be pointing from low toward high in order to oppose the gradient force — which puts the low on the parcel's left. That is Buys Ballot's law: stand with your back to the wind in the north and low pressure lies to your left. In the southern hemisphere the sense reverses.

Now the second half of the question, because this balance is not the whole story. Near the ground, air is dragged over trees, buildings and waves. Friction slows it. And because Coriolis is proportional to speed, slowing the air weakens the Coriolis force specifically, while leaving the pressure gradient force untouched. The balance tips, and the wind turns partway back toward the low — crossing the isobars by perhaps ten to twenty degrees over open ocean and thirty or more over rough land.

That leftover cross-isobar component matters enormously. It means surface air spirals inward toward a low from all sides, and air converging at the surface has nowhere to go but up; rising air cools, condenses, and makes cloud and rain. Around a high the argument runs backwards: air spirals outward, and air must sink to replace it, warming and drying. The reason lows bring weather and highs bring clear skies is precisely the small angle friction adds.

Three clarifications keep this honest.

Coriolis is not a force in the sense that pressure is. It is a bookkeeping term we add because we insist on describing motion in a rotating frame. Nothing pushes the air sideways; the ground turns underneath it. The term is nonetheless exactly right for predicting what an observer on the ground sees, which is what a weather chart is.

The balance describes a settled state, not a parcel starting from rest. Real air is already moving and the gradients are already there; the reasoning above shows why the settled state is the parallel one, and why a disturbed flow returns to it. It is an approximation with known limits: it fails near the equator, where the Coriolis term goes to zero, so tropical circulations obey different rules; it needs correction where isobars curve sharply, since going round a curve requires a genuine net force, giving what is called the gradient wind; and it holds poorly near fronts.

Finally, strength as well as direction is readable off the chart. Balance means the two forces are equal, and the pressure gradient force is set by how closely the isobars are packed — so tightly spaced lines mean strong wind. Meteorologists read speed off spacing for the same reason they read direction off orientation.

• Gradient wind balance, and why curved isobars mean a low's winds differ from a high's at the same spacing.
• The Ekman spiral — how the cross-isobar angle changes with height through the boundary layer.

Every term the collection defines is gathered in the glossary.