A conversation about winds and isobars

E. Linacre

6/'98

Q. Thereís something I donít understand concerning winds. Iím talking about winds above the influence of the surfaceís roughness, wetness, friction and irregularities, at a height of 1000 metres, say. Why doesnít the wind flow straight from where pressures are high to where they are low, just like rivers carving a valley down towards lower elevations? Why instead does the wind (aloft) go from a place at one pressure towards other places at the SAME pressure. If water flows along the same contour (on level ground), it stops flowing. Yet the winds aloft continuously blow ALONG the same isobar, not across it. To say that air flows along an isobar seems like claiming that water flows along contour lines AROUND a hill, instead of down. How do you explain this?

A. The explanation is that THE EARTH IS ROTATING, and the observer rotates with it. As a result, the initial motion of winds towards places of lower pressure appears to be deflected, to the left in the southern hemisphere. It looks as though there is a sideways force on the winds, in addition to the driving force due to the pressure difference. This is called the Coriolis effect. It is true that wind blowing along the isobars would slow down eventually, because it is only retarded be friction. But there is potential energy in a situation where cold air is next to warmer air (between the pole and the equator, or across a front). And this potential energy is continuously converted to kinetic energy, i.e. the airflow aloft.

 

Q. Please explain the Coriolis effect.

 

A. There are several ways of accounting for the apparent sideways deflection of moving objects, when viewed by a rotating observer.

1. There is a distinction between what we see and what is really happening, applied to the difference between the turning of an observer (O) and turning by what is observed (W). The difference could be due either to O turning or to W turning. However, in practice, O is unaware of her own twisting, so any difference is automatically attributed to rotation by W, even if this is untrue. The classic case is our Earthís daily rotation, which makes us interpret what we see in the sky as the circling of the Sun. Actually the Sun is still; its apparent westward movement is the result of our own turning eastward. Similarly, we (on the rotating Earth) see all large-scale winds as apparently rotating, i.e. constantly pushed sideways.

2. The spherical shape of the rotating Earth means that places at 30° S spin eastwards at about 410 m/s (ie 1,500 km/h), whilst those at 40° S turn at only 360 m/s. (We are quite unconscious of these enormous speeds because our whole environment moves at the same speed.) This means that a northerly wind at 30° S (simultaneously moving sideways at 410 m/s) is moving eastwards 50 m/s faster than the ground beneath, when it reaches 40° S. So the wind will now appear to be a westerly of 50 m/s. In moving to a higher latitude, the wind will seem to have turned to the left. You can work out likewise that a southerly wind from 40° S appears to turn, again leftwards, becoming an easterly of 50 m/s at 30° S.

3. In addition, there are several other ways of explaining the Coriolis effect by means of diagrams, or mathematically. Also, it can be shown that the Effect applies whatever the direction of the windís motion, and increases with the windís speed.

 

Q. But how does the Coriolis effect explain why winds flow ALONG isobars on the usual weather map?

 

A. Well, although winds start by flowing from high to low pressures, they look from the (rotating) ground to turn, leftwards in the southern hemisphere. The deflection is to the right in the northern hemisphere, where eastwards movement represents an anticlockwise revolution around the pole. The wind moves as though always pushed to the left, at the same time as it is constantly pulled towards the region of low pressure, which is in a direction at right angles to the isobar. So the wind gradually accelerates and turns, until an equilibrium is reached, with a balance between the pressure-difference force (pdf) across the isobars towards the right, opposite the Coriolis force to the left. Then the equality and exactly opposite directions of the two forces prevents further turning. Also, the wind is now flowing along the isobars, in order that the pdf (as well as the Coriolis force) is perpendicular to the motion.

 

Q. Thatís not easy to grasp.

 

A. True. Read it again slowly. Try drawing a diagram of what happens, showing the Coriolis always to the left at right angles to the wind, and the pdf at right angles to the isobars. Bear in mind that the wind will move in a direction between the directions of the two forces, like a mother tugged by a child on either side, with the one on the right (representing the pdf in the southern hemisphere) initially in front but gradually falling to the side as the mother accelerates. Youíll find such a diagram here.

 

Q. All right, Iíve got that. What does it mean in terms of winds around a high or a low?

 

A. In the case of a high, air escapes outwards, is then DEFLECTED LEFT (IN THE SOUTH HEMISPHERE) and consequently circles anticlockwise around the high. In that way, the outwards pressure-difference force matches the leftwards Coriolis force. For airflow into a low, it is again twisted left, so the balance of forces means a clockwise rotation about the lowís centre.

 

Q. Is this explanation realistic?

 

A. Well, fairly realistic. There are complications due to friction of the winds on the ground, and to an outwards centrifugal force on spinning objects, but for large-scale flow, they are less important than the Coriolis effect, except near the equator, where the effect is small. The complications mean that the winds do not flow exactly along isobars. Usually they tend slightly to flow towards lower pressure, especially near the ground. So they SPIRAL out from a high and into a low.

 

Q. Why did you say the effect is small near the equator?

 

A. Because places at the equator do not rotate in the same way that places at high latitudes do. A man standing at the north pole with arms outstretched finds his right hand advances towards the Sun during the day, and it is the left hand which advances for someone at the south pole, but a person at the equator does not turn about his own axis at all. Without such turning there is no Coriolis effect.

The opposite directions of turning in the two hemispheres explain the different directions of the Coriolis effect. One may thus consider the effect as positive in one hemisphere and negative in the other, from which it follows that it is zero at the equator between.

 

Q. Is there more could be said on this topic?

 

A. Yes, plenty. But thatís enough for one session.