Fundamental Forces in the Atmosphere Questions and Answers

Answer: C

Air moving poleward aloft conserves angular momentum and is deflected eastward by Coriolis, so by about thirty degrees the flow is almost entirely zonal and can carry heat no further poleward. The cell therefore closes and descends there, creating the subtropical highs and the desert belt. Friction acts at the surface rather than in the upper branch, and the pressure gradient does not reverse but is itself a consequence of the descent.

Answer: D

In the absence of friction the horizontal balance is between pressure gradient and Coriolis alone, which requires the wind to be along the isobars. Any cross-isobaric component in steady straight flow is evidence of a dissipative force. Constant wind with height would in fact indicate no thermal wind and hence no temperature gradient, light winds say nothing about friction, and time variation reflects the evolution of the pressure field.

Answer: A

Geostrophic balance is the exact opposition of the horizontal pressure gradient force and the Coriolis force, giving a wind that flows along the isobars with low pressure on the left in the northern hemisphere. Pressure gradient against friction alone describes flow deep within a very rough surface layer, gravity against buoyancy is a vertical relation, and the last pair describes neither a real balance nor a useful approximation.

Answer: B

Exact geostrophic balance requires the Coriolis force, which is perpendicular to the velocity, to oppose the pressure gradient force, which is perpendicular to the isobars, so the velocity must lie along the isobars. The thirty degree angle belongs to frictional surface flow, and a perpendicular wind would describe the instant of release from rest before any balance is reached. The angle does not depend on latitude in the geostrophic case.

Answer: C

Buys Ballot's law states that in the northern hemisphere an observer with their back to the wind has low pressure on the left, and the rule reverses in the southern hemisphere. It follows directly from the geostrophic balance and the rightward Coriolis deflection. The law is worth learning in the physical form rather than as a mnemonic, since it can then be reconstructed from the force balance whenever the hemisphere or the sign is in doubt.

Answer: D

The geostrophic wind is proportional to the pressure gradient, so packing the isobars twice as closely doubles it. The absolute pressure is irrelevant, since a uniform field exerts no force. Increasing the latitude increases \( f \) and so decreases the wind for a given gradient, and the depth of the layer does not enter a purely horizontal balance. Reasoning from the formula rather than from intuition avoids the common error over absolute pressure.

Answer: A

Since the geostrophic wind is the pressure gradient force divided by \( f \), and \( f \) grows with latitude, the same isobar spacing corresponds to a weaker wind nearer the pole. The stronger Coriolis force balances the same pressure gradient at a lower speed. Nothing reverses at any latitude in the same hemisphere, and the effect is substantial: the same spacing gives roughly forty per cent more wind at thirty degrees than at sixty.

Answer: B

Dividing by a vanishing \( f \) would give an infinite geostrophic wind, so the balance breaks down within roughly five degrees of the equator. Tropical dynamics therefore relies on different balances, and tropical pressure gradients are in fact very weak rather than strong. Friction is no more dominant there than elsewhere in the free atmosphere. This breakdown is why numerical analysis schemes must treat the tropics differently from mid-latitudes.

Answer: C

Synoptic scale vertical motion is of order one centimetre per second, some three orders of magnitude smaller than the horizontal wind, which is why it cannot be measured directly and must be inferred from divergence or from the omega equation. Convective updraughts reach several metres per second but are not large-scale. Appreciating this enormous disparity between horizontal and vertical scales is what justifies the hydrostatic approximation.

Answer: D

A vertical velocity of a centimetre per second is well below the accuracy of any routine wind measurement, so it is computed from the divergence of the horizontal wind or diagnosed from the omega equation instead. Instruments certainly can measure vertical motion in convective settings where it is large. The difficulty is entirely one of magnitude relative to measurement error, which is why small errors in horizontal divergence translate into large errors in the derived vertical velocity.