Fundamental Forces in the Atmosphere Questions and Answers

Answer: C

Hydrostatic balance states that the upward pressure gradient force per unit mass equals the acceleration due to gravity, and it holds to better than one part in a thousand for all large-scale motion. Buoyancy is precisely the small residual after that balance is removed, so it cannot be the balancing term itself. Coriolis acting on horizontal wind gives a vertical component far too small to matter, and centrifugal effects are absorbed into effective gravity. The balance is what makes pressure usable as a vertical coordinate.

Answer: D

The gravity we measure is the vector sum of Newtonian gravitational attraction and the outward centrifugal acceleration of the rotating Earth, which is why it points slightly away from the geocentre except at the poles and the equator. The Earth's equatorial bulge is itself the equilibrium response to this combination, so effective gravity is perpendicular to the geopotential surfaces everywhere. Crustal density variations, buoyancy and air drag produce much smaller effects that are not part of the definition.

Answer: A

The centrifugal acceleration is proportional to the distance from the rotation axis, so it is greatest at the equator and zero at the poles, reducing effective gravity by about 0.3 per cent between the two. The equatorial bulge adds a further reduction of similar size. Angular velocity is the same everywhere on a rigid Earth even though the linear speed differs, and neither atmospheric depth nor surface temperature enters the definition of gravity at all.

Answer: B

Geopotential surfaces are by definition the surfaces of constant potential energy per unit mass, so effective gravity, being the gradient of that potential, is normal to them everywhere. This is what allows geopotential height to replace geometric height as a vertical coordinate with gravity absorbed. Constant pressure and constant density surfaces are generally tilted with respect to these, and a spirit level in fact defines the local geopotential surface, so that option is a restatement rather than an alternative.

Answer: C

Turbulent stress transmits the drag of the surface upward through the planetary boundary layer, typically the lowest kilometre, and above that the free atmosphere is very nearly frictionless. Coriolis, pressure gradient and gravity all act at every level. The confinement of friction is what produces the characteristic cross-isobaric flow near the ground, the convergence into surface lows and the Ekman spiral, none of which has any counterpart in the free atmosphere above.

Answer: D

Friction reduces the wind speed, which weakens the Coriolis force, so the pressure gradient force is no longer balanced and the flow acquires a component directed towards low pressure. The resulting cross-isobaric angle is around ten to twenty degrees over the sea and thirty degrees or more over rough land. This inflow is what fills a surface low and drives the ascent above it, so friction is not merely a brake but an essential part of the life cycle of weather systems.

Answer: A

Mass converging into the low near the surface must leave, and the only available route is upward, producing the ascent that generates the cloud and precipitation associated with lows. The same argument gives descent and clear skies over surface highs. Friction removes energy so the circulation weakens rather than strengthens, a process known as spin-down, and the movement of a system is governed by the steering flow aloft rather than by friction.

Answer: B

The Rossby number is the ratio \( U/(fL) \), and when it is much less than one the Coriolis force dominates and the flow is very nearly geostrophic. For a synoptic system with \( U \) about 10 metres per second, \( L \) about 1000 kilometres and \( f \) about \( 10^{-4} \), the value is roughly 0.1. Richardson, Froude and Reynolds numbers compare other pairs of effects. Computing a Rossby number is the standard first step in deciding which approximation applies to a given flow.

Answer: C

Substituting gives \( Ro = 10/(10^{-4} \times 10^{6}) = 0.1 \), a value small enough that the geostrophic approximation is good to about ten per cent, which is the basis of quasi-geostrophic theory. A value near one would indicate that inertia and rotation compete, as in a tropical cyclone core, and a much larger value would describe a tornado or a laboratory flow where rotation is irrelevant. Making this estimate before choosing an approximation is a habit worth acquiring early.

Answer: D

A large Rossby number means the inertial acceleration greatly exceeds the Coriolis acceleration, so the Earth's rotation may be neglected, which is the case for a tornado, a dust devil or water leaving a basin. Geostrophy requires the opposite limit. Friction is measured by a different ratio, and the hydrostatic approximation depends on the aspect ratio of the motion rather than on the Rossby number. The popular claim that bath water circulates according to hemisphere fails precisely because of this scaling.