Fundamental Forces in the Atmosphere Questions and Answers

Answer: C

Hydrostatic balance requires the horizontal scale to greatly exceed the vertical scale, and in a convective updraught only a few kilometres wide but ten kilometres deep that condition fails, so vertical accelerations of order a metre per second squared occur. Cyclones, jets and anticyclones all have horizontal scales far greater than their depth. This is why convection-permitting forecast models must solve non-hydrostatic equations while global models traditionally did not.

Answer: D

A tornado has a Rossby number of order a thousand, so Coriolis is entirely negligible while the centrifugal term dominates, giving the cyclostrophic balance between pressure gradient and curvature. This is why tornadoes may rotate in either sense, though most rotate cyclonically because they inherit the rotation of their parent storm. Gravity has no horizontal component, and friction matters at the surface but does not define the balance in the vortex itself.

Answer: A

Cyclostrophic balance sets the pressure gradient force against the centrifugal force alone, which is appropriate when the Rossby number is very large. The pressure deficit at the centre of a tornado, of order a hundred hectopascals over a few hundred metres, is what sustains the enormous rotational speed. Geostrophic and Ekman balances belong to large-scale flow, and hydrostatic balance is vertical. Naming the four balances and the regime each describes is a standard examination requirement.

Answer: B

Ekman balance is the three-way balance of pressure gradient, Coriolis and frictional forces that holds within the planetary boundary layer, and its solution is the spiral in which the wind veers with height while increasing in speed towards the geostrophic value. Adding the centrifugal term instead gives gradient wind balance, buoyancy belongs to the vertical equation, and the Coriolis term acting on vertical velocity is what the traditional approximation discards.

Answer: C

As friction weakens upward, the cross-isobaric angle shrinks and the wind turns clockwise, or veers, towards the geostrophic direction while its speed increases. In the southern hemisphere the sense reverses. The idealised spiral is rarely observed exactly because eddy viscosity is not constant with height, but the veering and the strengthening are both robust features of the real boundary layer and are what the model is used to explain.

Answer: D

Convergence in the frictional layer beneath a cyclonic circulation forces air upward out of the boundary layer, and the resulting vertical velocity is proportional to the relative vorticity of the flow above. This is the mechanism by which friction spins down a vortex on a timescale of a few days. Turbulent momentum transport is the cause of the friction rather than the pumping, and tilting is a separate vorticity source discussed elsewhere in this subject.

Answer: A

Ekman pumping removes the vorticity of a synoptic vortex on a timescale of order the depth of the troposphere divided by the pumping velocity, which works out at roughly four days. That is far shorter than molecular diffusion would give and far longer than the rotation period of the vortex. It also matches the observed lifetime of decaying cyclones, which is the empirical check that makes the theory convincing rather than merely tidy.

Answer: B

A force perpendicular to the velocity has no component along the direction of motion, so its rate of doing work is zero and the kinetic energy of the parcel is unchanged. The reason is therefore exactly the explanation of the assertion. This is why Coriolis can organise a circulation but never energise one, and why the energy budget of a weather system is written in terms of pressure work and buoyancy alone.

Answer: C

The reason is a correct statement of the Coriolis effect, but the assertion is false because the Rossby number of a draining basin is enormous, so residual motion in the water overwhelms the Coriolis deflection completely. Careful experiments in very still, symmetrical vessels can demonstrate the effect, which is why the myth persists, but nothing in an ordinary sink does so. This is the standard illustration of why scale analysis must precede physical argument.

Answer: D

Because the residual vertical acceleration is around \( 10^{-7} \) metres per second squared against a gravitational acceleration near 10, the two vertical terms must balance to about one part in a hundred million. The reason is precisely why the assertion holds. The balance fails only where the horizontal scale of the motion becomes comparable with its depth, as in deep convection, which is exactly the case that non-hydrostatic models were developed to handle.