Vorticity and Circulation Questions and Answers

Answer: A

Where the vertical velocity varies horizontally, a horizontal vortex tube is tipped so that part of it points vertically, converting horizontal into vertical vorticity. This is the mechanism by which environmental shear becomes updraught rotation in a supercell. Horizontal transport is advection, frictional generation is a separate term, and latitude change is the beta effect acting through planetary vorticity. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: B

Environmental shear provides horizontal vorticity, and the updraught tilts it into the vertical, giving the rotating updraught that defines a supercell. Stretching then intensifies the rotation further. Synoptic cyclone intensification is dominated by stretching, Rossby waves depend on the beta effect, and the sea breeze arises from the solenoidal term, so none of the others requires tilting. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: C

With no divergence, no tilting, no solenoidal term and no friction, the vorticity equation reduces to the statement that the absolute vorticity is conserved following the motion. Relative vorticity is not conserved because planetary vorticity changes as the parcel changes latitude. Potential temperature is indeed conserved for adiabatic motion but that is a thermodynamic rather than a vorticity result. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: D

Moving poleward increases the planetary vorticity, so conservation of the sum requires the relative vorticity to decrease, becoming anticyclonic. The parcel therefore curves back towards the equator, which is the restoring mechanism of a Rossby wave. Absolute vorticity is by hypothesis conserved, so it cannot increase. This one argument accounts for the meandering of the upper westerlies.

Answer: A

A parcel displaced poleward acquires anticyclonic relative vorticity and turns back, while one displaced equatorward acquires cyclonic vorticity and does the same, giving a wave whose phase propagates westward relative to the mean flow. Gravity waves are restored by buoyancy and acoustic waves by compressibility, so their mechanisms are quite different. Kelvin waves are a special class of trapped wave relying on a boundary or on the equator. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: B

The phase speed of a Rossby wave is always westward relative to the mean flow, with a magnitude proportional to beta and to the square of the wavelength. Long waves may therefore be stationary or even retrogressive against a westerly flow, while short waves are carried eastward. This dependence of phase speed on wavelength is what separates the slowly moving long waves from the rapidly moving short waves on a chart. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: C

Setting the intrinsic westward phase speed equal and opposite to the eastward advection by the mean flow gives the stationary wavelength, typically several thousand kilometres in mid-latitudes. Waves longer than this retrogress and shorter ones progress. Orographically forced waves are stationary by construction, which is why the wavelength matters for understanding where the long wave troughs sit relative to the mountains. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: D

The beta term is the meridional wind multiplied by the meridional gradient of the Coriolis parameter, and it represents the change of relative vorticity required as a parcel changes latitude. It is the sole source of Rossby wave propagation. The other options name the stretching, tilting and frictional terms, each of which appears separately in the same equation and must be kept distinct from the beta effect. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: A

Ertel's potential vorticity is the absolute vorticity vector dotted with the gradient of potential temperature and divided by density, so it combines rotation with stratification. That combination is conserved following adiabatic frictionless motion in a fully three-dimensional stratified flow. The Coriolis parameter is already inside the absolute vorticity, and divergence and circulation are different quantities entirely. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: B

Ertel's theorem requires only that the motion be adiabatic and frictionless, with no restriction on baroclinicity, divergence or steadiness. That generality is what makes potential vorticity so much more useful than absolute vorticity. Motion does in fact stay on an isentropic surface when adiabatic, so the last option restates a consequence rather than an independent condition.