Vorticity and Circulation Questions and Answers

Answer: A

Forecasters track vorticity maxima on the 500 hectopascal chart because they move with the flow and their advection forces vertical motion downstream. Short wave troughs are the corresponding features in the height field and usually accompany them, jet streaks are wind speed maxima, and potential vorticity anomalies are the isentropic analogue. The terms are related but each refers to a specific field. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: B

Because vorticity is the Laplacian of the streamfunction, taking it amplifies short wavelengths, so weak short wave troughs invisible in the height field stand out clearly. That same amplification makes vorticity fields noisier rather than smoother, which is the price paid. Neither field is measured directly and vorticity takes both signs, so the other options are simply wrong.

Answer: C

Differentiating twice amplifies small-scale error, so a vorticity field derived from an imperfect height analysis contains a great deal of noise that must be filtered before use. Computation is possible wherever an analysis exists, however imperfect, and the field remains continuous. The relative vorticity of the actual wind is well defined regardless of balance, though its geostrophic estimate does degrade. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: D

Taking the curl of the geostrophic wind gives the relative vorticity as the Laplacian of geopotential divided by the Coriolis parameter. This is why a sharply curved trough, where the height field is strongly concave, is a vorticity maximum. The relation also underlies potential vorticity inversion, since it is the step that connects a vorticity distribution back to a height field.

Answer: A

Vorticity is the Laplacian of the height field, so it is largest where that field is most sharply concave, which occurs at the base of a well defined trough. A ridge crest is convex and gives a vorticity minimum. Straight evenly spaced contours give zero, and a col is a saddle at which the two curvatures largely cancel. Estimating vorticity from contour shape is a valuable analytical habit. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: B

In the barotropic model the absolute vorticity is simply advected by the non-divergent wind, which is enough to reproduce the movement of the long waves. It was the equation integrated in the first successful numerical forecast in 1950. Vertical velocity is identically zero in the model, temperature does not appear, and surface pressure tendency requires divergence that the model does not possess. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: C

With no divergence and no baroclinicity, the barotropic model conserves absolute vorticity and can move existing systems but cannot intensify them. That is why it forecasts the movement of long waves well and cyclogenesis not at all. Advection is precisely what it does represent, it integrates easily, and it needs only a single level wind or height analysis to start.

Answer: D

A baroclinic model carries at least two levels so that vertical motion, temperature advection and the conversion of available potential energy can be represented, which is what permits development. Friction and radiation are optional additions rather than the defining difference. The beta effect is present in barotropic models too and is indeed what allows them to propagate Rossby waves at all. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: A

If the ratio of absolute vorticity to depth is fixed, increasing the depth requires the absolute vorticity to increase in proportion. The reason therefore explains the assertion exactly. This single argument accounts for lee cyclogenesis east of mountain ranges, for the intensification of columns moving from shallow to deep water in laboratory experiments, and for much of the vorticity budget of developing cyclones.

Answer: B

Stretching amplifies the existing absolute vorticity, so with the planetary contribution zero and relative vorticity initially small there is nothing for the convergence to work on. The reason therefore explains the assertion. In practice storms require about five degrees of latitude, and the rare exceptions involve unusually strong pre-existing relative vorticity supplied by some other mechanism.