Vorticity and Circulation Questions and Answers

Answer: C

Terminal Doppler weather radars measure the radial velocity field close to the runway and detect the divergent signature of a microburst outflow directly. Low level wind shear alert systems using anemometer networks serve the same purpose. Barometers respond too slowly, radiosondes sample only one point in the vertical, and satellite imagery cannot resolve a feature only a few kilometres across near the surface. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: D

Mid-level convergence beneath the stratiform precipitation region stretches the column and concentrates the absolute vorticity into a mesoscale vortex. Such vortices sometimes go on to seed tropical cyclogenesis. The beta effect is negligible over the short lifetime and small scale, the solenoidal term is small in pressure coordinates, and friction acts to dissipate rather than concentrate at these levels. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: A

These vortices form near 600 to 700 hectopascals, in the layer of convergence beneath the stratiform anvil and above the evaporatively cooled downdraught. Their mid-level position is why they are often invisible on a surface chart yet clearly evident in satellite imagery and radar. A surface cold pool is divergent rather than convergent, and the tropopause level flow is divergent outflow.

Answer: B

The non-divergent wind is obtained from the streamfunction by taking its gradient and rotating, and taking the curl of that gives the Laplacian. Solving the resulting Poisson equation is how a streamfunction is recovered from a vorticity field, which is the essential step in potential vorticity inversion and in barotropic forecasting. The gradient rotation gives the wind rather than the vorticity. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: C

Since vorticity is the Laplacian of the streamfunction, recovering the streamfunction requires inverting the Laplacian, which is a Poisson problem needing boundary conditions on the domain. This is why vorticity inversion is a global rather than a local operation: a vorticity anomaly influences the flow everywhere, though the influence decays with distance. Continuity gives the divergent part instead. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: D

Because inverting the Laplacian spreads the influence of a point source over the whole domain, a compact vorticity anomaly induces a circulation that decays outward but never vanishes abruptly. This action at a distance is the basis of the potential vorticity thinking used to explain cyclogenesis. Boundary conditions matter greatly in a Poisson problem, and vorticity itself is computed locally from the wind field. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: A

Computing a derivative from scattered noisy observations amplifies the error, so vorticity fields are usually derived from an analysed wind field that has already been smoothed and balanced. Vertical velocity does not enter the vertical component of vorticity at all, vorticity is entirely physical, and the Coriolis parameter is known to far greater precision than anything else in the calculation. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: B

Because the Laplacian amplifies short wavelengths, raw vorticity computed from an analysis contains a great deal of small-scale noise that obscures the meteorologically significant maxima. A smoothing pass is therefore standard before display. Absolute vorticity, which retains the planetary part, is what is normally plotted, potential vorticity is a separate product, and anomalies from climatology are used for other purposes such as identifying unusual events rather than for routine synoptic tracking of short wave features.

Answer: C

Charts are labelled in units of \( 10^{-5} \) per second, so a typical mid-latitude absolute vorticity reads as about 10 and a strong maximum as 20 or more. Choosing a unit that makes the values order ten keeps the labels legible. Radians per second is dimensionally the same but gives inconveniently small numbers, and potential vorticity units belong to a different field entirely.

Answer: D

As a cyclone occludes, the vorticity maximum that was upstream of the surface low wraps around and becomes vertically aligned with it, giving a closed centre on the chart. That alignment marks the end of deepening. A pair of maxima can occur transiently during a merger, and a vorticity minimum would indicate anticyclonic flow, which is the opposite of what a cyclone possesses.