Geostrophic and Gradient Wind Questions and Answers

Answer: C

Given the radial pressure profile and the radius, the gradient wind equation gives the tangential wind that balances it, which is the basis of pressure-wind relationships used operationally. Storm motion is governed by the steering flow, and the eye radius and vertical extent are set by other aspects of the dynamics. The relationship is only approximate because real storms are unsteady and the balance is never exact, but it is accurate enough to be useful.

Answer: D

The relationship follows directly from assuming balance between the radial pressure gradient and the sum of Coriolis and centrifugal forces. Symmetry and steadiness improve the accuracy but are secondary, and a well defined eye is a feature of intense storms rather than a requirement. Departures from balance during rapid intensification are exactly why observed winds sometimes exceed the value the relationship predicts. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: A

Anticyclonic means rotating in the sense opposite to the local vertical component of the Earth's rotation, which is clockwise in the northern hemisphere and anticlockwise in the southern. The final option states the definition correctly in words but then applies it to the Earth as a whole rather than to the local vertical, which reverses the answer in the southern hemisphere. Anchoring the definition to the local vertical avoids that trap entirely. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: B

Relative vorticity is positive for anticlockwise rotation in the usual convention, so northern hemisphere anticyclonic flow has negative relative vorticity. In the southern hemisphere anticyclonic flow is anticlockwise and so has positive relative vorticity, which is why cyclonic is the safer word than any statement about sign. Divergence is an independent property that does not affect the sign of the vorticity.

Answer: C

Taking the curl of the geostrophic wind gives the relative vorticity as \( \nabla^{2}\Phi / f \), so a low is a region of positive geostrophic vorticity in the northern hemisphere. This is why the height field alone determines the vorticity in balanced flow, and it is the basis of potential vorticity inversion. The result also explains why sharp troughs, with strongly curved contours, correspond to large vorticity maxima. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: D

Because vorticity is the Laplacian of the height field, it is largest where the field is most sharply concave, which is at the base of a well defined trough. A ridge crest is convex and so a vorticity minimum. Straight evenly spaced contours give zero vorticity, and a col is a saddle point where the two curvatures largely cancel. Reading vorticity from the shape of the contours rather than from a separate field is a valuable analytical habit. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: A

The thermal wind is the vector difference between the geostrophic winds at the top and bottom of a layer, and it blows parallel to the layer mean isotherms with cold air on the left in the northern hemisphere. It is not itself a wind that anything experiences but a shear. Its existence follows from combining geostrophic and hydrostatic balance, so it applies wherever both do.

Answer: B

With cold air to the north, the thermal wind blows with cold air on its left, which means from the west. This is why the mid-latitude westerlies strengthen with height and why the jet stream sits above the strongest surface temperature gradient. The summer stratosphere does have temperature increasing polewards, which is exactly why its winds are easterly, and that reversal is a good check that the rule has been applied correctly. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: C

The thermal wind relation requires the westerly shear to be greatest where the horizontal temperature gradient is greatest, so the jet core lies directly above the polar front. Its seasonal strengthening in winter is also a thermal wind consequence, since the temperature contrast is then largest, but the positioning is the more fundamental point. The meandering and the fragmentation arise from wave dynamics rather than from the balance relation itself. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: D

In a barotropic atmosphere density depends only on pressure, so isobaric and isothermal surfaces are parallel and the thermal wind vanishes, leaving no vertical shear of the geostrophic wind. A baroclinic atmosphere is the opposite case and is where the available potential energy driving mid-latitude weather resides. Isentropic refers to constant potential temperature, and neutral stratification is a statement about the vertical lapse rate. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.