Geostrophic and Gradient Wind Questions and Answers

Answer: A

Setting the Coriolis force equal to the centripetal acceleration gives \( fV = V^{2}/R \), so \( R = V/f \). At mid-latitudes with \( f \) about \( 10^{-4} \) per second, a wind of 10 metres per second corresponds to a radius of 100 kilometres. This is comparable with the scale of a synoptic system, which is another way of seeing why rotation matters so much at that scale and so little at the scale of a thunderstorm. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: B

Writing the momentum equation along and normal to the flow makes the centrifugal term appear directly as the speed squared divided by the radius of curvature of the trajectory. That makes the gradient wind balance immediate rather than something to be extracted from vector algebra. Divergence and vorticity are derived from the wind field rather than appearing as terms in this equation, and the angle between wind and gradient is zero by construction in balanced flow.

Answer: C

Gradient wind balance involves the curvature of the parcel's actual path, whereas a chart shows instantaneous streamlines, and the two differ whenever the pattern is moving or developing. For a rapidly moving system the difference is substantial. The distinction is a classic source of error in hand analysis. The radius is of course measured within the system, and either vertical coordinate may be used provided the corresponding form of the pressure gradient term is taken.

Answer: D

For a steady pattern that neither moves nor changes shape, a parcel follows a streamline exactly and the two curvatures agree. When the pattern translates, the trajectory curvature may differ greatly, being larger than the streamline curvature when the system moves in the same sense as the flow. Blaton's equation relates the two quantitatively. The distinction has nothing to do with hemisphere or with constancy of speed alone. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: A

Contours of geopotential height on a constant pressure chart give the geostrophic wind directly through their spacing and orientation, which is why such charts are drawn in the first place. The gradient wind requires additional knowledge of the trajectory curvature, and the actual wind requires observations. The thermal wind is obtained by comparing two charts at different levels rather than from a single one.

Answer: B

The geostrophic value read from contour spacing must be reduced where the flow curves cyclonically and increased where it curves anticyclonically, and gradient wind scales built into plotting tools do exactly this. Latitude is already taken into account by the geostrophic scale itself, friction is irrelevant above the boundary layer, and density does not appear at all when pressure is the vertical coordinate.

Answer: C

With a Rossby number near 0.1, the ageostrophic wind is roughly a tenth of the geostrophic wind, so the approximation is good to about 10 per cent. That is accurate enough to be extremely useful and inaccurate enough that the residual carries all the interesting dynamics. A one per cent departure would describe a much larger scale flow, and the larger figures would place the flow outside the balanced regime altogether. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: D

A sea breeze with a speed of about 5 metres per second and a scale of a few tens of kilometres gives a Rossby number of order one, so rotation and inertia are comparable. This is why a sea breeze front turns noticeably during a long afternoon without being fully geostrophic. Cyclones and the global circulation have much smaller values, and a tornado has a value of order a thousand.

Answer: A

When the Rossby number is near unity the acceleration and Coriolis terms are comparable, so no simple balance applies and the full equations must be retained. Such flows include the sea breeze, the mountain and valley wind and the outer parts of a tropical cyclone. Turbulence depends on the Reynolds number, and the pressure gradient force is precisely what drives the motion in all these cases.

Answer: B

Outside the eyewall the curvature is significant but the Coriolis force is not negligible, so all three horizontal terms matter and gradient wind balance applies well. Closer to the centre the balance tends towards cyclostrophic as the radius shrinks. Purely geostrophic balance would badly overestimate the wind for the observed pressure gradient, and hydrostatic balance is a vertical relation that holds throughout but says nothing about the tangential wind.