Geostrophic and Gradient Wind Questions and Answers

Answer: C

In gradient wind balance the departure from geostrophy supplies exactly the net inward force needed to turn the parcel along its curved path. Around a low the actual wind is subgeostrophic and around a high it is supergeostrophic, and the difference in each case is the ageostrophic component. Friction contributes a separate ageostrophic component near the surface. Recognising curvature as a source of ageostrophic flow explains the jet entrance and exit circulations that dominate synoptic vertical motion.

Answer: D

Gradient wind balance sets the pressure gradient force against the sum of the Coriolis and centrifugal forces and applies wherever the trajectory is appreciably curved. Geostrophic balance is its straight-flow limit, obtained by letting the radius of curvature become infinite. Hydrostatic balance is vertical, and Ekman balance describes the frictional boundary layer. Naming the four balances with the term each retains or discards is a compact way to hold the family in mind.

Answer: A

Around a northern hemisphere low the pressure gradient force points inward while both the Coriolis and centrifugal forces point outward, so a smaller wind suffices to achieve balance and the flow is subgeostrophic. The typical shortfall is ten to twenty per cent for a synoptic system and much more for a tropical cyclone. Around a high the arrangement reverses and the flow is supergeostrophic, which is the source of the asymmetry between lows and highs discussed later in this topic. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: B

Around a high the pressure gradient force points outward and the centrifugal force points outward with it, while only the Coriolis force points inward, so a larger wind is needed for balance. The flow is therefore supergeostrophic. A real solution exists provided the pressure gradient stays below a limiting value, so the balance is well defined for all anticyclones actually observed, though that limit is what keeps observed anticyclones weak.

Answer: C

Solving the quadratic gradient wind equation for anticyclonic curvature gives a real root only while the pressure gradient force stays below \( f^{2}R/4 \), which is why anticyclones are always broad and gentle. No corresponding limit exists for cyclonic curvature, so lows may be small and intense. This single mathematical result accounts for one of the most striking asymmetries in observed weather charts and is well worth deriving once in full. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: D

Because the anticyclonic balance admits no solution beyond a limiting pressure gradient, there is a dynamical ceiling on the intensity of a high that has no cyclonic counterpart. Observed sea level pressure extremes bear this out, with record lows far further from the mean than record highs. The clear weather of a high follows from subsidence rather than from the balance limit, and the speed of movement is governed by the steering flow. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

In a tornado the Rossby number is of order a thousand, so the Coriolis term is negligible and the pressure gradient force is balanced entirely by the centrifugal force. That is cyclostrophic balance. It follows that a tornado may in principle rotate in either sense, though most rotate cyclonically because they inherit the rotation of a parent mesocyclone. Gradient wind balance reduces to the cyclostrophic case when the Coriolis term is dropped. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: B

The cyclostrophic equation contains the square of the wind speed, so it is satisfied equally by clockwise and anticlockwise circulation. Anticyclonic tornadoes are observed, though they are rare because most tornadoes descend from a cyclonically rotating mesocyclone. The pressure certainly is lower at the centre, but that constrains the magnitude of the wind rather than its sense. The angular momentum argument explains the observed preference without imposing any dynamical requirement.

Answer: C

With the pressure gradient force absent, the Coriolis force alone supplies the centripetal acceleration, so a parcel traces an inertial circle at constant speed. The circle is anticyclonic in both hemispheres and its period is a pendulum day. Such motion is rarely a good description of the atmosphere but is commonly observed in the ocean mixed layer after a storm has passed, where the currents spiral cleanly for several days. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: D

The Coriolis force acts to the right of the motion in the northern hemisphere, so it points towards the centre of a clockwise circle and provides the required centripetal acceleration. The motion is therefore anticyclonic, which surprises those who assume rotation defaults to cyclonic. The radius is the speed divided by \( f \), so a current of 0.5 metres per second traces a circle about 5 kilometres across, a scale readily seen in drifting buoy records.