Geostrophic and Gradient Wind Questions and Answers

Q: Which term does the ageostrophic wind balance in a steady curved flow?

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.

Q: Which balance includes the centrifugal term alongside the other two?

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.

Q: How does anticyclonic curvature alter the speed needed for balance?

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.

Q: Which limit applies to the pressure gradient in anticyclonic gradient flow?

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.

Q: Which observation does the anticyclonic limit explain?

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.

Q: Which balance describes a tornado?

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.

Q: Which conclusion follows from cyclostrophic balance about the sense of rotation?

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.

Q: Which balance describes motion with no pressure gradient at all?

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.

Q: Which sense do inertial circles have in the northern hemisphere?

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.

11.

Which term does the ageostrophic wind balance in a steady curved flow?

A.The pressure gradient
B.The vertical component of the Coriolis force acting on the ascending branch of the circulation
C.The centripetal acceleration
D.The frictional force, which is the only remaining term once the geostrophic balance has been removed

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.

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12.

Which balance includes the centrifugal term alongside the other two?

A.Geostrophic balance, in which the Coriolis force alone opposes the horizontal pressure gradient
B.Hydrostatic balance
C.Ekman balance, in which friction is added to the two forces present in the geostrophic approximation
D.Gradient wind balance

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.

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13.

Which relationship holds between the gradient and geostrophic winds around a low?

A.The gradient wind is weaker
B.The gradient wind is stronger because the centrifugal force adds to the inward pressure gradient force
C.They are equal
D.The gradient wind exceeds the geostrophic wind only when the radius of curvature is very small indeed

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.

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14.

How does anticyclonic curvature alter the speed needed for balance?

A.The gradient wind is undefined because the anticyclonic balance admits no real solution at any radius
B.The gradient wind is stronger
C.The gradient wind is weaker because the centrifugal force opposes the outward pressure gradient force
D.They are equal

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.

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15.

Which limit applies to the pressure gradient in anticyclonic gradient flow?

A.There is no limit
B.It cannot exceed the gradient that would be needed to produce a wind of one hundred metres per second
C.It cannot exceed a value proportional to the square of f times the radius
D.It cannot exceed the value that would produce a wind equal to the local speed of sound in the air

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.

Discuss in Forum

16.

Which observation does the anticyclonic limit explain?

A.Anticyclones move more slowly across the chart than cyclones of comparable size and intensity do
B.Highs bring clear weather
C.The strongest winds on a chart are usually found at the boundary between a high and a low centre
D.Deep lows are common while deep highs are not

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.

Discuss in Forum

17.

Which balance describes a tornado?

A.Cyclostrophic balance
B.Geostrophic balance, in which the Coriolis force alone opposes the horizontal pressure gradient force
C.Gradient wind balance
D.Ekman balance, which retains friction alongside the Coriolis force and the pressure gradient force

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.

Discuss in Forum

18.

Which conclusion follows from cyclostrophic balance about the sense of rotation?

A.The sense must match that of the parent storm because angular momentum is conserved during descent
B.Either sense of rotation is dynamically possible
C.Only cyclonic rotation is possible because the pressure at the centre of the vortex must be lower
D.Only anticyclonic rotation is possible

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.

Discuss in Forum

19.

Which balance describes motion with no pressure gradient at all?

A.Geostrophic balance
B.Gradient wind balance, in which all three of the horizontal forces are retained simultaneously
C.Inertial balance
D.Cyclostrophic balance, in which the pressure gradient is balanced entirely by the centrifugal force

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.

Discuss in Forum

20.

Which sense do inertial circles have in the northern hemisphere?

A.Anticlockwise, which is the same sense as the circulation observed around a surface low pressure area
B.Either sense
C.The sense alternates through the oscillation so that the trajectory closes on itself after two turns
D.Clockwise

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.

Discuss in Forum

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