Geostrophic and Gradient Wind Questions and Answers

Q: Which quantity is the radius of an inertial circle?

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.

Q: Which term does natural coordinates make explicit in the gradient wind equation?

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.

Q: Which distinction matters when applying gradient wind balance in practice?

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.

Q: Which relationship connects trajectory and streamline curvature?

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.

Q: Which wind does an isobaric chart most directly give?

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.

Q: Which correction must be applied to read the gradient wind from a chart?

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.

Q: Which typical departure from geostrophy does a mid-latitude synoptic flow show?

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.

Q: Which regime has a Rossby number close to one?

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.

Q: Which effect does a Rossby number of order one have on the flow?

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.

Q: Which balance governs the outer circulation of a mature tropical cyclone?

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.

21.

Which quantity is the radius of an inertial circle?

A.The speed divided by the Coriolis parameter
B.The speed multiplied by the Coriolis parameter and divided by the acceleration due to gravity there
C.The speed squared divided by f
D.The speed divided by the square of the Coriolis parameter at the latitude of the moving parcel

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.

Discuss in Forum

22.

Which term does natural coordinates make explicit in the gradient wind equation?

A.The angle between the wind vector and the local direction of the horizontal pressure gradient force
B.The curvature of the trajectory
C.The divergence of the wind field, which determines the vertical motion above the level considered
D.The vorticity

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.

Discuss in Forum

23.

Which distinction matters when applying gradient wind balance in practice?

A.The wind must be steady
B.The pressure gradient must be evaluated on a constant height surface rather than a pressure surface
C.Trajectory curvature differs from streamline curvature
D.The radius must be measured from the centre of the system rather than from the centre of the Earth

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.

Discuss in Forum

24.

Which relationship connects trajectory and streamline curvature?

A.They coincide whenever the wind speed is constant along the streamline being followed by the parcel
B.They never coincide
C.They coincide only in the southern hemisphere where the sign of the Coriolis parameter is negative
D.They coincide only when the pattern is not moving

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.

Discuss in Forum

25.

Which wind does an isobaric chart most directly give?

A.The geostrophic wind
B.The actual observed wind at the level of the chart including its ageostrophic and frictional parts
C.The gradient wind
D.The thermal wind, which is the vector difference between the winds at the top and base of a layer

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.

Discuss in Forum

26.

Which correction must be applied to read the gradient wind from a chart?

A.An allowance for the temperature of the layer since density enters the geostrophic relation directly
B.An allowance for the curvature of the contours
C.An allowance for the latitude at which the observation is being made across the chart being read
D.An allowance for friction

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.

Discuss in Forum

27.

Which typical departure from geostrophy does a mid-latitude synoptic flow show?

A.About one per cent
B.About ninety per cent, since the actual wind is dominated by its ageostrophic and frictional parts
C.About ten per cent
D.About fifty per cent, which is why the geostrophic approximation is of very limited practical value

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.

Discuss in Forum

28.

Which regime has a Rossby number close to one?

A.A mid-latitude cyclone, whose horizontal scale of about a thousand kilometres gives a small value
B.A tornado
C.The global circulation, whose planetary scale places it firmly within the strongly rotational regime
D.A sea breeze circulation

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.

Discuss in Forum

29.

Which effect does a Rossby number of order one have on the flow?

A.Neither rotation nor inertia may be neglected
B.The flow becomes exactly geostrophic because the two competing terms are of the same magnitude
C.The flow becomes turbulent
D.The pressure gradient force must vanish since it cannot balance two terms of comparable size at once

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.

Discuss in Forum

30.

Which balance governs the outer circulation of a mature tropical cyclone?

A.Hydrostatic balance, which relates the vertical pressure gradient to the density of the air present
B.Gradient wind balance
C.Geostrophic balance, since the storm lies at a latitude where the Coriolis parameter is appreciable
D.Cyclostrophic balance

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.

Discuss in Forum

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