Thermal Wind Balance Questions and Answers

Q: If the isobars and isopycnals are parallel to each other, the flow is said to be

The flow is barotropic.In a barotropic fluid the density depends only on pressure, so surfaces of constant pressure (isobars) and constant density (isopycnals) coincide or are parallel. In a baroclinic fluid they intersect, because density also depends on temperature or salinity; this gives the solenoidal term that generates vertical shear (the thermal wind).Geostrophic describes a balance between pressure gradient and Coriolis forces, which can hold in either case, and rotational refers to vorticity, not to the relation between pressure and density surfaces.

Q: In a Barotrophic atmosphere :

In a barotropic atmosphere the geostrophic wind does not change with height.In a barotropic atmosphere density depends only on pressure, so surfaces of constant pressure and constant temperature coincide and there are no horizontal temperature gradients on pressure surfaces. By the thermal wind relation, the vertical change (shear) of the geostrophic wind is proportional to the horizontal temperature gradient, so with no gradient the geostrophic wind is the same at all heights.Geostrophic winds that increase or decrease with height require a baroclinic atmosphere. 'Pressure a function of temperature only' reverses the definition: it is density that depends on pressure alone.

Q: Which physical quantity is the thermal wind?

The thermal wind is the vector difference between the geostrophic winds at the top and bottom of a layer, so it is a shear and not a wind at all. No parcel of air ever moves with it, and it cannot be measured by an anemometer. The name is unfortunate and misleads almost everyone on first acquaintance, which is why it repays being stated explicitly. Keeping the definition clear prevents the common error of adding the thermal wind to an observed wind as though the two were quantities of the same kind.

Q: Which orientation does the thermal wind take relative to the isotherms?

The thermal wind blows along the layer mean isotherms with cold air on its left in the northern hemisphere, exactly as the geostrophic wind blows along the isobars with low pressure on its left. The analogy is exact because thickness plays the role of geopotential height in the relation. Perpendicular flow would describe maximum thermal advection instead, and there is no latitude dependence in the geometry, only in the magnitude through the Coriolis parameter.

Q: Which side does cold air lie on for a northern hemisphere thermal wind?

Because low thickness corresponds to cold air and the thermal wind blows with low thickness on its left, cold air lies to the left in the northern hemisphere. The rule reverses in the southern hemisphere along with the sign of the Coriolis parameter. It is a direct transcription of Buys Ballot's law with thickness substituted for pressure, so anyone who has the geostrophic rule firmly in hand gets the thermal one free. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Q: Which wind results in the northern hemisphere when temperature falls towards the pole?

With cold air to the north, a wind blowing from the west has the cold air on its left, so the thermal wind is westerly and the geostrophic westerlies strengthen with height. This is why the mid-latitude jet stream exists at all. The summer stratosphere reverses the temperature gradient, with warm air over the sunlit pole, and its winds are correspondingly easterly, which is a useful check that the rule has been applied in the right sense. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Q: Which level does the mid-latitude westerly maximum occupy?

Westerly shear accumulates upward through the whole troposphere while the temperature gradient persists, so the wind reaches its maximum where that gradient reverses, which is at the tropopause. Above it the temperature gradient changes sign and the westerlies weaken again. The surface gradient may be sharp, but shear must be integrated over depth to produce a strong wind, which is precisely why the jet sits high rather than low. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Q: Which reversal above the tropopause weakens the westerlies?

In the lower stratosphere the polar region is warmer than the tropics, because the tropical tropopause is much higher and therefore much colder, so the thermal wind reverses to easterly. Integrating that reversed shear upward reduces the westerly wind above the jet core. The Coriolis parameter does not change sign within a hemisphere, and the geostrophic relation remains perfectly valid in the stratosphere.

If the isobars and isopycnals are parallel to each other, the flow is said to be

A.baroclinic
B.barotropic
C.geostrophic
D.rotational

Exam Year(s)

GATE XE - 2024,

Answer: B

The flow is barotropic.

In a barotropic fluid the density depends only on pressure, so surfaces of constant pressure (isobars) and constant density (isopycnals) coincide or are parallel. In a baroclinic fluid they intersect, because density also depends on temperature or salinity; this gives the solenoidal term that generates vertical shear (the thermal wind).

Geostrophic describes a balance between pressure gradient and Coriolis forces, which can hold in either case, and rotational refers to vorticity, not to the relation between pressure and density surfaces.

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In a Barotrophic atmosphere :

A.Geostrophic wind speed increases with height
B.Geostrophic wind speed decreases with height
C.Geostrophic wind does not change with height
D.Pressure is a function of temperature only

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: C

In a barotropic atmosphere the geostrophic wind does not change with height.

In a barotropic atmosphere density depends only on pressure, so surfaces of constant pressure and constant temperature coincide and there are no horizontal temperature gradients on pressure surfaces. By the thermal wind relation, the vertical change (shear) of the geostrophic wind is proportional to the horizontal temperature gradient, so with no gradient the geostrophic wind is the same at all heights.

Geostrophic winds that increase or decrease with height require a baroclinic atmosphere. 'Pressure a function of temperature only' reverses the definition: it is density that depends on pressure alone.

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Which two relations are combined to obtain the thermal wind?

A.Geostrophic balance and hydrostatic balance
B.Gradient wind balance and the ideal gas law for a dry atmosphere at ordinary temperatures
C.Continuity and the thermodynamic equation
D.The vorticity equation and the divergence equation written on a constant pressure surface

Answer: A

Differentiating the geostrophic relation with respect to pressure and substituting the hydrostatic relation eliminates the geopotential and leaves the vertical shear expressed through the horizontal temperature gradient. The thermal wind therefore inherits the validity conditions of both parent relations, failing wherever either fails. Continuity, the thermodynamic equation and the vorticity and divergence equations play no part in the derivation, though they are of course members of the same governing set and are used elsewhere in this subject for other purposes.

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Which physical quantity is the thermal wind?

A.A horizontal wind driven directly by the temperature gradient without any pressure gradient involved
B.A vertical shear of the geostrophic wind
C.An actual wind that a parcel of air would experience as it travels through the layer concerned
D.A vertical velocity

Answer: B

The thermal wind is the vector difference between the geostrophic winds at the top and bottom of a layer, so it is a shear and not a wind at all. No parcel of air ever moves with it, and it cannot be measured by an anemometer. The name is unfortunate and misleads almost everyone on first acquaintance, which is why it repays being stated explicitly. Keeping the definition clear prevents the common error of adding the thermal wind to an observed wind as though the two were quantities of the same kind.

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Which orientation does the thermal wind take relative to the isotherms?

A.At thirty degrees to them
B.At an angle that varies with latitude, approaching ninety degrees as the pole is drawn nearer
C.Parallel to them
D.Perpendicular to them, pointing from the warm side of the layer towards the colder side of it

Answer: C

The thermal wind blows along the layer mean isotherms with cold air on its left in the northern hemisphere, exactly as the geostrophic wind blows along the isobars with low pressure on its left. The analogy is exact because thickness plays the role of geopotential height in the relation. Perpendicular flow would describe maximum thermal advection instead, and there is no latitude dependence in the geometry, only in the magnitude through the Coriolis parameter.

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Which side does cold air lie on for a northern hemisphere thermal wind?

A.The right, so that an observer looking along the thermal wind vector finds warm air to the left
B.Directly ahead
C.Behind, since the shear vector points away from the coldest part of the layer being considered
D.The left

Answer: D

Because low thickness corresponds to cold air and the thermal wind blows with low thickness on its left, cold air lies to the left in the northern hemisphere. The rule reverses in the southern hemisphere along with the sign of the Coriolis parameter. It is a direct transcription of Buys Ballot's law with thickness substituted for pressure, so anyone who has the geostrophic rule firmly in hand gets the thermal one free. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

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Which wind results in the northern hemisphere when temperature falls towards the pole?

A.A westerly thermal wind
B.An easterly thermal wind, which is what is observed in the stratosphere during the summer months
C.A southerly thermal wind
D.A northerly thermal wind, blowing from the cold polar region towards the warmer air of the tropics

Answer: A

With cold air to the north, a wind blowing from the west has the cold air on its left, so the thermal wind is westerly and the geostrophic westerlies strengthen with height. This is why the mid-latitude jet stream exists at all. The summer stratosphere reverses the temperature gradient, with warm air over the sunlit pole, and its winds are correspondingly easterly, which is a useful check that the rule has been applied in the right sense. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

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Which feature of the troposphere does the poleward temperature gradient explain?

A.The diurnal variation of the surface wind speed, which peaks in the early afternoon on most days
B.Westerlies that strengthen with height
C.The trade winds, which blow steadily from the east across both of the tropical oceans all year
D.The Ekman spiral

Answer: B

The equator to pole temperature contrast requires, through the thermal wind relation, a westerly shear throughout the troposphere, which is why the wind at 250 hectopascals is so much stronger than that at the surface. The trade winds arise from the Hadley circulation, the Ekman spiral from friction, and the diurnal wind variation from the daily cycle of boundary layer mixing. Only the first is a direct thermal wind consequence and it is the most important single application of the relation.

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Which level does the mid-latitude westerly maximum occupy?

A.In the mid-stratosphere
B.At about 850 hectopascals, just above the top of the frictional boundary layer over most terrain
C.Near the tropopause
D.Near the surface, where the horizontal temperature gradient across the polar front is at its strongest

Answer: C

Westerly shear accumulates upward through the whole troposphere while the temperature gradient persists, so the wind reaches its maximum where that gradient reverses, which is at the tropopause. Above it the temperature gradient changes sign and the westerlies weaken again. The surface gradient may be sharp, but shear must be integrated over depth to produce a strong wind, which is precisely why the jet sits high rather than low. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

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10.

Which reversal above the tropopause weakens the westerlies?

A.The Coriolis parameter changes sign as the flow crosses from one hemisphere into the other one
B.The pressure gradient vanishes
C.The stratification becomes so strong that the geostrophic relation ceases to be valid at that level
D.The horizontal temperature gradient changes sign

Answer: D

In the lower stratosphere the polar region is warmer than the tropics, because the tropical tropopause is much higher and therefore much colder, so the thermal wind reverses to easterly. Integrating that reversed shear upward reduces the westerly wind above the jet core. The Coriolis parameter does not change sign within a hemisphere, and the geostrophic relation remains perfectly valid in the stratosphere.

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