Thermal Wind Balance Questions and Answers

Answer: C

A front is a zone of concentrated horizontal temperature gradient, typically a hundred kilometres wide, and by the thermal wind relation it is accompanied by strong vertical shear. That shear is the frontal jet. Anticyclones, cols and ridges are features of the pressure field whose thermal structure is comparatively weak, which is why they are not associated with the sharp shears characteristic of fronts.

Answer: D

A frontal zone slopes upward over the cold air with a gradient of about one in a hundred, and the thermal wind requires a corresponding zone of concentrated shear along that slope. The slope follows from the Margules relation between the temperature contrast and the wind change across the front. A vertical discontinuity would be dynamically impossible, since it would imply infinite shear and immediate instability. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: A

Margules related the slope of a frontal surface to the temperature difference across it and the change in geostrophic wind, giving slopes of order one in a hundred for typical values. It is essentially the thermal wind relation applied to a discontinuity. The hypsometric equation concerns thickness, the omega equation vertical motion, and the Sutcliffe equation development, so none of the others addresses frontal geometry. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: B

Cold fronts slope at roughly 1 in 50 to 1 in 100 and warm fronts more gently at about 1 in 200, so a frontal surface reaching 5 kilometres lies several hundred kilometres behind its surface position. This gentle slope is why warm front cloud extends so far ahead of the surface front. A slope of 1 in 10 would be dynamically unsustainable and 1 in 1000 would produce no recognisable front at all.

Answer: C

A deformation field with its axis of dilatation at a suitable angle to the isotherms concentrates them, and the resulting frontogenesis is what creates the sharp gradients observed. Confluence and differential vertical motion contribute similarly. Radiative cooling and subsidence act too slowly and too broadly, while turbulent mixing acts to weaken gradients rather than to sharpen them.

Answer: D

As deformation tries to sharpen the gradient, it disturbs thermal wind balance, and an ageostrophic circulation develops that restores the balance by lifting warm air and lowering cold air. That direct circulation is the source of frontal cloud and precipitation. The indirect sense would consume rather than release energy, and a purely horizontal response could not restore the balance that the deformation has upset. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: A

The Sawyer Eliassen equation diagnoses the cross-frontal circulation forced by frontogenesis within a semi-geostrophic framework, and it correctly gives the narrow sloping ascent observed at fronts. The quasi-geostrophic omega equation gives a broader and weaker circulation because it omits the ageostrophic advection. The vorticity and continuity equations are ingredients rather than the diagnostic relation itself. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: B

A systematic vector change of wind with height indicates a horizontal temperature gradient through the thermal wind relation, and its direction gives the orientation of the isotherms. This is why a single sounding contains information about the horizontal structure of the atmosphere. The lapse rate, the humidity and the pressure profile describe the vertical structure at that point and carry no such horizontal information. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: C

Through the thermal wind relation, the vector wind shear across a layer gives both the magnitude and the direction of the layer mean horizontal temperature gradient. That is a remarkable amount of horizontal information from a single vertical profile. It does not give absolute values at other points, and locating a front requires knowing the gradient over a region rather than at one place.

Answer: D

The relation is derived by combining geostrophic and hydrostatic balance, so it fails wherever either does, which means near the equator, in strongly curved flow and in convective systems. A gradient wind version exists but is much more complicated and rarely used. Cyclostrophic and Ekman balances are quite different regimes in which no simple thermal relation applies at all.