Thermal Wind Balance Questions and Answers

Answer: C

Sutcliffe expressed surface development in terms of the thermal advection and the thermal vorticity advection, giving forecasters a practical rule based on the thickness field. It was the working method of British forecasting for decades before numerical models. Margules concerns frontal slope, Charney-Drazin wave propagation into the stratosphere, and Eady the idealised theory of baroclinic growth.

Answer: D

Development occurs where the thermal steering carries positive vorticity over the surface system, which in practice means a surface low downstream of an upper trough within a strong thermal gradient. A barotropic atmosphere permits no development at all, and thickness contours parallel to isobars indicate no thermal advection. The theory is essentially a practical rendering of the omega equation.

Answer: A

A surface system tends to move along the thickness contours, which is the thermal steering rule, because the upper flow that steers it is itself largely determined by the thermal wind. The rate of deepening is given by the development terms rather than by the steering. Depth and intensity are separate properties, though a deepening system does tend to become more vertically upright as it matures.

Answer: B

A mature occluded low becomes vertically upright and slow moving, and the thermal steering rule then gives little guidance because the system is no longer being carried by the flow above. The rule works best during the developing stage. It uses thickness rather than direct upper air observations, applies to deepening and filling systems alike, and does give an indication of speed from the strength of the thermal wind. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: C

Growth requires the upper trough to lie upstream of the surface low, so the tilt is greatest while the system is deepening most rapidly. As the system occludes the two become vertically aligned and deepening ceases. The wave stage has a modest tilt and the decaying stage may even tilt the other way. Recognising tilt as a signature of active development is one of the most useful practical applications of this theory. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: D

A westward tilt with height means warm air rises and cold air sinks systematically, lowering the centre of gravity of the atmosphere and releasing available potential energy as kinetic energy. Eastward tilt reverses the conversion and describes a decaying system. Vertical alignment gives no net conversion at all, which is precisely why a vertically stacked low stops deepening.

Answer: A

Eady considered a uniformly stratified fluid with constant vertical shear between two rigid lids and showed that disturbances grow by drawing on the available potential energy of that shear. The shear is exactly the thermal wind. The barotropic model has no shear and hence no baroclinic instability, while the Ekman and Hadley models address friction and the meridional circulation respectively.

Answer: B

The Eady model gives a most unstable wavelength of roughly 4000 kilometres, close to the observed spacing of mid-latitude cyclones, and a growth rate corresponding to an e-folding time of about a day. The agreement with observation is what made the model so influential. The deformation radius is smaller by a factor of about four and sets the scale rather than the most unstable wavelength directly.

Answer: C

The maximum growth rate is proportional to the shear divided by the buoyancy frequency, giving an e-folding time near 24 hours for typical mid-latitude values. That matches the observed pace at which cyclones develop from a barely visible wave to a mature system in two or three days. The rate depends strongly on the shear, which is the thermal wind, so it is not a function of latitude alone.

Answer: D

Eady placed rigid horizontal boundaries at the ground and at the tropopause, which allows edge waves to exist at each and lets the pair interact to produce growth. The interaction of two counter-propagating edge waves is the cleanest available account of baroclinic instability. A free surface, periodicity or a radiation condition would each change the character of the solution, and the Charney model, which replaces the upper lid with an unbounded atmosphere on a beta plane, gives a somewhat different and more realistic answer at the cost of much greater complexity.