Baroclinic Instability Questions and Answers

Answer: A

A horizontal temperature gradient means that the mass of the atmosphere could be rearranged to lower its centre of gravity, and the energy released by that rearrangement is the available potential energy. Baroclinic instability is the process that taps it. Barotropic instability draws on the horizontal shear instead, latent heat is a separate source that amplifies the process, and the total internal energy is enormous but almost entirely unavailable because the atmosphere is already close to its lowest attainable arrangement.

Answer: B

Lorenz showed the available portion to be around 0.5 per cent of the total, because most of the mass is already near its lowest attainable arrangement. Even that small fraction is about ten times the kinetic energy of the general circulation, so it is more than sufficient to drive the observed weather. The calculation is a useful corrective to the intuition that a large reservoir must imply a large usable supply. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: C

The tilt places rising motion in the warm air and sinking motion in the cold air, which lowers the centre of gravity and converts available potential energy into eddy kinetic energy. An eastward tilt reverses the conversion and describes a decaying system, while a vertically upright structure gives no net conversion at all. This is why occlusion, which brings the structure upright, marks the end of deepening. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: D

Eady considered a uniformly stratified fluid with constant vertical shear between two rigid lids on an f-plane, and showed that disturbances grow by drawing on the available potential energy of that shear. The absence of beta makes the mathematics tractable and isolates the essential mechanism. The barotropic model has no shear and hence no baroclinic instability, and the other models address friction and the meridional circulation.

Answer: A

Two rigid horizontal boundaries each support an edge wave, and the interaction of the pair is what produces growth. Instability therefore requires both boundaries in this model. The Charney model replaces the upper lid with an unbounded atmosphere on a beta plane, giving bottom-trapped modes and a somewhat more realistic answer at the cost of considerably greater mathematical complexity. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: B

Each boundary supports a wave propagating against the local flow, and at the most unstable wavelength the pair lock into a fixed phase relationship with a westward tilt and amplify each other. Growth therefore requires both. Latent heat is absent from the dry model although important in reality, friction is neglected entirely, and gravity wave reflection describes a different class of solution carrying no available potential energy.

Answer: C

The Eady model gives a most unstable wavelength close to 4000 kilometres for typical mid-latitude parameters, in good agreement with the observed spacing of cyclones along a storm track. The deformation radius is smaller by a factor of about four and sets the scale rather than giving the answer directly. That agreement between an idealised calculation and observation is what established the theory. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: D

The maximum growth rate is proportional to the shear divided by the buoyancy frequency, giving an e-folding time close to 24 hours for typical values. That matches the observed pace at which a cyclone develops from a barely visible wave into a mature system over two or three days. A shear-independent growth rate would contradict the strong observed dependence of cyclogenesis on the strength of the baroclinic zone. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: A

Below a critical wavelength the two edge waves cannot influence one another across the depth of the layer, so phase locking is impossible and the disturbance merely propagates. This short wave cut-off is a robust feature appearing in every baroclinic instability model. The Eady model has no long wave cut-off, which is a consequence of omitting the beta effect. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: B

The beta effect opposes the interior potential vorticity gradient created by the shear, and below a critical shear it cancels it so the Charney-Stern criterion is not satisfied. It also stabilises the longest waves, producing a bounded unstable band. Comparing the Eady and two-level models is the clearest way to see exactly what beta contributes to the problem. The shared properties explain why these belong to one family, and the differences explain why more than one exists.