Baroclinic Instability Questions and Answers

Answer: C

The criterion requires the meridional gradient of potential vorticity to change sign somewhere in the domain, with boundary temperature gradients counted as delta functions in that gradient. It generalises Rayleigh's barotropic result to the stratified rotating case. Charney-Drazin concerns wave propagation, and the Richardson and Miles-Howard criteria concern shear instability at much smaller scales. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: D

A flow satisfying the criterion may nonetheless be stable, so the condition rules out instability when it fails but does not guarantee it when it holds. Examination questions frequently turn on exactly this word. The criterion applies to arbitrary shear profiles, and its power lies in reducing a difficult stability calculation to an inspection of a single gradient. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: A

The Eady model has zero interior potential vorticity gradient, so the required change of sign comes entirely from the two boundary temperature gradients, which Bretherton showed to be equivalent to delta functions of potential vorticity. The beta effect is absent by construction. This equivalence is what allows a model with no interior gradient at all to satisfy the criterion. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: B

Charney worked on a beta plane with an unbounded atmosphere above, so the interior potential vorticity gradient is non-zero and instability arises from its interaction with the surface temperature gradient. The resulting modes are bottom-trapped with a depth set by the Rossby height. Latent heat, friction and realistic stability are absent from both idealised models, which is what keeps them tractable. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: C

The Charney mode is confined to a depth of order the Rossby height, which is the horizontal scale multiplied by the ratio of the Coriolis parameter to the buoyancy frequency. That gives roughly the depth of the troposphere for a synoptic scale disturbance, so the confinement is not severe. The absence of an upper lid is exactly what allows the mode to decay rather than being reflected back. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: D

Multiplying the horizontal scale by \( f/N \), about one in a hundred in the troposphere, gives the depth over which a disturbance of that width influences the flow. A synoptic scale disturbance a thousand kilometres wide therefore reaches through about ten kilometres, which is the whole troposphere. This is the vertical counterpart of the deformation radius and explains the observed aspect ratio of weather systems.

Answer: A

The Eady growth rate parameter, proportional to the Coriolis parameter times the vertical shear divided by the buoyancy frequency, combines exactly the ingredients the theory identifies. Maps of it show maxima off the eastern coasts of Asia and North America in winter, coinciding with the observed storm tracks. The Richardson number and convective energy concern much smaller scale instabilities. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: B

Strong shear and modest stratification combine off the coasts of Japan and North America in winter, exactly where the observed storm tracks begin. The agreement between the theoretical parameter and the observed climatology is striking. The equator has almost no Coriolis parameter, deserts have weak shear despite hot surfaces, and continental inversions represent strong stratification that suppresses growth. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: C

The Gulf Stream and Kuroshio carry warm water poleward alongside cold continental air, producing intense low level baroclinicity that anchors the storm track entrance. Ocean circulation therefore controls where mid-latitude storms form. Uniform ocean temperature would remove the gradient entirely, and mountains and snow cover contribute elsewhere but not to this particular feature. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: D

Storm tracks are identified as bands of maximum synoptic scale variance, running northeastward across the Atlantic and Pacific in the northern hemisphere. They begin where the Eady growth rate is largest and decay downstream. The polar front and jet stream are related features of the same baroclinic zone, and the Ferrel cell is the zonally averaged circulation that the eddies themselves maintain. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.