I need Help with these 3 questions 2) Potential Vorticity (21 pts) In the absenc

Question

I need Help with these 3 questions

2) Potential Vorticity (21 pts) In the absence of an external torque, will a constant thickness water parcel spin (1) faster, (2) slower, or (3) at a constant rate, if it begins to drift as described? Why? (Justify your answer briefly.) (a) A clockwise rotating eddy in the northern hemisphere drifting northward. (b) A counterclockwise rotating eddy in the southern hemisphere drifting southward (c) A cyclonic eddy in the northern hemisphere drifting northward. (d) An anticyclonic eddy in the southern hemisphere drifting southward. (e) A clockwise rotating eddy in the northern hemisphere drifting westward. (f) A counterclockwise rotating eddy in the southern hemisphere drifting northeastward. (g) A clockwise rotating eddy at the equator drifting northward 3) Return Flows and Potential Vorticity (20 pts) (a) What is a return flow and why is it necessary? (b) On what side of ocean basins are return flows located? Why? (c) How can westward intensification be explained by conservation of PV? (d) How is the Sverdrup balance related to conservation of PV? 4) More Sverdrup dynamics (10 pts) Compute the Sverdrup transport (in units of Sverdrups, Sv, where 1 Sv -106 m3/s) across 35° N in an ocean that is 6500 km wide at that latitude, if the curl of the wind stress is -10-7 Pa/m. What is the direction of this transport?

Explanation / Answer

1)

The possible vorticity (PV) is the total flow of an air parcel that is covered flanked by two isentropic surface. If PV is display on a surface of steady potential heat, then it is formally called IPV (isentropic potential vorticity). Of course, PV could also be display on another surface, for illustration a pressure surface. Note from the relative lower, that PV is fundamentally the invention of inclusive vorticity on an isentropic surface and static solidity. So PV consists, in difference to vorticity on isobaric surface, of two issue, a dynamical element and a thermodynamical ingredient.

It can be shown during a mixture of the first law of thermodynamics and momentum preservation that potential vorticity can only be distorted by diabatic heat (such as latent heat released from condensation) or frictional process.

This conservation is the impressive corresponding to angular momentum. A spinning ice skater with her arms increase out crossways can go faster her rate of spin by constricting her arms. likewise, when a vortex of air is broad, it is in turn, slow.

When the air converge, to keep up budding vorticity, the air haste increase, ensuing in a stretched ring vortex. difference cause the vortex to extend, slow down the speed of spin.

2)

1)First is the leeway of a passage contain a Bernoulli budding greater than the upstream value for watery that has a return flow in the course. This happen because the streamline in closed gyres do not create in the upstream area.

2) flow is toward the channel along the right-hand wall and gone from the course along the left-hand wall. Regions upstream of deep-sea sills may sensibly have parameter in the range 299.1 , b , 299, with current along both walls flowing toward the channel and inactive flow in the core

3) presume we have an air parcel drifting west to east over a mass, between two possible heat level:

close to the surface, possible temperature lines go after the outside very closele. Though at higher levels, likely temperature surface change height beyond upstream and downstream of the mountain. So as an air bundle approach from the left, it initially is stiff vertically, thus h increase and by Eq. (9) + f must increase to preserve PV. This will cause the air parcel to turn cyclonically as it approach the mountain, as shown in Fig. 4.9b above (note that as latitude increase, f will increase, thus lessening the magnitude of necessary to conserve PV).

4) In the real ambience, vertical motion are generally dormant and most flows do not go over the top of mountain barrier but approximately them.

• These examples exemplify the swerdrup PV Conservation Law, which state that a modify in deepness is energetically similar to a alter in the Coriolis stricture for a barotropic fluid.

The end effect is a wave-like pattern downstream of the fence, with a lee-side trough follow by an alternating edge and channel pattern. This is regularly used to give details the inclination of lee-side cyclogenesis.

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