2. Geostrophic adjustment. Assume that the atmosphere can be approximated as a f

Question

2. Geostrophic adjustment. Assume that the atmosphere can be approximated as a fluid of constant density with an average depth H-10 km (about the scale height of the atmosphere). To answer the following questions, use equations from the geostrophic adjustment lecture and reading. Keep in mind, however, that the equations in the lecture and the reading describe a system in which fluid depth changes in the x direction. In this problem, the fluid depth changes in the y direction. It will be helpful to think about this problem from a physical standpoint more so than a purely mathematical standpoint. (a) 5 points. What is the Rossby radius of deformation for this atmosphere at a latitude of 50°N in units of m, km and degrees latitude? (b) 5 points. Imagine the atmosphere is initially at rest and has a step function change in its height at 50°N. The height goes from 1 km south of 50'N to 9 km north of S0°N. Find the maximum wind speed in m s after geostrophic adjustment occurs. The wind maximum is located at the center of the jet that forms in the process of geostrophic adjustment. (c) 5 points. Make a sketch of the height of the atmosphere between 0 and 90°N before and after the adjustment. On the sketch, indicate the location of the jet and its direction with an appropriate symbol. Is the direction of the wind northerly, easterly, southerly, or westerly? Also indicate on your sketch the direction of the horizontal pressure gradient force (PGF) and Coriolis Force (CF) at the location of the jet

Explanation / Answer

In atmospheric dymanics and physical oceanography,the rossby radius of deformation is the length scale at which rotaional effects become as important as buoyancy or gravity wave effects in the evolution of the flow about some disturbances.

For a barotropic oceanLr=(gD)1/2/f, where g is the gravitaional acceleration,D is the water depth,and f is the Coriolis parametr.

In Earth's atmosphere,the ratio N/f0 is typically of order 100,so the Rossby radius is about 100 times the vertical scale height,H.

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