The zonal component of the wind increases linearly from u = 0 at the ground to u
ID: 802090 • Letter: T
Question
The zonal component of the wind increases linearly from u = 0 at the ground to u = 10 m s^-1 at a height of one kilometer. In the same region, the vertical velocity increases linearly from w = 0 at some point to w = 1 m s^-1 at a distance one kilometer to the north, (a) Compute the rate of increase in the vertical relative vorticity. Your solution should have units of s^-2, (b) At this rate, how long will it take for air of initially zero relative vertical vorticity to reach a value 10^-3 s^-1? Report your answer in hours to one significant figure.Explanation / Answer
a vertical relative vorticity=dv/dx-du/dy
du= 10-0=10 ms-1
vertical distance y=1km=1000m
du/dy=10/1000=0.01s-1
dv=1-0=1ms-1
x=1km=1000m
Now dv/dx=1/1000=0.001s-1
Rate of increase in vertical vorticity=dv/dx-du/dy
=0.001-0.01=0.009s-1
b. Final relative vorticity=10-3 s-1
Initial relative vorticity=0
Rate of change in vorticity=0.009s-1
Now, Rate of change= relative vertical vorticity/time
10^-3s-1/time
0.009=10^-3/time
time=10^-3/0.009
=0.11s
To convert into hour
1 hour=3600 sec
therefore 0.11/3600
=3.05*10^-5 hour
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