For this problem, use the MATLAB code provided in coriolis.zip, which has been posted to eClass. The main code is coriolis.m, which depends on the two other files included in the zip file. (Keep all three files in the same directory.) This code numerically integrates the horizontal accelerations assuming conservation of angular momentum, including meridional variations in the Coriolis parameter. Such integration, without assuming the Coriolis parameter is constant, is often intractable to do analytically, and computational tools are indispensable in these situations. In coriolis.m, vertical velocity is assumed to be zero, and there are no pressure gradient effects included in the model. When you run coriolis.m, it will prompt you for inputs (provided below), and it will produce two figures. Figure 1 shows the trajectory with curvature terms included, and Figure 2 shows the trajectory with curvature terms neglected. The diamond on each plot marks the initial point. Run coriolis.m with initial latitude 30? , initial eastward velocity u = 40 m s-1 , and initial northward velocity v = 0 m s-1 . Specify an integration time of 2 days. (“Integration time” refers to the time period that the model will simulate. It should only take about a second for your computer to simulate this time period.)
(a) Submit the two figures generated by coriolis.m.
(b) In both figures, why is the parcel’s final position west of its initial position? Is that not paradoxical, given that air generally flows eastward in the midlatitudes? Explain.
(c) Compare the trajectory including curvature terms with the trajectory neglecting curvature terms. Are the trajectories qualitatively similar or different? How? Are the trajectories quantitatively similar or different? How?
(d) Write down the equation for the meridional acceleration due to Coriolis force, including any curvature terms that remain after setting the vertical velocity to zero.
(e) Using the equation from part d, qualitatively explain the differences between the trajectories in Figures 1 and 2. Specifically, as the parcel of air moves from 30? latitude to latitudes closer to the equator, how will the curvature term influence the meridional acceleration? How does this influence explain the differences between the two trajectories?
(f) Based on these results, is it troubling that curvature terms are typically neglected in models? Why or why not?
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