7/27/2019 Sandy Project problem statement "60038_1_ME-G0200-HW2-Stream-copy"

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ME G0200 Applied Fluid Mechanics

HW #2: Flowlines of Hurricane Sandy (Equivalent to a quiz)

This is an intense hurricane season and this assignment aims at some understanding of the basic

fluid mechanical features of hurricanes. A hurricane can be considered, after some significantsimplifications, as a vortex of circulation carried away by its self-induced velocity Ucapplied atits center. The vortex can be assumed as a two-dimensional line vortex of infinite length with itsaxis perpendicular to wind velocity all the times.

The circulation is defined as rdUC

r where Uris the radial component on a circle C which

encloses the vortex. If you consider C to be the outer circle of the core of the vortex i.e. the eye of

the hurricane, then cr rU 2max, . You can find typical values of U r, maxfrom hurricane Sandy

data in the web.You can also find information of location of the center of the hurricane in Geographic coordinatesystem x, y (latitude and longitude), time, ground speed (=U c) and maximum speed at the tip ofthe core (=Ur, max)Typical values for Ur, maxare between 60 to 80 miles/h. Try to find the size of the core from other

web sites. You have to superimpose the translational velocity field with the rotational induced

flow field Urand u where u is given by r2u / .At time t=0 the vortex is at the origin of the coordinate system (0, 0) which is somewhere in theCaribbean.

7/27/2019 Sandy Project problem statement "60038_1_ME-G0200-HW2-Stream-copy"

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1. You need to establish Isaacs UCvelocity from the information of its location (x, y)along its path by computing the velocity components dx/dt and dy/dt as a function of

(x, y)2. Estimate its strength as a function of time/location (x, y) along its path from

cr rU 2max, You need to know rcas a function of time for this. If you cannot find it

assume it is 5km.3. Find the streamlines, pathlines and streaklines of the flow field passing through the point(x0, y0) which is the location of Miami. Use several values of (x 0, y0) to demonstrate theeffects on other cities like New York, Philadelphia, Havana etc...

4. Draw the streamlines, pathlines and streaklines of the two-dimensional flow field withvalues of parameters according to your selection and put the regional map in the

background.

Plot streamlines which correspond to fraction of the time needed to arrive in (x0, y0) which is

given by 0212

0

2

0 Uyx /)( / . This time is of the order of a few days.

Plot pathlines passing through several points (x0, y0) for all times.Plot streaklines passing through several points (x0, y0) for all times.

(x0, y0)= various cities

Use only numerical techniques(not exact solutions) to compute the flowlines mentioned above.You should program in symbolic language MATLAB only and submit m-files. Your m files

should run by itself and through past and run.You are also free to plot the results on any software package you have available.In order to have meaningful results determine, by trial and error, a more restricted range of whatis suggested above.You are required to submit:

1. A report, which will contain the programming you carried out and the graphs properlyplotted and explained on the same figure.

2. A cd with a copy of your .m file with the program and the word file with your report.Your program will be tested with the input data from the range mentioned above.

No email submission!!

Due October 16, 2013.

Your grade will be based mostly on:

1. Completeness of the program. Several tests with different initial points will be tried.2. Robustness of your program. The program should work for almost any point. Make sure

there is no division by zero. Test with various values of (x0, y0) coordinates.3. Quality of graphs and plotting.