ENE 512 Final Project This is an individual project. You may discuss with classmates, but all work must be completed independently. The answers to the questions below must be provided to Prof. Lynett as a single PDF document. Due Date: December 2nd Develop a Dispersion Model for a Complex, Turbulent Flow You are given a data file which provides flow information for a shallow channel. The channel is ~15 m wide and ~70 m long. In the middle of the channel, there is an underwater bump, which leads to an oscillating wake (known as a von Karman vortex street) downstream of the bump. The data files can be downloaded here: http://coastal.usc.edu/ENE512/ENE512_prob2.zip (note: its 851 MB). You may use the “ENE512_prob2.m” MATLAB script to help you plot basic information about the flow. Also, the scripts “ENE512_particle_tracking.m” will show you how to create a simple particle tracking code, using the full (non-averaged) velocity field, and the script “ENE512_particle_tracking_stats.m” will show you an approach to derive statistics of the particle “plume.” Your goal in this problem is to develop a particle dispersion model for the mean (time-averaged) flow and a particle dispersion model for the cross-channel averaged mean flow. For this problem, you need only consider the dispersion of particles that originate at mid-channel at the upstream end of the domain. You will use information from the full (non-averaged) velocity field as well as inference from the Navier-Stokes equations (as done in class for Taylor Dispersion). The following items should be addressed (report format not necessary; include discussion, plots, and code for each item) 1) Calculate and plot the time-averaged velocity components; this should be an “nx” by “ny” sized 2D surface for each component 2) Calculate and plot the turbulence intensity in the flow; this should be an “nx” by “ny” sized 2D surface 3) Calculate and plot the time and cross-channel averaged velocity components; this should be an “nx” length 1D vector for each component 4) Calculate and plot root mean square cross-channel velocity fluctuations; this should be an “nx” length 1D vector for each component 5) Using the various averaged forms of the Navier-Stokes equations discussed in class, provide a general, or expected physical form for the dispersion coefficients related to a) time-averaging and b) cross-channel averaging. Note that these dispersion coefficients should not be “closed form”, meaning that there should be coefficients or functions that are unknown 6) Use the flow information and particle tracking results from the provided full velocity field to constrain and calibrate your dispersion models 7) Show that your particle tracking with calibrated dispersion model for both time-averaged and channel-averaged flows exhibits some measure of statistical agreement with the particle dispersal found in the provided full velocity field particle tracking.
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