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gtspring2009:2dturbulence [2009/03/26 11:18]
paprocki
gtspring2009:2dturbulence [2010/02/02 07:55] (current)
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 ====== The experiment ====== ====== The experiment ======
 +The following are recurrence plots for runs with DC current at 3V, 6V, 9V, 12V and 15V respectively:​
 +
 +{{:​gtspring2009:​recplot_3v.jpg|}} ​ {{:​gtspring2009:​recplot_6v.jpg|}} ​ {{:​gtspring2009:​recplot_9v.jpg|}} ​
 +{{:​gtspring2009:​recplot_12v.jpg|}} ​ {{:​gtspring2009:​recplot_15v.jpg|}}
 +
 +The following videos correspond to the above plots: ​
 +
 +3V: [[http://​www.youtube.com/​watch?​v=HRbT2zgkMkg]]
 +6V: [[http://​www.youtube.com/​watch?​v=BtSvv9C9HJI&​feature=channel_page]] ​
 +9V: [[http://​www.youtube.com/​watch?​v=44kXAITPM1A&​feature=channel]] ​
 +12V: [[http://​www.youtube.com/​watch?​v=s2VSBRYrpIU&​feature=channel]] ​
 +15V: [[http://​www.youtube.com/​watch?​v=SanCC1bl6hY&​feature=channel]]
 +
 +
  
 {{:​gtspring2009:​paprocki1.jpg?​24}} Here's a description of the experiment, currently in progress: {{:​gtspring2009:​paprocki1.jpg?​24}} Here's a description of the experiment, currently in progress:
  
-In general, we are investigating what is going on with forced two-dimensional turbulence. ​ We have a thin layer of electrically conducting fluid on top of a bed of strong magnets, with glass separating the fluid and the magnets. ​ Currently, the fluid is salt water. ​ Then, we drive current through the water using two large electrodes hooked up to a power source and a function generator. ​ The only signal we've tested thus far is a sine wave.  The current goal is to search for a regime of flow somewhere between periodic and turbulent motion.+In general, we are investigating what is going on with forced two-dimensional turbulence. ​ We have a thin layer of electrically conducting fluid on top of a bed of strong magnets, with glass separating the fluid and the magnets. ​ Currently, the fluid is salt water. ​ Then, we drive current through the water using two large electrodes hooked up to a power source and a function generator. ​ The only signal we've tested thus far is a sine wave.  The current goal is to find a regime of flow somewhere between periodic and turbulent motion.
  
 Once we have enough preliminary data to know what we're actually looking for and what the parameters we'll be using are, we'll switch out the salt water for sulfuric acid, and make sure to keep the molarity consistent. ​ We'll also be using a voltage to current converter so that we'll be keeping the current consistent rather than the voltage, which is what is more important. Once we have enough preliminary data to know what we're actually looking for and what the parameters we'll be using are, we'll switch out the salt water for sulfuric acid, and make sure to keep the molarity consistent. ​ We'll also be using a voltage to current converter so that we'll be keeping the current consistent rather than the voltage, which is what is more important.
  
-We have a few different ways to look at data graphically right now.  The first one is the velocity field data.  Using particle image velocimetry software, we plug in a movie of the experiment into MATLAB and it spits out velocity field data, giving us an idea of which areas of the experiment have fluid moving in what direction. ​ From velocity field data, we can make recurrence plots, which are what is plastered all over this blog.  It's a scalar field that takes in the velocity field for two times, T + t and t, and finds the difference. ​ The formula is Sum over velocity field of |U(T+t)-U(t)|. ​ This will give a range of values, which is then assigned to different colors, and these colors are plotted on the recurrence plot.  We can also make recurrence plots for individual vectors in the vector field. ​ The horizontal axis is the t axis, and the vertical axis is the T axis.  The units are in seconds. ​ This allows us to spot periodicity better than a formula like |U(T)-U(t)|. ​ The last way we are currently looking at data are time series, which are plots of the magnitude of a given vector or entire vector field over time.+We have a few different ways to look at data graphically right now.  The first one is the velocity field data.  Using particle image velocimetry software, we plug in a movie of the experiment into MATLAB and it spits out velocity field data, giving us an idea of which areas of the experiment have fluid moving in what direction. ​ From velocity field data, we can make recurrence plots, which are what is plastered all over this blog.  It's a scalar field that takes in the velocity field for two times, T + t and t, and finds the difference. ​ The formula is Sum over velocity field of |U(T+t)-U(t)|. ​ This will give a range of values, which is then assigned to different colors, and these colors are plotted on the recurrence plot.  We can also make recurrence plots for individual vectors in the vector field.  Recurrence plots appear to be "​missing"​ the upper triangle of the graph - this is intentional,​ as there isn't actually any data in that region to be looked at.  The horizontal axis is the t axis, and the vertical axis is the T axis.  The units are in seconds. ​ This allows us to spot periodicity better than a formula like |U(T)-U(t)|. ​ The last way we are currently looking at data are time series, which are plots of the magnitude of a given vector or entire vector field over time.
  
 //​[[jon.paprocki@gatech.edu|Jon Paprocki]] 2009-03-26 2:18 PM// //​[[jon.paprocki@gatech.edu|Jon Paprocki]] 2009-03-26 2:18 PM//
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 You can see a very clear jump from vaguely semi-periodic to completely periodic motion between .25 and .5 Hz.  .0625, .125, and .25 Hz all appear to be just plain turbulent to the naked eye, but the recurrence data suggests otherwise. You can see a very clear jump from vaguely semi-periodic to completely periodic motion between .25 and .5 Hz.  .0625, .125, and .25 Hz all appear to be just plain turbulent to the naked eye, but the recurrence data suggests otherwise.
  
-Also, I'm giving a talk on this project for the undergrad research symposium on April 1st in room 320 of the student center at 1:40 PM, if you're interested in something more detailed than this ramshackle blog that is still lacking a description of what's going on (maybe I'll get to that today, too!).+Also, I'm giving a talk on this project for the undergrad research symposium on April 1st in room 320 of the student center at 1:40 PM, if you're interested in something more detailed than this ramshackle blog.
  
 EDIT: movies of these posted above in movies section EDIT: movies of these posted above in movies section
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 --pivDifArray.m -> takes in a correlation.mat file and outputs a difArray.mat that essentially is just converting the structure array of correlation.mat into a more usable array containing only the velocity data.  This makes it easier to use vectorized code.  This isn't the original use of the function so it isn't very aptly named...\\ ​ --pivDifArray.m -> takes in a correlation.mat file and outputs a difArray.mat that essentially is just converting the structure array of correlation.mat into a more usable array containing only the velocity data.  This makes it easier to use vectorized code.  This isn't the original use of the function so it isn't very aptly named...\\ ​
 ---pivRecurrencePlot.m -> takes in a difArray.mat file and outputs a recurrencePlot.mat file containing recurrence data.\\ ​ ---pivRecurrencePlot.m -> takes in a difArray.mat file and outputs a recurrencePlot.mat file containing recurrence data.\\ ​
 +---PivRecurrencePlotNew.m -> uses the new formula for recurrence plots (doesn'​t square the difference vectors); outputs a recurrencePlotNew.mat file.\\
 +----piv1DRecSlicet.m -> grabs a "​slice"​ of the recurrence plot at a given time along the t axis and plots it.\\
 +----piv1DRecSliceTT.m -> grabs a slice of the recurrence plot at a given time along the T axis and plots it.\\
 +----minFinderY.m -> "​filters"​ out a recurrence plot by blotting out all the points that aren't minima along the Y axis, to some sensitivity.\\
 +----minFinderX.m -> same as minFinderY, but along the X axis.\\
 ---pivRecurrencePlotOne.m -> same as pivRecurrence,​ but only does it for one specified point and ouputs a recurrenceDataLoc###​.mat file\\ ​ ---pivRecurrencePlotOne.m -> same as pivRecurrence,​ but only does it for one specified point and ouputs a recurrenceDataLoc###​.mat file\\ ​
 ----pivRecurrenceImage.m -> takes in a recurrencePlot.mat or recurrenceDataLoc###​.mat file and outputs an image of it.\\  ----pivRecurrenceImage.m -> takes in a recurrencePlot.mat or recurrenceDataLoc###​.mat file and outputs an image of it.\\ 
gtspring2009/2dturbulence.1238091535.txt.gz ยท Last modified: 2009/03/26 11:18 by paprocki