movies
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movies [2009/03/04 09:29] gibson |
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| ====== Movies of plane Couette flow ====== | ====== Movies of plane Couette flow ====== | ||
| - | These movies are designed to convey the main ideas of our research in plane Couette flow. | + | These movies are designed to convey the main ideas of my research in plane Couette flow. |
| - | For more details, please see [[http://cns.physics.gatech.edu/~gibson/publications/index.html|our papers]]. | + | For more details, please see [[http://cns.physics.gatech.edu/~gibson/publications/index.html|my papers]]. |
| + | ===== Visualization scheme ===== | ||
| + | |||
| + | |||
| + | The movies show plane Couette flow in a rectangular box of size [Lx, Ly, Lz] with solid walls on the top and | ||
| + | bottom (y = -Ly/2 and Ly/2). The top wall and the upper half of the fluid are cut away to show what happens | ||
| + | at the midplane y=0. The walls slide at constant speeds in opposite directions along x, | ||
| + | the top wall slides towards the back of the box, the bottom towards the front. | ||
| + | |||
| + | Arrows indicate in-plane velocity. The **color indicates the streamwise velocity**, that is, the speed of the fluid in the direction of the wall motion: | ||
| + | * <html><span style="color:red"> Red </span></html> indicates fluid moving in the <html><span style="color:red"> positive </span></html> streamwise direction (<html><span style="color:red">away from</span></html> the viewer) | ||
| + | * <html><span style="color:blue"> Blue </span></html> indicates fluid moving in the <html> <span style="color:blue"> negative </span> </html> streamwise direction (<html><span style="color:blue">towards </span></html>the viewer) | ||
| + | |||
| + | The x,y,z directions are streamwise, wall-normal, and spanwise. The rectangular cell is periodic in x and z, so that the front and back slices match, and the left and the right. | ||
| - | [[movies:hkw | Turbulent dynamics in the HKW cell]] | ||
| ====== Coherent structures in shear flows ====== | ====== Coherent structures in shear flows ====== | ||
| Line 24: | Line 36: | ||
| * 250 < t < 300 : less organized flow ensues, with roll-streak patterns emerging here and there, now and then | * 250 < t < 300 : less organized flow ensues, with roll-streak patterns emerging here and there, now and then | ||
| + | ====== Turbulent dynamics in a 'minimal flow unit' ====== | ||
| + | |||
| + | <flashplayer width="720" height="500">file=/movies/tutorial/hkws1s2.flv&image=/movies/tutorial/hkws1s3movie.png&repeat=none</flashplayer> | ||
| + | |||
| + | The dynamics of the system above are complex, so for the time being we focus on a cell with smaller aspect ratios, | ||
| + | just big enough to contain one pair of alternating roll-streak structures. The cell size of [1.75 π, 2, 1.2 π] | ||
| + | and Reynolds number of 400 is from Hamilton, Kim, and Waleffe (1995), an important paper that identified the | ||
| + | dynamics seen above as a 'self-sustaining process' in plane Couette flow. Observe this repetitive but nonperiodic | ||
| + | cycle of behavior | ||
| + | |||
| + | - streaks and rolls that are nearly uniform in x, the streamwise direction | ||
| + | - growth of a roughly sinusoidal-in-x instability in the roll-streak structures | ||
| + | - destruction of the structures, finer scale fluctuations, and higher dissipation | ||
| + | - reformation of the roll-streak structures | ||
| + | |||
| + | ====== Periodic orbits ====== | ||
| + | |||
| + | <flashplayer width="400" height="320">file=/movies/hkw/P68p07.flv&image=/movies/hkw/P68p07.png&repeat=none</flashplayer> | ||
| + | <flashplayer width="400" height="320">file=/movies/hkw/P99p70.flv&image=/movies/hkw/P99p70.png&repeat=none</flashplayer> | ||
| + | We have computed a number of //exact periodic orbits// in the system seen above. Two are shown above; there are more | ||
| + | in the [[database:hkw|channelflow database of exact solutions]]. The periodic orbits repeat themselves exactly after a | ||
| + | finite time. This opens up a number of | ||
| + | interesting possibilities for //dynamical analysis of turbulence//. For example, we can compute the eigenvalues and | ||
| + | eigenfunctions of the orbits and so determine the linear stability of turbulent trajectories. The orbits also do quite | ||
| + | well in capturing first and second-order statistics of the turbulent flow, i.e. the mean flow and Reynolds stresses. | ||
movies.1236187741.txt.gz · Last modified: 2009/03/04 09:29 by gibson
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