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| - | [[movies:hkw | Turbulent dynamics in the HKW cell]] | + | ====== Movies of 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|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. | ||
| + | |||
| + | ====== Coherent structures in shear flows ====== | ||
| + | |||
| + | <flashplayer width="720" height="320">file=/movies/tutorial/bigbox.flv&image=/movies/tutorial/bigbox.png&repeat=none</flashplayer> | ||
| + | |||
| + | This movie show the formation of `coherent structures' in plane Couette flow, with fairly large | ||
| + | aspect-ratio cell: [Lx,Ly,Lz] = [16, 2, 16]. The initial condition is a random perturbation of | ||
| + | laminar flow that meets boundary and divergence-free conditions, has roughly the spectral | ||
| + | characteristics of turbulent fields, and is about 10% in magnitude of the laminar flow (or 1% | ||
| + | in energy). | ||
| + | |||
| + | Observe | ||
| + | * 0 < t < 10 : the random perturbations grow and no apparent order | ||
| + | * 10 < t < 100 : there is little discernable order | ||
| + | * 100 < t < 200 : the flow organizes into alternating +/- streamwise-moving streaks (red/blue) associated with `rolls' visible in the front y,z plane, which draw the + streamwise (red) fluid down from the top wall and - streamwise (blue) up from the bottom | ||
| + | * 200 < t < 250 : an instability grows and destroys the system of streaks and rolls | ||
| + | * 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.1233162974.txt.gz · Last modified: 2009/01/28 09:16 by wikiadmin
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