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====== Movies of plane Couette flow ====== These movies are designed to convey the main ideas of our research in plane Couette flow. For more details, please see [[http://cns.physics.gatech.edu/~gibson/publications/index.html|our papers]]. [[movies:hkw | Turbulent dynamics in the HKW cell]] ====== 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
