2c. Turbulence in a small aspect ratio cell

What is striking about the large aspect simulations is that all non-laminar initial conditions appear to settle into similar patterns of behavior, consisting of episodes of highly ordered motion along streamwise counter-rotating rolls, interspersed by turbulent episodes.

This observation motivates the empirical search for small aspect cells sufficiently large to accommodate a pair of unstable counter rotating rolls, following Hamilton, Kim and Waleffe. This movie shows that their small aspect cell exhibits qualitatively similar behavior:

[MOVIE] Random initial condition.

The cell size here is the "HKW cell," Lx = 7π/4 = 5.50, Lz = 6π/5 = 3.76, found empirically by Hamilton, Kim and Waleffe to be the smallest that appears to sustain turbulence. The initial condition is a random perturbation from laminar flow. (2007-09-04, 15 MB)

We sometimes find it convenient to compute in a smaller cell, [L_x, L_y, L_z] = [5.51, 2, 2.51] , used by Waleffe.