While direct numerical simulation helps us understand the
statistics of turbulent fluid flows, understanding the geometry of
turbulent flows in phase space requires the computation of steady
states, traveling waves, periodic motions, and close recurrences. In
plane Couette flow, two parallel walls move in opposite directions and
drive the fluid in-between. Turbulence results if the walls drive the
fluid too hard and the Reynolds number is high enough. This talk will
describe accurate and well resolved computations of 3-dimensional
traveling periodic solutions within plane Couette turbulence. The
computed solutions and analogy to the Lorenz equations will be used
as a basis to discuss the manner in which the geometry of turbulent
dynamics in phase space can be understood.
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