From the Kuramoto-Sivasinsky example you learn that "viscous fluids" near the first onset of linear instability can be described by low-dimensional ODEs, and hopefully get some feeling why the 2-d stationary flow bifurcating into a Hopf limit cycle offers also a normal-form description of an "infinite-dimensional" PDE instability onset. It's a long (and so far unexplored) way from this first instability to an honest theory of turbulence, sorry.

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