Although turbulence presents some of the most challenging unsolved problems in theoretical physics and applied mathematics, there are quantities we may hope to be able to bound even when we cannot compute them exactly. In this report we describe some of the ways of doing this within the context of a flow in a shear layer with injection and suction at the boundaries. We obtain bounds on the rate of viscous energy dissipation, valid for turbulent flows as well as for any laminar (steady or unsteady) flows, that may be directly compared to that in an exact solution for a flow with the same boundary conditions.
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