In a fully turbulent flow, at high Reynolds number, we have large eddies breaking up into smaller ones, and those break up as well until finally the eddies are so small that they are dissipated by viscosity. If the system is in a steady state, this means that at every scale energy is being received from larger scales and supplied to smaller scales at the same rate, and so by extension the energy supplied at the largest scales is the same as the energy dissipated by viscosity. Clearly the scale at which dissipation occurs depends on the viscosity.
A poem by Lewis Fry Richardson:
Big whirls have little whirls, Which feed on their velocity, And little whirls have lesser whirls, and so on to viscosity.