The role of the clump lifetime logarithmically dependent on small scales, in determining the fluctuation level for forced, dissipative turbulence is reconsidered with the aid of an exactly solvable rapid-change model of passive advection. It is shown in mathematical detail that the common procedure of approximating the steady-state fluctuation level by , where is the production rate or source of fluctuations, is invalid when a clean distinction can be made between energy-containing and inertial ranges. The correct result is where is a macroscopic diffusion time that does not depend on the small scales.
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