From AMS Glossary
In general, the continuum hypothesis used to generalize Newton's laws for point masses to continuous media such as fluids or gases.
At any point in the continuous media it must be possible to identify volumes small enough that derivatives exist, yet large enough to contain sufficient particles that the average macroscopic property (such as momentum, mass, or temperature) may be defined. The eddy continuum hypothesis is used to extend the concept of a fluid continuum to a turbulent flow in which small- scale eddies are substituted for fluid particles. To apply the eddy continuum hypothesis, a scale analysis must be performed to verify that the averaging periods are sufficiently long that enough small-scale turbulent eddies are sampled that their dynamical effect on the mean flow is captured. If the eddies' length scales are comparable to the mean flow length scales, the eddy continuum most likely can be defined. The eddy continuum hypothesis is often applied in the study of large- scale organization (of the smaller-scale turbulent eddies) in the planetary boundary layer turbulence.
Brown, R. A. 1990. Fluid Mechanics of the Atmosphere. Academic Press, . 490 pp.