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(Also called statistical stationarity.) For turbulent flow, the property of having the spatial, temporal and ensemble averages all converge to the same mean.

This can only be true if the flow is stationary and homogenous. As a consequence, the autocorrelation of an ergodic flow variable is zero as either the averaging length, time, or number of realizations goes to infinity.
See ensemble average.

Hinze, J. O. 1975. Turbulence. 2d ed., McGraw–Hill, . p. 5.

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