Ergodicity: Difference between revisions

Latest revision as of 15:11, 20 February 2012

ergodicity

(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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-<div class="definition"><div class="short_definition">(<br/>''Also called'' statistical stationarity.) For [[turbulent flow]], the property of having the spatial,  temporal and [[ensemble averages]] all converge to the same mean.</div><br/> <div class="paragraph">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. <br/>''See'' [[ensemble average]].</div><br/> </div><div class="reference">Hinze, J. O. 1975. Turbulence. 2d ed., McGraw&ndash;Hill, . p. 5. </div><br/>
+<div class="definition"><div class="short_definition">(''Also called'' statistical stationarity.) For [[turbulent flow]], the property of having the spatial,  temporal and [[ensemble averages]] all converge to the same mean.</div><br/> <div class="paragraph">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. <br/>''See'' [[ensemble average]].</div><br/> </div><div class="reference">Hinze, J. O. 1975. Turbulence. 2d ed., McGraw&ndash;Hill, . p. 5. </div><br/>
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