View source for First-order closure



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== first-order closure ==
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<div class="definition"><div class="short_definition">An approximation made to solve [[turbulence]] equations that assumes turbulent  fluxes of a quantity such as [[moisture]] flow down the [[mean]] gradient of moisture, where the rate  of flow is proportional to an [[eddy diffusivity]].</div><br/> <div class="paragraph">The symbol for eddy diffusivity is often K, hence this theory is also known as [[K-theory]]. By  first order, it is implied that any turbulence [[statistics]] of second or higher order ([[variances]],  [[covariances]], etc.) that appear in the governing equations are replaced by approximations that  depend only on first-order statistics (i.e., mean values of the [[dependent variables]] and of [[independent  variables]]). Such an approximation reduces the number of unknowns in the governing  equations, allowing them to be mathematically closed, thereby allowing them to be solved for the  approximate flow state. First-order closure can be applied locally (as in K-theory) or nonlocally  (as in [[transilient turbulence theory]]). <br/>''See also'' [[closure assumptions]], [[closure problem]].</div><br/> </div>
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