# First-order closure

From AMS Glossary

## first-order closure

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.

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).

*See also*closure assumptions, closure problem.