# Higher-order closure

From AMS Glossary

## higher-order closure

An approximation to turbulence that retains prognostic equations for mean variables (such as potential temperature and wind) as well as for some of the higher-order statistics including variance (such as turbulence kinetic energy

*or*temperature variance) or covariance (kinematic fluxes such as for heat and momentum).Regardless of the statistical order of the forecast equations, other high-order statistical terms appear in those equations, the solutions of which require approximations known as turbulence closure assumptions. While usually considered more accurate than first-order closures (K-theory), higher-order closure solutions are computationally more expensive. Turbulence closures are often classified according to two attributes: the order of statistical closure, and the degree of nonlocalness. Common types of higher-order closure include (in increasing statistical order): one-and-a-half order closure (also known as

*k*-ε closure), second-order closure, and third-order closure. All turbulence closures are designed to reduce an infinite set of equations that cannot be solved to a finite set of equations that can be solved approximately to help make weather forecasts and describe physical processes.*See*Reynolds averaging;*compare*zero-order closure, half-order closure.