# Eddy viscosity

From AMS Glossary

## eddy viscosity

The turbulent transfer of momentum by eddies giving rise to an internal fluid friction, in a manner analogous to the action of molecular viscosity in laminar flow, but taking place on a much larger scale.

The value of the coefficient of eddy viscosity (an exchange coefficient) is of the order of 1 m where

^{2}s^{-1}, or one hundred thousand times the molecular kinematic viscosity. Eddy viscosity is often represented by the symbol K, and the turbulence parameterization that uses eddy viscosity is called K-theory. In this theory, the eddy flux in kinematic units is related to the mean vertical gradient, such as in this example for vertical flux of horizontal momentum:*w*is vertical velocity,*U*is horizontal wind in the*x*direction, the overbar represents an average, and the prime denotes the deviation or perturbation from an average. Eddy viscosity is a function of the flow, not of the fluid. It is greater for flows with more turbulence. The eddy viscosity or K-theory approach is a parameterization for the eddy momentum flux (Reynolds stress) that works reasonably well when only small eddies are present in the flow, but that behaves poorly when large-eddy coherent structures, such as thermals in the convective mixed layer, are present.*See*Reynolds stresses, eddy correlation;*compare*transilient turbulence theory.