Eddy viscosity

From Glossary of Meteorology

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 m2 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:
where 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.