# Viscous fluid

From Glossary of Meteorology

## viscous fluid

A fluid for which the molecular viscous effects of diffusion and dissipation can have significant effects on the flow.

The importance of viscosity depends on the relevant velocity and length scales of the flow and the viscosity of the fluid. The nondimensional measure of the relative importance of viscosity is the reciprocal of the Reynolds number, Re. For typical atmospheric flows, Re > 10

^{7}, implying that viscous effects may be neglected relative to the leading [*O*(1)] terms in the Navier–Stokes equations. However, in a turbulent flow, such as in the boundary layer, vortex stretching causes a continuous nonlinear cascade of turbulence kinetic energy, TKE, from large scales to smaller scales. The largest-scale eddies are responsible for the Reynolds stresses and conversion of mean flow energy into TKE. At some point in the cascade, the eddies will have length and velocity scales that are sufficiently reduced for the Reynolds number to be of order 1. At these scales the TKE of eddies can be converted into internal energy through viscous dissipation. These small eddies will have a much shorter timescale than the largest eddies in the flow and are thus statistically independent of the large-scale motion. For a developed turbulent flow, the rate at which the mean flow energy is converted into turbulence at the largest scales must be equal to the rate at which it is ultimately dissipated by viscosity by the small-scale eddies. These smallest eddies have scales that are very much larger than those of the molecular motions, and the continuum hypothesis is still valid for describing eddies of this size. Although dissipation occurs at the smallest possible eddies in the flow and the TKE is contained in the largest-scale eddies, the viscous dissipation is a leading term in the TKE budget and may not be ignored.*See*turbulence spectrum, turbulence length scales.Tennekes, H., and J. L. Lumley 1972. A First Course in Turbulence. MIT Press, . 256–262.