From Glossary of Meteorology
(Redirected from Viscous dissipation)


(Also called viscous dissipation.) In thermodynamics, the conversion of kinetic energy into internal energy by work done against the viscous stresses.

Sometimes the rate of conversion per unit volume is meant. If the Navier–Stokes equations of viscous flow are employed, Rayleigh's mathematical expression for the rate of viscous (or frictional) dissipation per unit volume is
where μ is the dynamic viscosity. The Navier–Stokes assumptions thus satisfy the primary requirement of the second law of thermodynamics that the rate of dissipation be positive and the process irreversible. In a turbulent fluid, which the atmosphere usually is, dissipation is the end result of the turbulent scale process, by which kinetic energy is transferred from its originating, or outer, scale to the dissipation scales by nonlinear dynamical interactions. Most dissipation occurs at scales near the Kolmogorov microscale λd, given by
where ν is the kinematic viscosity and ε is the rate of energy dissipation per unit mass.
See also stress tensor, energy equation.

Brunt, D. 1941. Physical and Dynamical Meteorology. 285–286.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.