Dissipation

From Glossary of Meteorology
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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
ams2001glos-De26
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
ams2001glos-De27
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.


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