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
, 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.
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