# Dissipation rate

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## dissipation rate

Defined as where (

*u*′,*v*′,*w*′) are the turbulent perturbation velocities (instantaneous deviations from respective mean velocities) in the (*x*,*y*,*z*) directions, ν is the kinematic viscosity of air, and the overbar indicates an average. This conversion always acts to reduce turbulence kinetic energy and means that turbulence is not a conserved variable. It also causes turbulence to decay to zero unless there is continual regeneration of turbulence by other mechanisms. Turbulence dissipation is greatest for the smallest-size eddies (on the order of millimeters in diameter), but turbulence is usually produced as larger eddies roughly the size of the atmospheric boundary layer (on the order of hundreds of meters). The transfer of turbulence kinetic energy from the largest to the smallest eddies is called the inertial cascade, and the rate of this energy transfer is directly proportional to the dissipation rate for turbulence that is stationary (steady state). The medium- size eddies where turbulence is neither created nor destroyed is called the inertial subrange. Similarity theory (dimensional analysis) allows calculation of the dissipation rate from measurements of turbulence spectral intensity*S*(κ) at wavelength κ, via ε = 0.49*S*^{3/2}κ^{5/2}. Typical orders of magnitude for ε are 10^{-2}to 10^{-3}m^{2}s^{-3}during daytime convection, and 10^{-6}to 10^{-4}m^{2}s^{-3}at night.Stull, R. B. 1988. An Introduction to Boundary Layer Meteorology. 347–404.