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| | | #REDIRECT [[Dissipation rate]] |
| #REDIRECT [[dissipation rate]] | |
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| == dissipation rate ==
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| <div class="definition"><div class="short_definition">The rate of conversion of [[turbulence]] into [[heat]] by [[molecular viscosity]].</div><br/> <div class="paragraph">Defined as <div class="display-formula"><blockquote>[[File:ams2001glos-De30.gif|link=|center|ams2001glos-De30]]</blockquote></div> 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''<sup>3/2</sup>κ<sup>5/2</sup>. Typical orders of magnitude for ε are 10<sup>-2</sup> to 10<sup>-3</sup> m<sup>2</sup> s<sup>-3</sup> during daytime [[convection]], and 10<sup>-6</sup> to 10<sup>-4</sup> m<sup>2</sup> s<sup>-3</sup> at night.</div><br/> </div><div class="reference">Stull, R. B. 1988. An Introduction to Boundary Layer Meteorology. 347–404. </div><br/>
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