Eddy viscosity: Difference between revisions
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<div class="definition"><div class="short_definition">The turbulent [[transfer]] of [[momentum]] by [[eddies]] giving rise to an internal fluid [[friction]], in a manner analogous to the action of [[molecular viscosity]] in [[laminar flow]], but taking place on a much larger [[scale]].</div><br/> <div class="paragraph">The value of the [[coefficient of eddy viscosity]] (an [[exchange coefficient]]) is of the order of 1 m<sup>2</sup> s<sup>-1</sup>, or one hundred thousand times the molecular [[kinematic viscosity]]. Eddy viscosity is often represented by the symbol K, and the [[turbulence]] parameterization that uses eddy viscosity is called [[K-theory]]. In this theory, the [[eddy flux]] in kinematic units is related to the mean vertical [[gradient]], such as in this example for vertical [[flux]] of horizontal [[momentum]]: <div class="display-formula"><blockquote>[[File:ams2001glos-Ee8.gif|link=|center|ams2001glos-Ee8]]</blockquote></div> where ''w'' is [[vertical velocity]], ''U'' is horizontal [[wind]] in the ''x'' direction, the overbar represents an average, and the prime denotes the [[deviation]] or [[perturbation]] from an average. Eddy viscosity is a function of the flow, not of the fluid. It is greater for flows with more turbulence. The eddy viscosity or K-theory approach is a [[parameterization]] for the eddy [[momentum flux]] (Reynolds stress) that works reasonably well when only small eddies are present in the flow, but that behaves poorly when large-eddy [[coherent structures]], such as thermals in the [[convective mixed layer]], are present. <br/>''See'' [[Reynolds stresses]], [[eddy correlation]]; <br/>''compare'' [[transilient turbulence theory]].</div><br/> </div> | <div class="definition"><div class="short_definition">The turbulent [[transfer]] of [[momentum]] by [[eddies]] giving rise to an internal fluid [[friction]], in a manner analogous to the action of [[molecular viscosity]] in [[laminar flow]], but taking place on a much larger [[scale]].</div><br/> <div class="paragraph">The value of the [[coefficient of eddy viscosity]] (an [[exchange coefficients|exchange coefficient]]) is of the order of 1 m<sup>2</sup> s<sup>-1</sup>, or one hundred thousand times the molecular [[kinematic viscosity|kinematic viscosity]]. Eddy viscosity is often represented by the symbol K, and the [[turbulence]] parameterization that uses eddy viscosity is called [[K-theory]]. In this theory, the [[eddy flux]] in kinematic units is related to the mean vertical [[gradient]], such as in this example for vertical [[flux]] of horizontal [[momentum]]: <div class="display-formula"><blockquote>[[File:ams2001glos-Ee8.gif|link=|center|ams2001glos-Ee8]]</blockquote></div> where ''w'' is [[vertical velocity]], ''U'' is horizontal [[wind]] in the ''x'' direction, the overbar represents an average, and the prime denotes the [[deviation]] or [[perturbation]] from an average. Eddy viscosity is a function of the flow, not of the fluid. It is greater for flows with more turbulence. The eddy viscosity or K-theory approach is a [[parameterization]] for the eddy [[momentum flux]] (Reynolds stress) that works reasonably well when only small eddies are present in the flow, but that behaves poorly when large-eddy [[coherent structures]], such as thermals in the [[convective mixed layer]], are present. <br/>''See'' [[Reynolds stresses]], [[eddy correlation]]; <br/>''compare'' [[transilient turbulence theory]].</div><br/> </div> | ||
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Latest revision as of 15:52, 25 April 2012
eddy viscosity
The turbulent transfer of momentum by eddies giving rise to an internal fluid friction, in a manner analogous to the action of molecular viscosity in laminar flow, but taking place on a much larger scale.
The value of the coefficient of eddy viscosity (an exchange coefficient) is of the order of 1 m2 s-1, or one hundred thousand times the molecular kinematic viscosity. Eddy viscosity is often represented by the symbol K, and the turbulence parameterization that uses eddy viscosity is called K-theory. In this theory, the eddy flux in kinematic units is related to the mean vertical gradient, such as in this example for vertical flux of horizontal momentum: where w is vertical velocity, U is horizontal wind in the x direction, the overbar represents an average, and the prime denotes the deviation or perturbation from an average. Eddy viscosity is a function of the flow, not of the fluid. It is greater for flows with more turbulence. The eddy viscosity or K-theory approach is a parameterization for the eddy momentum flux (Reynolds stress) that works reasonably well when only small eddies are present in the flow, but that behaves poorly when large-eddy coherent structures, such as thermals in the convective mixed layer, are present.
See Reynolds stresses, eddy correlation;
compare transilient turbulence theory.
See Reynolds stresses, eddy correlation;
compare transilient turbulence theory.
