Structure function: Difference between revisions

Latest revision as of 07:44, 30 March 2024

The variance of the difference of a turbulence quantity in space or time, given by

where q is a scalar or a velocity component.
For small separations (r ≤ z, where z is the height above the surface), this equation may be written

where b is about 0.7 for temperature and 0.76 for humidity, χ_q is the rate of destruction of q²/2 by molecular diffusion, and ε is the rate of dissipation of turbulence energy into heat. The coefficient

is called the structure constant of q. This formulation eliminates the mean component of a fluctuating quantity and provides a measure of fluctuation variance within a band of wavelengths (or frequencies) determined by the separation distance (or lag time).
Panofsky, H. A., and J. A. Dutton 1984. Atmospheric Turbulence. Wiley, . 182–183.

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+{{Term
+|Display title=structure function
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+|Meaning=
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+The [[variance]] of the difference of a [[turbulence]] quantity in space or time,  given by  <blockquote>[[File:ams2001glos-Se78.gif|link=|center|ams2001glos-Se78]]</blockquote> where ''q'' is a [[scalar]] or a [[velocity]] component.<br/> For small separations (''r'' &le; ''z'', where ''z'' is the height above the surface), this equation may be  written  <blockquote>[[File:ams2001glos-Se79.gif|link=|center|ams2001glos-Se79]]</blockquote> where ''b'' is about 0.7 for [[temperature]] and 0.76 for [[humidity]], &#x003c7;<sub>''q''</sub> is the rate of destruction of ''q''<sup>2</sup>/2 by [[molecular diffusion]], and &#x003b5; is the rate of [[dissipation]] of [[turbulence energy]] into [[heat]].  The coefficient  <blockquote>[[File:ams2001glos-Se80.gif|link=|center|ams2001glos-Se80]]</blockquote> is called the [[structure constant]] of ''q''. This formulation eliminates the mean component of a  fluctuating quantity and provides a measure of [[fluctuation]] variance within a [[band]] of [[wavelengths]]  (or frequencies) determined by the separation distance (or [[lag time]]).<br/> Panofsky, H. A., and J. A. Dutton 1984. Atmospheric Turbulence. Wiley, . 182&ndash;183.
-  <div class="term">
+}}
-== structure function ==
+}}
-  </div>
-<div class="definition"><div class="short_definition">The [[variance]] of the difference of a [[turbulence]] quantity in space or time,  given by  <div class="display-formula"><blockquote>[[File:ams2001glos-Se78.gif|link=|center|ams2001glos-Se78]]</blockquote></div> where ''q'' is a [[scalar]] or a [[velocity]] component.</div><br/> <div class="paragraph">For small separations (''r'' &le; ''z'', where ''z'' is the height above the surface), this equation may be  written  <div class="display-formula"><blockquote>[[File:ams2001glos-Se79.gif|link=|center|ams2001glos-Se79]]</blockquote></div> where ''b'' is about 0.7 for [[temperature]] and 0.76 for [[humidity]], &#x003c7;<sub>''q''</sub> is the rate of destruction of ''q''<sup>2</sup>/2 by [[molecular diffusion]], and &#x003b5; is the rate of [[dissipation]] of [[turbulence energy]] into [[heat]].  The coefficient  <div class="display-formula"><blockquote>[[File:ams2001glos-Se80.gif|link=|center|ams2001glos-Se80]]</blockquote></div> is called the [[structure constant]] of ''q''. This formulation eliminates the mean component of a  fluctuating quantity and provides a measure of [[fluctuation]] variance within a [[band]] of [[wavelengths]]  (or frequencies) determined by the separation distance (or [[lag time]]).</div><br/> </div><div class="reference">Panofsky, H. A., and J. A. Dutton 1984. Atmospheric Turbulence. Wiley, . 182&ndash;183. </div><br/>
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-[[Category:Terms_S]]