https://glossary.ametsoc.org/w/index.php?title=Power-law_profile&feed=atom&action=historyPower-law profile - Revision history2024-03-28T14:46:05ZRevision history for this page on the wikiMediaWiki 1.39.5https://glossary.ametsoc.org/w/index.php?title=Power-law_profile&diff=5038&oldid=prevUnknown user at 00:39, 26 April 20122012-04-26T00:39:13Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:39, 25 April 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9">Line 9:</td>
<td colspan="2" class="diff-lineno">Line 9:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><div class="definition"><div class="short_definition">A formula for the [[variation]] of [[wind]] with height in the [[surface boundary layer]].</div><br/> <div class="paragraph">It is an alternative to the [[logarithmic velocity profile]], and the assumptions are the same, with the exception of the form of the dependence of [[mixing length]] ''l'' on height ''z''. Here <div class="display-formula"><blockquote>[[File:ams2001glos-Pe44.gif|link=|center|ams2001glos-Pe44]]</blockquote></div> Then <div class="display-formula"><blockquote>[[File:ams2001glos-Pe45.gif|link=|center|ams2001glos-Pe45]]</blockquote></div> where <div class="inline-formula">[[File:ams2001glos-Pex07.gif|link=|ams2001glos-Pex07]]</div> is the [[mean velocity]], ''u''<sub>&#x0002a;</sub> the [[friction velocity]], &#x003bd; the [[kinematic viscosity]], and <div class="display-formula"><blockquote>[[File:ams2001glos-Pe46.gif|link=|center|ams2001glos-Pe46]]</blockquote></div> For moderate [[Reynolds numbers]], ''p'' = 6/7 (the seventh-root profile) is empirically verified, but for large Reynolds numbers ''p'' is between this value and unity. It is to be noted that if <div class="inline-formula">[[File:ams2001glos-Pex08.gif|link=|ams2001glos-Pex08]]</div> is proportional to ''z''<sup>''m''</sup>, and if the [[stress]] is assumed independent of height, then the [[eddy viscosity]] &#x003bd;<sub>''e''</sub> is proportional to ''z''<sup>1-''m''</sup>. These relations are known as Schmidt's conjugate-power laws.</div><br/> </div><div class="reference">Sutton, O. G. 1953. Micrometeorology. 78&ndash;85. </div><br/> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><div class="definition"><div class="short_definition">A formula for the [[variation]] of [[wind]] with height in the [[surface boundary layer]].</div><br/> <div class="paragraph">It is an alternative to the [[logarithmic velocity profile]], and the assumptions are the same, with the exception of the form of the dependence of [[mixing length]] ''l'' on height ''z''. Here <div class="display-formula"><blockquote>[[File:ams2001glos-Pe44.gif|link=|center|ams2001glos-Pe44]]</blockquote></div> Then <div class="display-formula"><blockquote>[[File:ams2001glos-Pe45.gif|link=|center|ams2001glos-Pe45]]</blockquote></div> where <div class="inline-formula">[[File:ams2001glos-Pex07.gif|link=|ams2001glos-Pex07]]</div> is the [[mean velocity]], ''u''<sub>&#x0002a;</sub> the [[friction velocity]], &#x003bd; the [[<ins style="font-weight: bold; text-decoration: none;">kinematic viscosity|</ins>kinematic viscosity]], and <div class="display-formula"><blockquote>[[File:ams2001glos-Pe46.gif|link=|center|ams2001glos-Pe46]]</blockquote></div> For moderate [[Reynolds numbers]], ''p'' = 6/7 (the seventh-root profile) is empirically verified, but for large Reynolds numbers ''p'' is between this value and unity. It is to be noted that if <div class="inline-formula">[[File:ams2001glos-Pex08.gif|link=|ams2001glos-Pex08]]</div> is proportional to ''z''<sup>''m''</sup>, and if the [[stress]] is assumed independent of height, then the [[eddy viscosity]] &#x003bd;<sub>''e''</sub> is proportional to ''z''<sup>1-''m''</sup>. These relations are known as Schmidt's conjugate-power laws.</div><br/> </div><div class="reference">Sutton, O. G. 1953. Micrometeorology. 78&ndash;85. </div><br/> </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
</table>Unknown userhttps://glossary.ametsoc.org/w/index.php?title=Power-law_profile&diff=5037&oldid=prevUnknown user at 22:53, 20 February 20122012-02-20T22:53:23Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:53, 20 February 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9">Line 9:</td>
<td colspan="2" class="diff-lineno">Line 9:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><div class="definition"><div class="short_definition">A formula for the [[variation]] of [[wind]] with height in the [[surface boundary layer]].</div><br/> <div class="paragraph">It is an alternative to the [[logarithmic velocity profile]], and the assumptions are the same, with the exception of the form of the dependence of [[mixing length]] ''l'' on height ''z''. Here <div class="display-formula"><blockquote>[[File:ams2001glos-Pe44.gif|link=|center|ams2001glos-Pe44]]</blockquote></div> Then <div class="display-formula"><blockquote>[[File:ams2001glos-Pe45.gif|link=|center|ams2001glos-Pe45]]</blockquote></div> where <div class="inline-formula">[[File:ams2001glos-Pex07.gif|link=|ams2001glos-Pex07]]</div> is the [[mean velocity]], ''u''<sub>&#x0002a;</sub> the [[friction velocity]], &#x003bd; the [[kinematic viscosity]], and <div class="display-formula"><blockquote>[[File:ams2001glos-Pe46.gif|link=|center|ams2001glos-Pe46]]</blockquote></div> For moderate [[Reynolds numbers]], ''p'' = 6/7 (the seventh-root profile) is empirically verified, but for large Reynolds numbers ''p'' is between this value and unity. It is to be noted that if <div class="inline-formula">[[File:ams2001glos-Pex08.gif|link=|ams2001glos-Pex08]]</div> is proportional to ''z''<sup>''m''</sup>, and if the [[stress]] is assumed independent of height, then the [[eddy viscosity]] &#x003bd;<sub>''e''</sub> is proportional to ''z''<sup>1<del style="font-weight: bold; text-decoration: none;">&minus;</del>''m''</sup>. These relations are known as Schmidt's conjugate-power laws.</div><br/> </div><div class="reference">Sutton, O. G. 1953. Micrometeorology. 78&ndash;85. </div><br/> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><div class="definition"><div class="short_definition">A formula for the [[variation]] of [[wind]] with height in the [[surface boundary layer]].</div><br/> <div class="paragraph">It is an alternative to the [[logarithmic velocity profile]], and the assumptions are the same, with the exception of the form of the dependence of [[mixing length]] ''l'' on height ''z''. Here <div class="display-formula"><blockquote>[[File:ams2001glos-Pe44.gif|link=|center|ams2001glos-Pe44]]</blockquote></div> Then <div class="display-formula"><blockquote>[[File:ams2001glos-Pe45.gif|link=|center|ams2001glos-Pe45]]</blockquote></div> where <div class="inline-formula">[[File:ams2001glos-Pex07.gif|link=|ams2001glos-Pex07]]</div> is the [[mean velocity]], ''u''<sub>&#x0002a;</sub> the [[friction velocity]], &#x003bd; the [[kinematic viscosity]], and <div class="display-formula"><blockquote>[[File:ams2001glos-Pe46.gif|link=|center|ams2001glos-Pe46]]</blockquote></div> For moderate [[Reynolds numbers]], ''p'' = 6/7 (the seventh-root profile) is empirically verified, but for large Reynolds numbers ''p'' is between this value and unity. It is to be noted that if <div class="inline-formula">[[File:ams2001glos-Pex08.gif|link=|ams2001glos-Pex08]]</div> is proportional to ''z''<sup>''m''</sup>, and if the [[stress]] is assumed independent of height, then the [[eddy viscosity]] &#x003bd;<sub>''e''</sub> is proportional to ''z''<sup>1<ins style="font-weight: bold; text-decoration: none;">-</ins>''m''</sup>. These relations are known as Schmidt's conjugate-power laws.</div><br/> </div><div class="reference">Sutton, O. G. 1953. Micrometeorology. 78&ndash;85. </div><br/> </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
</table>Unknown userhttps://glossary.ametsoc.org/w/index.php?title=Power-law_profile&diff=5036&oldid=prevUnknown user: Created page with " {{TermHeader}} {{TermSearch}} <div class="termentry"> <div class="term"> == power-law profile == </div> <div class="definition"><div class="short_definition">A formula..."2012-01-27T01:44:41Z<p>Created page with " {{TermHeader}} {{TermSearch}} <div class="termentry"> <div class="term"> == power-law profile == </div> <div class="definition"><div class="short_definition">A formula..."</p>
<p><b>New page</b></p><div><br />
<br />
{{TermHeader}}<br />
{{TermSearch}}<br />
<br />
<div class="termentry"><br />
<div class="term"><br />
== power-law profile ==<br />
</div><br />
<br />
<div class="definition"><div class="short_definition">A formula for the [[variation]] of [[wind]] with height in the [[surface boundary layer]].</div><br/> <div class="paragraph">It is an alternative to the [[logarithmic velocity profile]], and the assumptions are the same, with the exception of the form of the dependence of [[mixing length]] ''l'' on height ''z''. Here <div class="display-formula"><blockquote>[[File:ams2001glos-Pe44.gif|link=|center|ams2001glos-Pe44]]</blockquote></div> Then <div class="display-formula"><blockquote>[[File:ams2001glos-Pe45.gif|link=|center|ams2001glos-Pe45]]</blockquote></div> where <div class="inline-formula">[[File:ams2001glos-Pex07.gif|link=|ams2001glos-Pex07]]</div> is the [[mean velocity]], ''u''<sub>&#x0002a;</sub> the [[friction velocity]], &#x003bd; the [[kinematic viscosity]], and <div class="display-formula"><blockquote>[[File:ams2001glos-Pe46.gif|link=|center|ams2001glos-Pe46]]</blockquote></div> For moderate [[Reynolds numbers]], ''p'' = 6/7 (the seventh-root profile) is empirically verified, but for large Reynolds numbers ''p'' is between this value and unity. It is to be noted that if <div class="inline-formula">[[File:ams2001glos-Pex08.gif|link=|ams2001glos-Pex08]]</div> is proportional to ''z''<sup>''m''</sup>, and if the [[stress]] is assumed independent of height, then the [[eddy viscosity]] &#x003bd;<sub>''e''</sub> is proportional to ''z''<sup>1&minus;''m''</sup>. These relations are known as Schmidt's conjugate-power laws.</div><br/> </div><div class="reference">Sutton, O. G. 1953. Micrometeorology. 78&ndash;85. </div><br/> <br />
</div><br />
<br />
{{TermIndex}}<br />
{{TermFooter}}<br />
<br />
[[Category:Terms_P]]</div>Unknown user