Nonlocal flux: Difference between revisions

Latest revision as of 09:29, 27 March 2024

The vertical turbulent transport of a quantity such as heat per unit area per time across any height index k, between source heights j to destination heights i, where i and j are on opposite sides of k vertically.

It is nonlocal because i and j need not be neighbors. Using kinematic heat flux as an example,

where n is the total number of grid cells in a vertical column, Δz is the vertical thickness of each grid cell (i.e., spacing between grid points), Δt is the time increment over which eddies transport heat starting from time t, θ_a is the potential temperature at grid cell a, and c_ab is the transilient matrix specifying the fraction of air that ended in destination cell a originated at source cell b, for a and b dummy indices.
See transilient turbulence theory, nonlocal mixing.

@@ Line 1: / Line 1: @@
+{{Term
+|Display title=nonlocal flux
-{{TermHeader}}
+|Definitions={{Definition
-{{TermSearch}}
+|Num=1
+|Meaning=The vertical [[turbulent transport]] of a quantity such as [[heat]] per unit area per time  across any height index ''k'', between [[source]] heights ''j'' to destination heights ''i'', where ''i'' and ''j'' are  on opposite sides of ''k'' vertically.
-<div class="termentry">
+|Explanation=It is nonlocal because ''i'' and ''j'' need not be neighbors. Using kinematic [[heat flux]] as an example,   <blockquote>[[File:ams2001glos-Ne7.gif|link=|center|ams2001glos-Ne7]]</blockquote> where ''n'' is the total number of [[grid]] cells in a vertical column, &#x00394;''z'' is the vertical thickness of each  grid cell (i.e., spacing between grid points), &#x00394;''t'' is the time increment over which [[eddies]] transport  heat starting from time ''t'', &#x003b8;<sub>''a''</sub> is the [[potential temperature]] at grid cell ''a'', and ''c''<sub>''ab''</sub> is the [[transilient matrix|transilient  matrix]] specifying the fraction of air that ended in destination cell ''a'' originated at source cell ''b'',  for ''a'' and ''b'' dummy indices. <br/>''See'' [[transilient turbulence theory]], [[nonlocal mixing]].
-  <div class="term">
+}}
-== nonlocal flux ==
+}}
-  </div>
-<div class="definition"><div class="short_definition">The vertical [[turbulent transport]] of a quantity such as [[heat]] per unit area per time  across any height index ''k'', between [[source]] heights ''j'' to destination heights ''i'', where ''i'' and ''j'' are  on opposite sides of ''k'' vertically.</div><br/> <div class="paragraph">It is nonlocal because ''i'' and ''j'' need not be neighbors. Using kinematic [[heat flux]] as an example,   <div class="display-formula"><blockquote>[[File:ams2001glos-Ne7.gif|link=|center|ams2001glos-Ne7]]</blockquote></div> where ''n'' is the total number of [[grid]] cells in a vertical column, &#x00394;''z'' is the vertical thickness of each  grid cell (i.e., spacing between grid points), &#x00394;''t'' is the time increment over which [[eddies]] transport  heat starting from time ''t'', &#x003b8;<sub>''a''</sub> is the [[potential temperature]] at grid cell ''a'', and ''c''<sub>''ab''</sub> is the [[transilient matrix|transilient  matrix]] specifying the fraction of air that ended in destination cell ''a'' originated at source cell ''b'',  for ''a'' and ''b'' dummy indices. <br/>''See'' [[transilient turbulence theory]], [[nonlocal mixing]].</div><br/> </div>
-</div>
-{{TermIndex}}
-{{TermFooter}}
-[[Category:Terms_N]]