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| Titel |
Application of the theory of contrast structures to describe the turbulent exchange at the forest edges |
| VerfasserIn |
Natalia Levashova, Julia Muhartova, Alexander Olchev, Natalia Shapkina |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250096862
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| Publikation (Nr.) |
 EGU/EGU2014-12389.pdf |
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| Zusammenfassung |
| An adequate description of the exchange processes different substances between spatially
inhomogeneous forest vegetation with e.g. treefall gaps, clearing of different size and the
atmosphere requires an accurate parameterization of the wind and turbulent at the
forest boundaries (forest edges), as well as descriptions of exchanges processes
within the vegetation cover. As an attempt to solve this problem, we developed a
mathematical model of turbulent exchange based on the theory of "contrast structures"
(CS).
CS is a function the graph of which has an interior layer. Some boundary value problems
can have a solution in form of CS. The main advantage of the CS method is that it gives a
possibility to find a stable stationary solution for the Navier-Stokes system of equations for
the interior layer.
The developed 2D model was applied to describe the 2D wind vectors and turbulent
coefficients at some typical forest edge and to analyse how the forest canopy with different
structure (different tree height, density), different wind speed and wind direction can
influence the spatial patterns of the modeled parameters.
We consider the system of equations in 2dimensional coordinate system - horizontal x
and vertical z. According to our model the wind speed profile near the forest edge is
described by a system of three differential equations: two momentum equations and the
equation of continuity:
K -2u+K -2u- -u-= u-u-+w -u+F , K -2w+K -2w- -w-= u -w+w -w+F ,
x -x2 z-z2 -t -x -z x x-x2 z-z2 -t -x -z z
-u-= - -w-
-x -z
in a rectangle 0 -¤ x -¤ 1000m, 0 -¤ z -¤ 100m over a period of time 0 -¤ t -¤ T .
The boundary conditions at the borders are as follows:
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-u|| = -u-|| = -w-|| = -w-|| = 0 ;
-x|x=0,x=1000 -z|z=100 -x |x=0,x=1000 -z |z=100
u|z=0 = uinit(x), w |z=0 = winit(x) .
where u and w are horizontal and vertical components of the wind speed, respectively, Kx
and Kz- turbulence coefficients, Fx and Fz are some nonlinear functions of pressure
gradient, change of air density and the drag coefficients of vegetation. In our study we set
them as continuous functions of the coordinates and the wind speed components so that the
solution of the boundary value problem had interior layers in the vicinity of the plane
x = 500m.
Results of modeling experiments indicates that an implementation of the CS theory in our
model allows to describe adequately the turbulent exchange within and above a non-uniform
forest canopy using the minimum number of equations.
This study was supported by grants of the Russian Foundation for Basic Research (RFBR
14-04-01568-a and 13–01–00200). |
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