Geoscience Reference
In-Depth Information
For stable conditions both shear and buoyancy play a role. However, if conditions
become very stable vertical motion is so much suppressed that the low no longer
experiences the presence of the ground. Hence the height above the ground becomes
irrelevant as a length scale, hence the name
z
-less scaling. Because one still needs a
length scale, height needs to be replaced by a length scale that indicates the extent
of possible vertical motion. A logical choice would be the depth over which kinetic
energy is converted into potential energy in a stratiied luid, a buoyancy length scale
(see Van de Wiel et al.,
2008
). In terms of MOST scaling this leads to an expression
of the form
φ
h
~
z
L
, which is indeed consistent with the expressions given in Eq. (
3.28
)
for large
z/L
.
Deviations from MOST
The simplicity of MOST is partly due to the strict conditions for its validity: stationar-
ity, horizontal homogeneity and irrelevance of processes in the boundary-layer (above
the surface layer). These conditions limit the number of relevant variables. In reality
however, violations of one or more of the strict conditions for MOST are the rule
rather than the exception: for example, most natural surfaces are heterogeneous and
conditions are often non-stationary, as the diurnal cycle is omnipresent. Furthermore,
there is no strict separation between turbulence in the surface layer and turbulence in
the boundary layer (see, e.g., McNaughton et al.,
2007
).
One of the consequences of the assumptions underlying MOST is that similarity
relationships should be identical for all scalars, and the correlation between scalar
luctuations should be either +1 or −1 (Hill,
1989
). This is due to the fact that all mean
turbulent quantities (gradients, variances) are determined solely by the vertical con-
trast over the surface layer, which in turn is related to the surface lux of the quantity
under consideration. All scalars have the same source/sink location: the surface.
If not all conditions for MOST are met, decorrelation between scalars may occur.
In the case of surface heterogeneity (e.g., dry and wet patches) this is due to the fact
that different scalars have different dominating source locations (humidity from the
wet patch, temperature from the dry patch, see Moene and Schüttemeyer,
2008
). Ver-
tical differences in source location occur if the relative importance of the surface
lux and entrainment lux is different for different scalars: differences in entrainment
regime (see Moene et al.,
2006
; Lahou et al.,
2010
). Other causes for decorrelation
of scalars are the active role of temperature and humidity, modulations of the surface
layer by the outer layer (and unsteadiness) and advective conditions (see Katul et al.,
2008
, for an extensive review of literature on this subject).
Conclusion
The main result of
Section 3.5
is that vertical luxes of a certain quantity can be
expressed in terms of vertical gradients or vertical differences of the transported
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