Geoscience Reference
In-Depth Information
to as the
dynamic sublayer
. Under neutral conditions, the whole surface layer behaves
as a dynamic layer.
Finally, in the immediate vicinity of the surface, the turbulence is strongly affected by
the structure of the roughness elements, or it is greatly damped by the viscous effects; in
most cases it is subjected to both effects. The region nearest to the surface where these
effects are most important, is sometimes referred to as the
interfacial (transfer) sublayer
.
In the case of smooth flow, as may occur for example over snow, water or salt flats, it
is referred to as the
viscous sublayer
. Experiments have shown that its thickness is of
the order of 5
ν/
u
∗
, in which
ν
is the viscosity of the air; the flow may be considered
smooth when (
u
∗
h
0
/ν
1, approximately, in which again
h
0
is the average height
of the surface roughness elements. Experiments have also shown that a surface can
be considered rough, when (
u
∗
h
0
/ν
)
<
>
15, approximately; in this case the interfacial
sublayer may be referred to as a
roughness sublayer
, and its thickness is of the order
of the mean height of the roughness obstacles. When the roughness obstacles consist of
vegetation, which is more or less porous or permeable for the air stream, the interfacial
sublayer is commonly referred to as the
canopy sublayer
.
)
2.5
TURBULENCE SIMILARITY
Over the past century or so, various turbulence closure schemes have been proposed,
essentially by invoking similarity on the basis of dimensional analysis. In this type of
approach, after the relevant physical quantities are identified, either from the governing
equations or simply by inspection, they are organized into a reduced number of dimen-
sionless quantities. Dimensional analysis only establishes the possible existence of a
functional relationship between these dimensionless quantities, and it is incapable of
providing the specific form of the functional relationship; the form of that function must
usually be determined by experiment or on the basis of some conceptual transport model
or other theoretical considerations. This section does not present an exhaustive review
but only a few ideas that will be useful in the determination of evaporation in Chapter 4.
2.5.1
Parameterization of the turbulent transport
Most similarity formulations of turbulent flux have the common feature, that the mean
of the product of temporal fluctuations in expressions such as (2.29), (2.30) and (2.31),
i.e. the second moment, is replaced simply by the product of the spatial changes of
the corresponding mean quantities, i.e. of the first moments. In the case of the specific
humidity flux this is in general
w
q
=−
Ce(
u
2
−
u
1
)(
q
4
−
q
3
)
(2.33)
where the subscripts 1 through 4 refer to the measurement heights above the surface
and Ce is a dimensionless parameter, also called the water vapor transfer coefficient,
or the Dalton number; Ce depends on the heights of the reference levels 1 through 4,
beside a number of other (dimensionless) factors, as will be shown below; the minus
sign indicates that the flux points in the direction of negative increments of
q
. Note that
