fluxes from gradients, measurements of vertical gradients of scalar and vector
quantities need to be carried out in the inertial sublayer.
In simple terms, incompressible turbulent flow in the surface layer follows
Prandtl's theory for the mixed layer. This theory described in detail elsewhere (e.g.,
Tennekes and Lumley 1980), presumes that certain assumptions hold true, which in
real situations is not the case. Correct use of the mixed layer theory, adapted from
the kinetic theory for gases, should be checked to see if the momentum transport
model holds true using a velocity gradient. However, this is only possible if the
length scales for turbulent transport flows are lower than the length scales in which
mean gradients vary significantly. In biophysical systems such as forestry ecosystems, the opposite occurs and transport phenomena are mainly due to intermittent
downwind structures or eddies with length scales several times the tree height
(Blanken et al. 1998).
It is also assumed that momentum is conserved when particles move between
two distinct points, although, in practice, this does not hold true. Also, a relationship between stress and strain in fluid flow, parameterized by a proportionality
constant, the eddy diffusion constant K (e.g. Tennekes and Lumley 1980), is not
always applicable as the velocity standard deviation and length scales vary a great
deal, and so that the proportionality constant varies across the velocity fields. For
the strict application of these principles, a fundamental assumption of equality of
the length scales is made, despite that eddies of distinct class sizes participate in
energy and mass transportation processes. Notwithstanding these limitations, in
most situations, simplified analysis of the surface layer can be used to analyze
fluxes and mass-energy balances of microsystems in the realm of environmental
physics.
As mentioned before, mass and energy vertical fluxes produced by turbulence
near the surface are retarded because of the friction effect of the terrain on the
horizontal wind. This friction delay is a continuous process of absorption of linear
wind momentum that is responsible for the downward vertical flow of motion
quantities. In this way, tangential stresses are produced resulting from the strong
interaction between the mean flow and fluctuations in turbulent velocity. Thus, the
flux of momentum in combination with velocity profiles and roughness parameters
serve to evaluate turbulence efficiency for the vertical transport of heat and mass.
The laminar boundary layer contacts with surfaces such as terrain, or obstacles
such as plants, animals, and houses. In this thin layer, with a thickness of the order
of several millimeters, the air adjacent to the surfaces moves in laminar flow, and
the respective streamlines are parallel to the surface. Among practical examples of
laminar flow, are a layer of smoke from a smoldering cigarette sliding along its
surface and a thin layer of water flowing slowly from a faucet.
The thickness of the boundary layer gradually increases until a critical combination of factors (flow velocity, distance, and viscosity) induce instability in the
flow, leading to a radical change characterized by eddies and wave motion typical
of turbulent flow. The Reynolds number (Eq. 6.16), which is the ratio between
inertial and viscous forces, can be used as a criterion to mark the transition between
the laminar and turbulent flow.
2.1 General Considerations
15
quantities need to be carried out in the inertial sublayer.
In simple terms, incompressible turbulent flow in the surface layer follows
Prandtl's theory for the mixed layer. This theory described in detail elsewhere (e.g.,
Tennekes and Lumley 1980), presumes that certain assumptions hold true, which in
real situations is not the case. Correct use of the mixed layer theory, adapted from
the kinetic theory for gases, should be checked to see if the momentum transport
model holds true using a velocity gradient. However, this is only possible if the
length scales for turbulent transport flows are lower than the length scales in which
mean gradients vary significantly. In biophysical systems such as forestry ecosystems, the opposite occurs and transport phenomena are mainly due to intermittent
downwind structures or eddies with length scales several times the tree height
(Blanken et al. 1998).
It is also assumed that momentum is conserved when particles move between
two distinct points, although, in practice, this does not hold true. Also, a relationship between stress and strain in fluid flow, parameterized by a proportionality
constant, the eddy diffusion constant K (e.g. Tennekes and Lumley 1980), is not
always applicable as the velocity standard deviation and length scales vary a great
deal, and so that the proportionality constant varies across the velocity fields. For
the strict application of these principles, a fundamental assumption of equality of
the length scales is made, despite that eddies of distinct class sizes participate in
energy and mass transportation processes. Notwithstanding these limitations, in
most situations, simplified analysis of the surface layer can be used to analyze
fluxes and mass-energy balances of microsystems in the realm of environmental
physics.
As mentioned before, mass and energy vertical fluxes produced by turbulence
near the surface are retarded because of the friction effect of the terrain on the
horizontal wind. This friction delay is a continuous process of absorption of linear
wind momentum that is responsible for the downward vertical flow of motion
quantities. In this way, tangential stresses are produced resulting from the strong
interaction between the mean flow and fluctuations in turbulent velocity. Thus, the
flux of momentum in combination with velocity profiles and roughness parameters
serve to evaluate turbulence efficiency for the vertical transport of heat and mass.
The laminar boundary layer contacts with surfaces such as terrain, or obstacles
such as plants, animals, and houses. In this thin layer, with a thickness of the order
of several millimeters, the air adjacent to the surfaces moves in laminar flow, and
the respective streamlines are parallel to the surface. Among practical examples of
laminar flow, are a layer of smoke from a smoldering cigarette sliding along its
surface and a thin layer of water flowing slowly from a faucet.
The thickness of the boundary layer gradually increases until a critical combination of factors (flow velocity, distance, and viscosity) induce instability in the
flow, leading to a radical change characterized by eddies and wave motion typical
of turbulent flow. The Reynolds number (Eq. 6.16), which is the ratio between
inertial and viscous forces, can be used as a criterion to mark the transition between
the laminar and turbulent flow.
2.1 General Considerations
15