Conductances for Heat and Mass Transfer
transport heat or mass depends directly on the size of the vertical fluctuations. Because of the proximity of the surface, the magnitude of w'
is limited near the surface. Farther from the surface, transport is more
efficient because the eddies are larger. Transport is therefore expected to
increase with height. Increased intensity of turbulence will also increase
vertical transport. Since turbulence is generated by mechanical action of
wind moving over a rough surface, transport should increase as wind
speed and surface roughness increase. It is also known that turbulence is
generated by buoyancy, so when there is strong heating at the surface,
turbulent transport should increase. Strong cooling at the surface should
result in reduced transport.
Both the turbulence and the heat or mass being carried by it are generated or absorbed at the surface. The sources and sinks are patchy, so
near the surface the concentrations are not well related to the transport.
The mixture becomes more homogeneous with distance from the surface, and fluxes can then be predicted from concentration gradients. The
equations used for this are similar to those used for molecular transport,
but, of course, the mechanism for transport is quite different. We simply
define transport coefficients for turbulent diffusion that replace the molecular viscosity and diffusivities in Eqs. (6.1) through (6.3). The resulting
equations are the basis for what is known as K-theory. The equations are
where KM is the eddy viscosity, KH is the eddy thermal diffusivity, and
K, is the eddy vapor diffusivity. These are steady-state flux equations
for the surface boundary layer of the atmosphere. The flux of heat or
mass is intuitive, but the flux of momentum is somewhat less intuitive
for most people. From introductory physics, momentum is mass times
velocity. With a solid object of a given mass that is moving at some
velocity, the momentum is obvious. With a fluid these quantities are less
obvious because the amount of mass depends on what volume is being
considered; further, a given mass of fluid can have a range of velocities.
Therefore with fluids the mass per unit volume is used instead of just
mass so what is referred to as momentum is actually momentum per unit
volume or concentration of momentum (pu). The flux of any quantity
can be written as a product of the concentration of that quantity times
the appropriate velocity. In the surface layer, the appropriate velocity is
referred to as the friction velocity, which is represented by the symbol
u*(m/s), and is defined as u* = (tip) 'I2. Effects of wind speed, surface
roughness, and surface heating are all included in the shear stress term
(TI.
transport heat or mass depends directly on the size of the vertical fluctuations. Because of the proximity of the surface, the magnitude of w'
is limited near the surface. Farther from the surface, transport is more
efficient because the eddies are larger. Transport is therefore expected to
increase with height. Increased intensity of turbulence will also increase
vertical transport. Since turbulence is generated by mechanical action of
wind moving over a rough surface, transport should increase as wind
speed and surface roughness increase. It is also known that turbulence is
generated by buoyancy, so when there is strong heating at the surface,
turbulent transport should increase. Strong cooling at the surface should
result in reduced transport.
Both the turbulence and the heat or mass being carried by it are generated or absorbed at the surface. The sources and sinks are patchy, so
near the surface the concentrations are not well related to the transport.
The mixture becomes more homogeneous with distance from the surface, and fluxes can then be predicted from concentration gradients. The
equations used for this are similar to those used for molecular transport,
but, of course, the mechanism for transport is quite different. We simply
define transport coefficients for turbulent diffusion that replace the molecular viscosity and diffusivities in Eqs. (6.1) through (6.3). The resulting
equations are the basis for what is known as K-theory. The equations are
where KM is the eddy viscosity, KH is the eddy thermal diffusivity, and
K, is the eddy vapor diffusivity. These are steady-state flux equations
for the surface boundary layer of the atmosphere. The flux of heat or
mass is intuitive, but the flux of momentum is somewhat less intuitive
for most people. From introductory physics, momentum is mass times
velocity. With a solid object of a given mass that is moving at some
velocity, the momentum is obvious. With a fluid these quantities are less
obvious because the amount of mass depends on what volume is being
considered; further, a given mass of fluid can have a range of velocities.
Therefore with fluids the mass per unit volume is used instead of just
mass so what is referred to as momentum is actually momentum per unit
volume or concentration of momentum (pu). The flux of any quantity
can be written as a product of the concentration of that quantity times
the appropriate velocity. In the surface layer, the appropriate velocity is
referred to as the friction velocity, which is represented by the symbol
u*(m/s), and is defined as u* = (tip) 'I2. Effects of wind speed, surface
roughness, and surface heating are all included in the shear stress term
(TI.