Turbulent flows occur at high Reynolds numbers, wherein inertia forces associated
with convective effects predominate over viscous forces associated with diffusivity.
These convective effects are primarily responsible for large diffusivity of turbulence
that causes a huge increase in transfer processes for heat, mass, and linear
momentum. Turbulent transport is, therefore, far more effective than transport by
molecular diffusion.
Turbulent flow is based on random velocity fluctuations and thus the respective
instantaneous values u I must be a sum of the average of the mean velocity u over a
period with fluctuations around this mean value. Turbulence is a characteristic of
the flow and not of the fluid itself. Even small length scalars that are dynamically
significant are larger than intermolecular distances or the molecules themselves.
The main features of turbulence prevalent at high Reynolds number conditions are
not conditioned by the molecular properties of the fluids.
Turbulent flow is rotational, three dimensional, and continuous, and can be
characterized using equations of fluid mechanics. Its random and non-linear nature
makes for a complex mathematical treatment of turbulence because of the closure
problem, in which there are more unknowns than equations.
Viscous shear stresses dissipate kinetic energy from turbulent flow, increasing
the internal energy of the fluid. The viscous dissipation prevents the infinitely small
eddies from forming by converting the energy in these low-dimensional scales into
heat (Tennekes and Lumley 1980; Shaw 1995a). Maintaining the turbulent flow
characteristics requires a mechanism that will continuously supply energy, to
compensate for losses through viscosity. As noted above, this energy can be
mechanically derived from tangential stresses of the mean flow or from buoyancy.
Turbulent eddies have characteristic dimensional and time scales, ranging from
molecular dimensions lasting fractions of a second, to millimeters or to kilometers,
lasting hours. Turbulent eddies can be considered as air parcels with uniform
thermodynamic properties, with small-scale eddies coalescing to form bigger ones,
due to surface roughness and flow velocity. The largest eddies are atmospheric
pressure systems (Foken 2017). Since the equations for motion are non-linear, each
individual flow pattern will depend significantly on the initial and boundary conditions. Thus, despite common properties, each turbulent flow is different,
depending on the specificities of the surrounding environment. The interaction
between this environment and turbulence results in a situation of permanent
adjustment or dynamic equilibrium that is never truly reached.
In practice, for simplifying the analysis of turbulence empirical concepts such as
mixing length can be used, by analogy with the kinetic theory of gases. Such
concepts can be valid for hypothetical conditions where the length scales and
velocities are constant, easily characterized, and of reduced dimension, as compared
with scalars of typical dimensions for the mean flow. Under laboratory conditions,
for example, using flat surfaces, one can identify distinct stages in the transition
from laminar to turbulent flow. The initial stage creates primary instability with the
formation of small eddies. This instability leads to pronounced highly unstable
tri-dimensional secondary movements that amplify locally into three-dimensional
34
3 Characterization of Turbulent Flow in the Surface Boundary Layer
with convective effects predominate over viscous forces associated with diffusivity.
These convective effects are primarily responsible for large diffusivity of turbulence
that causes a huge increase in transfer processes for heat, mass, and linear
momentum. Turbulent transport is, therefore, far more effective than transport by
molecular diffusion.
Turbulent flow is based on random velocity fluctuations and thus the respective
instantaneous values u I must be a sum of the average of the mean velocity u over a
period with fluctuations around this mean value. Turbulence is a characteristic of
the flow and not of the fluid itself. Even small length scalars that are dynamically
significant are larger than intermolecular distances or the molecules themselves.
The main features of turbulence prevalent at high Reynolds number conditions are
not conditioned by the molecular properties of the fluids.
Turbulent flow is rotational, three dimensional, and continuous, and can be
characterized using equations of fluid mechanics. Its random and non-linear nature
makes for a complex mathematical treatment of turbulence because of the closure
problem, in which there are more unknowns than equations.
Viscous shear stresses dissipate kinetic energy from turbulent flow, increasing
the internal energy of the fluid. The viscous dissipation prevents the infinitely small
eddies from forming by converting the energy in these low-dimensional scales into
heat (Tennekes and Lumley 1980; Shaw 1995a). Maintaining the turbulent flow
characteristics requires a mechanism that will continuously supply energy, to
compensate for losses through viscosity. As noted above, this energy can be
mechanically derived from tangential stresses of the mean flow or from buoyancy.
Turbulent eddies have characteristic dimensional and time scales, ranging from
molecular dimensions lasting fractions of a second, to millimeters or to kilometers,
lasting hours. Turbulent eddies can be considered as air parcels with uniform
thermodynamic properties, with small-scale eddies coalescing to form bigger ones,
due to surface roughness and flow velocity. The largest eddies are atmospheric
pressure systems (Foken 2017). Since the equations for motion are non-linear, each
individual flow pattern will depend significantly on the initial and boundary conditions. Thus, despite common properties, each turbulent flow is different,
depending on the specificities of the surrounding environment. The interaction
between this environment and turbulence results in a situation of permanent
adjustment or dynamic equilibrium that is never truly reached.
In practice, for simplifying the analysis of turbulence empirical concepts such as
mixing length can be used, by analogy with the kinetic theory of gases. Such
concepts can be valid for hypothetical conditions where the length scales and
velocities are constant, easily characterized, and of reduced dimension, as compared
with scalars of typical dimensions for the mean flow. Under laboratory conditions,
for example, using flat surfaces, one can identify distinct stages in the transition
from laminar to turbulent flow. The initial stage creates primary instability with the
formation of small eddies. This instability leads to pronounced highly unstable
tri-dimensional secondary movements that amplify locally into three-dimensional
34
3 Characterization of Turbulent Flow in the Surface Boundary Layer