Geoscience Reference
In-Depth Information
Figure 2.1 The turbulent wake of a bullet, which is several hundred wake diame-
ters to the left. This shadowgraph shows the strikingly sharp, irregular boundary
between the turbulent fluid and the almost motionless fluid outside. Photograph
courtesy Army Research Laboratory. From
Va n Dy k e
(
1982
).
•
Isotropic turbulence
has statistical properties that are independent of translation, rotation,
and reflection of the coordinate axes. It must decay in time, for the productionmechanisms
that maintain stationary turbulence are anisotropic
(Chapter 6)
. Isotropy of the smallest
spatial scales is called
local isotropy
(Chapter 14)
.
•The
logarithmic profile
(or
law of the wall
) and the
constant-stress layer
refer to the height
variation of mean velocity and the Reynolds shear stress, respectively, in the turbulent
boundary layer over a flat surface. Like the Reynolds stresses themselves (which G. I.
Taylor
(
1935
) called “virtual mean stresses”) they exist only as averages.
•The
Gaussian plume
refers to a mean effluent plume in homogeneous turbulent flow, not
an instantaneous plume.
•A
well-mixed
state of a convective atmospheric boundary layer
(Chapter 11)
has
mean
,
not instantaneous, profiles of potential temperature and water-vapor mixing ratio that are
essentially uniform with height.
•A
turbulent flux
of a property is the
mean
, not instantaneous, amount of that property
flowing through unit area per unit time due to the turbulent velocity.
2.2 Averaging
All the dependent variables in a turbulent flow - velocity, vorticity, temperature (if
there is heat transfer), density of an advected constituent (if there is mass transfer),
pressure - are turbulent. At any instant they are distributed irregularly in space, at
any point in space they fluctuate chaotically in time, and at given point and a given
time they vary randomly from realization to realization. Since Osborne Reynolds'
