Geoscience Reference
In-Depth Information
Figure 1.1 Instability of an axisymmetric jet. A laminar stream of air flows from a
circular tube at the left at Reynolds number 10000 and is made visible by a smoke
wire. The edge of the jet develops axisymmetric oscillations, rolls up into vortex
rings, and then abruptly becomes turbulent. Photograph courtesy Robert Drubka
and Hassan Nagib. From
Va n Dy k e
(
1982
).
1.2 The origins and nature of turbulence
Turbulent rather than smooth,
laminar
flow of a fluid, liquid or gas, normally occurs
if a dimensionless flow parameter called the
Reynolds number Re
UL/ν
exceeds
a critical value. Here
U
and
L
are velocity and length scales of the flow
†
and
ν
is the kinematic viscosity (dynamic viscosity
μ
/density
ρ
)ofthefluid.Theatmo-
spheric boundary layer is turbulent, but as we shall see in
Part II
stable density
stratification can strongly modulate its depth and the intensity and scale of its tur-
bulence. Winter sunrises here in central Pennsylvania often reveal laminar chimney
plumes in the very stably stratified flow caused by the overnight cooling of the
earth's surface. The turbulent eddies
‡
so prominent in cumulus clouds and flow-
ing streams can be revealed in laboratory turbulence through flow-visualization
techniques
(Figure 1.1)
.
There are two types of turbulence with quite different physics. The most common
type,
three-dimensional turbulence
, arises from the tendency of fluidmotion of large
Re
to be turbulent and the tendency of turbulence to be three dimensional. But
two-
dimensional turbulence
is also of interest; it causes the darting of the colors in soap
films and is a model of the largest-scale motions of the atmosphere. We shall discuss
it in
Chapter 7
.
=
†
For example, in
Figure 1.1
U
is the velocity averaged over the tube cross section and
L
is the tube diameter.
‡
To paraphrase
Batchelor
(
1950
), “eddy” does not refer to any specific local distribution of velocity; it is simply a
concise term for local turbulent motion with a certain length scale - an arbitrary local flow pattern characterized
by size alone. A turbulent flow has a spectrum of eddies of different size, determined by an analysis of the
velocity field into sinusoidal components of different wavelengths
(Chapter 15)
.
