Flow, deformation, and transport - Physical Processes in Earth and Environmental Sciences - page 110

Re = 500
Laminar flow

Prandtl

Velocity vector

Tellurium wire

Rate
of increase of
velocity decreases
with height

Line of bubbles

Velocity vector

Velocity
profile

Solid lower boundary

Fig. 4.11 Flow visualization of laminar flow boundary layer by a cloud of H 2 bubbles released by continuous hydrolysis.

1000 no slip

Dots are individual
measurements

300

100

Re =1 10 4

30.0

wind 1

10.0

Note how rate of
increase of velocity
decreases upward
away from bottom
surface

3.0

1.0

0.3

0.1

wind 2

0.03

0.01

1.0 3.0 5.0 7.0

Air velocity, u , m s -1

Fig. 4.12 Measurements of wind speed with height above the floor
of a wind tunnel to illustrate boundary layers.

Bed of sediment grains

Fig. 4.13 Instantaneous photo of strain markers in a turbulent shear
flow of water to show heterogeneous strain in a boundary layer.
Water flows left to right past a speck-insulated vertical platinum
wire; pulsed voltage across the wire gives hydrolysis and production
of initially square blocks of hydrogen bubbles. Blocks are released
0.2 s apart. Compare this with the smoothly varying gradient of
velocity in the laminar flow case in Fig. 4.11. Note the progressive
deformation of individual bubble block strain markers from left to
right and the very high strains and strain rates close to the lower
flow boundary over a roughened surface of sand grains.

force. It follows that there must be important localization
of stresses close to the boundary.
4 The fluid molecules immediately adjacent to the solid
boundary surface have not moved at all. It is a character-
istic of all moving fluid that there is no “slip,” that is, no
mean drift, downstream at a solid boundary.

4.3.3 Boundary layer concept

fluid dynamic problems because any natural or experimen-
tal flow may be considered to comprise two parts: (1) the
boundary layer itself, in which the velocity gradient is large
enough to produce appreciable viscous and turbulent

The theory of the boundary layer was first proposed by
Prandtl in 1904. The concept simplifies the study of many