Flow, deformation, and transport - Physical Processes in Earth and Environmental Sciences - page 202

Box 4.6 Some Prandtl numbers
for common fluids.

Box 4.7 Rayleigh number: Ratio of
buyoancy to viscous and thermal diffusivity

Fluid Prandtl no

Ra = ga ( ∆ T ) d 3 / nk

Air 0.71

Steam 0.93

a = expansion coefficient,
∆ T = temperature difference across fluid,
d = distance across fluid,
n

Water 7.0

Crude oil 1000

= kinematic viscosity,
k = thermal diffusivity.

giving the ratio of advection to conduction of heat.
At small values of Pe the flow has a negligible effect on the
temperature distribution, which can be analyzed as if the
fluid were stationary. Finally, there is a criterion, the
Rayleigh number , that establishes whether convection is

possible at all (Box 4.7). This is useful for remotely deter-
mining whether convection can occur in Earth's mantle,
for example (Section 5.2). For convection in a horizontal
slot Ra must exceed about 2,000, a value thought to be far
exceeded in the mantle.

Further reading

Fishbane et al . (cited for Part 3) is again useful for basic
physics. Basic concepts in fluid mechanics have never
been better explained than by A. H. Shapiro in Shape and
Flow (Doubleday, New York, 1961). Introductory fluid
dynamics presented in a careful, rigorous way, but with-
out undue mathematical demands, features in B. S.
Massey's Mechanics of Fluids (Van Nostrand Reinhold,
1979) and M. W. Denny's Air and Water (Princeton,
1993). Beautiful and inspirational photos of fluid flow
visualization may be found in M. Van Dyke's An Album
of Fluid Motion (Parabolic Press, 1982) and M. Samimy
et al .'s A Gallery of Fluid Motion (Cambridge, 2003).
The topic of gravity currents in all their various forms is

dealt with in J. Simpson's elegant and clearly written
(with many superb photographs) Gravity Currents
(Cambridge, 1997). Folds and faults are related to stress
and strain as in G. H. Davies' and S. J. Reynolds's
Structural Geology of Rocks and Regions (Wiley, 1996), R.
J. Twiss and E. M. Moores' Structural Geology (Freeman,
1992), and J. G. Ramsay's and M. I. Huber's The
Techniques of Modern Structural Geology , vol. 2
(Academic Press, 1993). Seismology is clearly introduced
and explained in B. A. Bolt's Inside the Earth (Freeman,
1982) and the concepts beautifully illustrated in his more
popular Earthquakes and Geological Discovery (Scientific
American Library, 1993).