Forces and dynamics - Physical Processes in Earth and Environmental Sciences - page 54

differing density does not “feel” the same gravitational
attraction as it would if the ambient medium were not
there. For example, a surface ocean current of density

that of the ambient lake or marine waters (Fig. 2.12); these
are termed turbidity currents (Section 4.12).
Motion due to buoyancy forces in thermal fluids is
called convection (Section 4.20). This acts to redistribute
heat energy. There is a serious complication here because
buoyant convective motion is accompanied by volume
changes along pressure gradients that cause variations of
density. The rising material expands, becomes less dense,
and has to do work against its surroundings (Section 3.4):
this requires thermal energy to be used up and so cooling
occurs. This has little effect on the temperature of the
ambient material if the adiabatic condition applies: the net
rate of outward heat transfer is considered negligible.

1
may be said to “feel” reduced gravity because of the posi-
tive buoyancy exerted on it by underlying ambient water
of slightly higher density,

2 . The expression for this

reduced gravity, g 2 . We noted earlier

that for the case of mineral matter, density

, is g g ( 2 1 )/

m , in atmos-

phere of density a , the effect is negligible, corresponding

to the case m a .

3.6.3 Natural reasons for buoyancy

We have to ask how buoyant forces arise naturally.
The commonest cause in both atmosphere and ocean is
density changes arising from temperature variations acting
upon geographically separated air or water masses that
then interact. For example, over the c .30

3.6.4 Buoyancy in the solid Earth:
Isostatic equilibrium

C variation in
near-surface air or water temperature from Pole to equa-
tor, the density of air varies by c .11 percent and that of
seawater by c .0.6 percent. The former is appreciable, and
although the latter may seem trivial, it is sufficient to drive
the entire oceanic circulation. It is helped of course by
variations in salinity from near zero for polar ice meltwater
to very saline low-latitude waters concentrated by evapora-
tion, a maximum possible variation of some 4 percent.
Density changes also arise when a bottom current picks up
sufficient sediment so that its bulk density is greater than

In the solid Earth, buoyancy forces are often due to
density changes owing to compositional and structural
changes in rock or molten silicate liquids. For example, the
density of molten basalt liquid is some 10 percent less than
that of the asthenospheric mantle and so upward
movement of the melt occurs under mid-ocean ridges
(Fig. 3.27). However we note that the density of magma is
also sensitive to pressure changes in the upper 60 km or so
of the Earth's mantle (Section 5.1).
In general, on a broad scale, the crust and mantle are
found to be in hydrostatic equilibrium with the less dense

mountain range

thickness of iceberg root
h ir =

r i / ( r w - r i )

h mr

ocean, r w r w

h o

r i

crustal equilibrium
thickness of crustal root,
h cr =

crust

r c

r c / ( r w - r c )

h ar

antiroot

Moho

thickness
of
crustal
antiroot,
h ar = (

crustal

h cr mantle

“root”

r m

r c - r w ) / ( r m - r c )

h ir

level of buoyancy compensation: all pressures are equal

r w

Fig. 3.28 Sketches to illustrate the Airy hypothesis for isostasy, analogos to the “floating iceberg” principle.