Flow, deformation, and transport - Physical Processes in Earth and Environmental Sciences - page 102

Calculated for:
r water = 1,000 kg m -3
r rock = 2,380 kg m -3

4 Flow, deformation,
and transport

Geostatic
gradient

Hydrostatic
gradient

4.1 The origin of large-scale fluid flow

Earth is a busy planet: what are the origins of all this
motion? Generally, we know the answer from Newton's
First Law that objects will move uniformly or remain sta-
tionary unless some external force is applied. The uniform
motion of fluids must therefore involve a balance of forces in
whatever fluid we are dealing with. In order to try to predict
the magnitude of the motion we must solve the equations of
motion that we discussed previously (Section 3.12). Bulk
flow (in the continuum sense, ignoring random molecular
movement) involves motion of discrete fluid masses from
place to place; the masses must therefore transport energy:
mechanical energy as fluid momentum and thermal energy
as fluid heat. There will also be energy transfers between the
two processes, via the principle of the mechanical equivalent
of heat energy and the First Law of Thermodynamics
(Section 2.2, conservation of energy). For the moment we
shall ignore the transport of heat energy (see
Sections 4.18-4.20) since radiation and conduction intro-
duce the very molecular-scale motions that we wish to
ignore for initial simplicity and generality of approach.

with the ambient medium? If so, at what rate? How does
the interaction look physically?
4 What is the origin and role of variation in flow velocity
with time (unsteadiness problem)? It is to be expected that
accelerations will be very much greater in the atmosphere
than in the oceans and of negligible account in the solid
earth (discounting volcanic eruptions and earthquakes).
Why is this?

4.1.2 Horizontal pressure gradients and flow

Static pressure at a point in a fluid is equal in all directions
(Section 3.5) and equals the local pressure due to the
weight of fluid above. Notwithstanding the universal truth
of Pascal's law, we saw in Section 3.5.3 that horizontal
gradients in fluid pressure occur in both water and air.
These cause flow at all scales when a suitable gradient
exists. The simplest case to consider is flow from a fluid
reservoir from orifices at different levels (Fig. 4.1). Here
the flow occurs across the increasingly large pressure gra-
dient with depth between hydrostatic reservoir pressure
and the adjacent atmosphere.
The gradient of pressure in moving water (Fig. 4.1) is
termed the hydraulic gradient , and the flow of subsurface
water leads to the principle of artesian flow and the basis of
our understanding of groundwater flow through the oper-
ation of Darcy's law (developed from the Bernoulli
approach in Sections 4.13 and 6.7). The flow of a liquid
down a sloping surface channel is also down the hydraulic
gradient.
Similar principles inform our understanding of the slow
flow of water through the upper part of the Earth's crust.
Here, pressures may also be hydrostatic, despite the fluid
held in rock being present in void space between solid rock
particles and crystals (Fig. 4.2); this occurs when the rocks

4.1.1 Very general questions

1 How does fluid flow originate on, above, and within the
Earth? For example, atmospheric winds and ocean currents
originate somewhere and flow from place to place for certain
reasons. This raises the question of “start-up,” or the begin-
nings of action and reaction.
2 If fluid flow occurs from place A to place B, what hap-
pens to the fluid that was previously at place A? For exam-
ple, the arrival of an air mass must displace the air mass
previously present. This introduces the concept of an
ambient medium within which all flows must occur.
3 How does moving fluid interact with stationary or mov-
ing ambient fluid? For example, does the flow mix at all