Flow, deformation, and transport - Physical Processes in Earth and Environmental Sciences - page 105

Table 4.1 Nomenclature and possible types of density currents.

Gas ve Gas Gas ve Liquid ve (e.g. Liquid Liquid ve

(e.g. cooler air) neutral (e.g. warmer air) Cooler/more saline/ neutral ( Warmer/

suspensions of solids) less saline)

Ambient gas Sinking plume Neutral stability Rising plume River flow downslope NA NA

Bottom-spreading and No flow Interface-spreading

undercutting current jet

Ambient liquid NA NA Degassing bubbles in Sinking plume Neutral Rising plume

magma or lava Bottom-spreading stability Spreading jet

and undercutting wall jet

4.1.3 Flow in the atmosphere and oceans

Coriolis force (not considered in Fig. 27.4), are quite
sufficient to drive the entire average surface oceanic circu-
lation (discussed in Sections 6.2 and 6.4).

The atmosphere and oceans are in a constant state of flux,
both experiencing “weather”; that is, the velocity of the
ocean waters and atmosphere is unsteady with respect to
either magnitude or direction over timescales of minutes
to months. Here we briefly note that their longer-term
average flow approximates to the geostrophic condition
(see also Section 3.12). This is when pressure gradients are
balanced by the Coriolis force alone, with no other forces
involved: the fluid is assumed ideal , that is, inviscid.
In terms of the relevant equations of motion, we have
F (pressure)

4.1.4 Buoyancy/density flow

Many flows that take place in, on, and above the solid
Earth occur because density contrasts,

, give rise to
buoyancy forces (Section 3.6). The resulting flows are
termed density or gravity currents. These may act between
different parts of the same general state of matter (e.g. air,
water, magma) or between different states of matter (e.g.
water in and under air, gases in magma). We may illustrate
the various possibilities for water and air by means of
thought experiments with gravity lockboxes (Fig. 4.5).
The lockbox is of unit volume with any side that can be
opened instantaneously so that the contained fluid, air, or
water, may be smoothly introduced within ambient masses
of similar or different fluid. In all cases the gas phase has a
lower density than the liquid phase. For simplicity, we
examine the gravity lock in two dimension only, opening
the locks in the top, bottom, or side as appropriate. The
sketches show the expected flow direction as each box is
opened; the types of flows possible are summarized in
Table 4.1.

F (Corioli s ).
In the atmosphere, the pressure variations that cause
geostrophic flow are up to 6 percent and are caused by lat-
eral variations in air density between regional pressure cells
like the Iceland Low or the Azores High in the northern
hemisphere (see Fig. 3.21). Water density also varies with
depth in the oceans but in the well-mixed surface layers of
the open oceans this density variation is not so important.
Regional ocean pressure gradients are set up due to varia-
tions in the elevation of the mean sea surface (Fig. 4.4),
ignoring short-term topography due to storms, waves, and
tides. The slopes involved are very small, up to 3 m over
distances of a thousand kilometers or so, that is, gradients
of c .3 · 10 6 . These tiny gradients, in conjunction with the

4.2 Fluid flow types

There is something immensely satisfying in discovering the
efforts of pioneering scientists to reduce apparently compli-
cated natural phenomena to simple essentials governed by
some overall guiding principle. One such contribution that
stands out in the area of fluid flow was that by Reynolds.
Before Reynolds' contribution was published in 1883, it
was generally recognized from observations in natural
rivers, from experiments on flow in pipes (by Darcy),
and from work on capillary flow in very narrow tubes

(by Pouisseille, simulating the flow of blood in veins and
arteries), that fluid flow could exhibit two basic kinds of
behavior while in motion and that two flow “laws” must
exist to explain the forces involved. In Reynolds' elegant
words, “either the elements of the fluid follow one another
along lines of motion which lead in the most direct manner
to their destination, or they eddy about in sinuous paths
the most indirect possible.” In a series of careful experi-
ments (Fig. 4.6), Reynolds visualized these flow types by