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The nature of gravity currents

1.1 Introduction

Gravity

currents,

sometimes called density currents

buoyancy currents,

occur in both natural and man-made

situations.

These

currents are primarily

horizontal

flows

and

may be

generated

by a

density difference of only

few

per cent.

An important part

played in many different scientific disciplines by

gravity

currents.

In the atmosphere, for

example,

most of the severe squalls

associated with thunderstorms are caused

the arrival of an enormous gravity

current of cold dense

air.

One such advancing atmospheric gravity current in the

Sudan

shown in figure

1.1.

In this case the dense

air,

which

moving from

right to left in the picture,

clearly outlined

sand and dust which have been

raised from the ground

the strong turbulent

wind.

The

dust cloud

about

1000

metres high and the front

advancing at about

ms"

; some idea of

the scale can

gained from the houses which can just be made out in the

distance.

Figure

1.1

The front of a gravity current of cold air in the

atmosphere, made visible by suspended sand and dust.

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John E Simpson

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The

nature of gravity currents

Knowledge of the properties of these gravity currents

obviously

important for aircraft safety.

The

fronts produce large changes in horizontal

wind and areas of intense turbulence.

they are not

always so

clearly marked

dust

the example in the photograph, it

possible to fly

into

them without

any warning. Encounters of this kind

have

been responsible for serious

accidents, both at take-off and at landing.

Another, less intense, manifestation of atmosphere gravity currents

appears in the sea-breeze front. These fronts form near the coast, and many

of them propagate up to 200 km inland. They

have

important effects on the

transport of airborne pollution, and also on the distribution of insect pests.

Avalanches of airborne

snow,

which are a severe hazard in the mountains,

are gravity currents in which the density difference

supplied

the suspension

of snow

particles.

For many years attempts have been made to reduce the damage

caused

avalanches and there are research establishments devoted solely

the

investigation of this special type of gravity current.

industrial problem which has received much attention recently

the

accidental release of

dense

gas,

which maybe poisonous or

explosive.

Serious

accidents have occurred in the resulting spread, which usually starts as

gravity

current. Much experimental and theoretical work

has

been carried out on this

problem, leading

possible methods of controlling such escapes.

Even in the

home,

problems with gravity currents are common. If the door

warm house

held open for

few seconds on

cold day it

easy

detect

the gravity current of cold air flowing along the ground into the house.

This open door experiment

recommended to the reader, who may

care

use soap bubbles or puffs of smoke to detect the sudden onset of the gravity

current of dense cold air after the door has been opened.

This

topic

dealt with

in more detail in Chapter 14.

In the ocean, large volumes of warm or fresh

water,

less dense than the

neighbouring salty water, flow

gravity currents along the surface. Gravity

currents in the ocean are not

obvious to the casual observer

some

atmospheric gravity

currents,

but lines of foam and debris on the surface may

point to their

presence.

These lines are caused

the convergence of the flows

there, and

are well

known to fishermen, since these currents have important

effects on the distribution of fish.

Fresh-water gravity currents often flow along the surface in estuaries and

fjords,

above

the more dense sea water. Figure 1.2 shows an echo-sounding of such

a surface flow, made in the Fraser

River

Canada.

This

shows the cross-section

gravity current of fresh water advancing from the right,

above

the denser salt

water from the

sea.

The

leading

edge

of this current

has a

'head' which

deeper

than the following

flow,

feature which

seen in most gravity currents.

The oil slick

an example of

man-made environmental problem.

oil

spillage from a ship forms

non-mixing gravity current of less dense fluid on the

sea surface. It

important to understand the development of this flow and find

possible methods for both its containment and its dispersal.

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Dam break 3

1.2 Dam break

understand the physics of

gravity current it will help to consider what

happens when the wall of

dam breaks and releases the water behind it.

A mass

of suddenly released water

will

start

collapse and flow

horizontally.

The

main force acting on the water in such a

flow

is due to gravity,

and acts vertically

downwards.

This

results in

downward motion of the water

which can only occur if the water spreads horizontally.

the potential energy

of the water due to its height

continuously converted into the kinetic energy

of the horizontal motion.

If the

flow

spreads mainly in one direction, for example along the bottom

valley,

rough idea of the

velocity,

in that direction can

obtained

equating the

values

of the potential energy

loss

and the kinetic energy gain,

i.e.

(ml/

)/2=mgH/2

U=V(gH)

where

m is

the

mass,

H/2

the mean height of the centre of gravity and

the

acceleration due to

gravity.

If for example the water was originally

m deep,

the velocity would

about

m s~\ or roughly

mph.

Viscous forces in the fluid can also have important effects. Viscosity may

be likened to friction, in that

a viscous

fluid

exerts retarding forces on those parts

of itself which are trying

to move

with greater velocity than the

rest,

just as

retarding forces due to friction occur between

two

solid surfaces in relative

motion.

The

lower layers of the water in the dam-break

flow

are retarded

the

Figure

1.2

An echo-sounding made in the Fraser River in Canada.

The front of a gravity current of fresh water is moving above sea

water. (Courtesy of David Farmer.)

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4 The nature of gravity currents

ground, and have

considerable effect on the form of the leading

edge

the fluid.

1.3 Gravity currents

The

water in

dam-break

flow

is submerged in the atmosphere, but this has only

very small effect on its behaviour. If the air

replaced

by a

fluid

which

only

few per cent

less

dense than the collapsing

fluid,

then the

flow

will

different.

If in this 'dam-break analogy'

flow

the density difference between the two

fluids were only

1%,

the effective driving force would then have been reduced to

only

of normal. Unless the coefficient of viscosity

large,

or the scale

very

small, the main controlling forces will

gravitational and inertial, due to the

displacement of the fluid around the advancing current.

Due

to the net

gravitational acceleration of the collapsing

fluid

being now only g/100, the

previous dam-break

flow

will

replaced

by one

appearing

move 'in slow

motion'.

typical

gravity current

of dense

fluid

now

moving forwards into a slightly

less dense

fluid.

In this case its rate of advance

U can be

approximated by

or, in

general,

p is

the density of the

less

dense

fluid

and

Ap is

the density

difference,

The term

g (Ap\p)

will usually

denoted

the

symbol

g', and called 'reduced

gravity'.

The

fluid

gravity current

may be

chemically different from the

surroundings and have

different molecular

weight,

but often the difference in

specific weight that provides the driving force

due to dissolved material or to

temperature difference.

The

large-scale gravity current in the atmosphere shown

in Figure

1.1

was caused

temperature differences. If the temperature was

about 12

°C,

this would

give a

density difference of about

4%.

The value

of g

will

be 0.39 m

With

current height of 1000

would expect the rate of

advance to

about

(g'H)^

which

just under

m s"

1.3.1 Suspension

flows;

turbidity currents

One way

in which the overall density of a

fluid

can

increased

is by

the

suspension of many small dense particles within

it.

Such suspension currents

may be formed in

various

ways.

One of the most important processes is the

raising of material from the ground and its suspension

the turbulence within

a gravity current.

This

suspended material increases the density and hence the

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Bores

speed and turbulence within the current.

The

process can thus become 'self

stoking' in

current on

slope,

further increasing the strength of the current.

example of such a suspension current

shown in Figure

1.3.

This

illustrates

a suspension current of kaolin in water advancing through water towards the

camera in the laboratory.

This

photograph shows very clearly the complicated

shifting instability patterns manifested

by a

gravity current advancing along

a plane surface.

Self-stoking gravity currents containing suspended matter also occur in the

ocean.

They start on slopes near the coast

mud-slides which increase in

intensity until a suspension current

formed. These

turbidity currents

may

become large enough to travel at speeds of over

ms"

They

can gouge out

vast

channels in the

sea

bed and their progress has been followed

monitoring the

successive breaking of submarine telephone

cables,

showing that they can travel

for hundreds of kilometres.

1.4 Bores

related phenomenon

the

bore,

which

also concerned with mass transport

and has many features in common with the gravity currents already described.

The

best-known type of bore

is a

tidal disturbance which moves upstream

in some rivers and

may be

very violent at spring

tides.

an example of a

hydraulic jump in which there

a sudden increase of the water depth associated

with

change in the flow rate.

If the increase of depth at the front of

bore

less than about

third of

the undisturbed water depth, a series of smooth

waves

appears at the leading

edge and the

bore is

called 'undular'.

For

larger steps the tidal bore

turbulent

and it advances as

a wall

of tumbling

breakers;

the structure

similar to that

of breakers advancing towards the sea-shore.

Bores appear in rivers where the tidal range

large and the form of the

estuary

suitable. Conditions are favourable in several rivers in England: on the

River Severn the bore has been ridden

experienced surfers and journeys of

Figure

1.3

suspension

current in the laboratory,

advancing towards the

observer. (Courtesy of

J.H.R.

Allen.)

Hfc M

••

^Jkjrft--

:::;:

:rf:

:::

*t: ifc

tfftfc*

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6 The nature of gravity currents

two or three miles

have

been achieved. However, since they are produced

tides,

surfers who miss their moment may

have to

wait over

hours for the next

breaker!

Figure 1.4 shows

rider on

surf board using one of the

waves

at the

front of the Severn

bore.

The

bore shown here

an undular

one,

but breaking

waves are forming in the shallower water near the banks of the river.

The conditions ahead of

hydraulic jump or

bore can

related to those

behind it in

simple mathematical treatment.

In figure 1.5 the jump

shown brought

rest in

moving frame of

reference; h

and

are the height and velocity on the two sides of the

jump.

Figure

1.4

A surfer on the advancing bore on the River Severn.

(Courtesy of the Severn-Trent Water Authority.)

A I R

5*w Jump

WATER

Figure

1.5

The flow through a hydraulic

jump.

The axes have been

taken to bring the jump to rest, and \,\J

and

are the height

and the velocity on the two sides of the

jump.

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Internal

bores

The

volume flux

Qjper

unit

width,

passing in unit

time,

is,

since mass is

conserved,

change in momentum across the jump

caused

the pressure

difference. If density

since mean pressures at both sections

are gph

and

gph

/2,

the equation of momentum is

hence

=gh

]

)/2

The

energy,

however, does not balance and the

loss

of energy per unit time is

which can

shown

This loss of

energy,

which must occur at

bore,

is mostly effected in the

undular

case by

the

waves,

each of which carries energy

moves away

from

the front.

The

more intense bores cannot carry

away

enough energy

this

method and the energy

excess

is dissipated

turbulence in the tumbling

breakers at the leading edge.

1.5 Internal bores

The previous section considered bores at the free surface of

water flow.

somewhat similar

class

of internal bores can

formed at an interface between

two

fluids,

one lying on top of another which

perhaps only

few per cent

denser. Compared with surface

bores,

these internal bores appear

move

'in slow motion', since the buoyancy forces are very much reduced.

Internal bores have been described theoretically and investigated in

laboratory

experiments.

Figure 1.6 shows such an experimental arrangement

in which an obstacle

towed along the bottom of

tank containing

two-fluid

system.

The

obstacle

moving to the right and displacing an undular internal

bore which steadily

moves

along the interface ahead of it. If the moving obstacle

is replaced

an advancing gravity current of dense

fluid

similar effect can

be produced.

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The

nature of gravity currents

Such experiments

have

been very helpful in understanding the physics

of undular

bores

and will

described in more detail in Chapter

13.

During the last few

years,

internal bores have provided an explanation for

an increasing number of phenomena in the environment, both in the ocean and

in the atmosphere.

They may

for example

formed in the ocean

tidal effects

on fresh-water

layers

near the coast. In the atmosphere they

are

formed in dense

stable layers

advancing

flows

of cold dense air from thunderstorms, and they

are also associated with sea-breeze fronts.

Figure

1.6

The production of an internal bore by a moving

obstacle (black) in an experimental laboratory tank, in which a

layer of fresh water (clear) lies above salt water

(shaded).

The bore

is moving to the right along the interface between the two fluids,

faster than the moving obstacle.

Figure

1.7

Clouds marking an undular internal bore in the

atmosphere, the 'Morning Glory' in North Australia. (Courtesy of

Roger Smith.)

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Solitary waves

When the ratio of the height

behind the jump

(see

figure 1.6) to that in

front of it,

is less than about

then the internal bore

undular. In much

deeper internal

bores

the leading

edge is

turbulent and appears very similar to

the front of

gravity current.

The

photograph in

figure

1.7 shows the clouds

forming at an atmospheric undular

bore

in Northern

Australia.

This

phenomenon appears in the early morning and

marked

by a

spectacular roll of

cloud; its striking appearance has led to its name, the 'Morning Glory'.

1.6 Solitary waves

'Gravity currents' and 'gravity waves' are sometimes confused and the distinction

between them

not

always

apparent. Here the name 'gravity current' will be

applied to a phenomenon in which there

is a

clear transfer of mass (usually

horizontal). In gravity waves there

little transfer of mass and the main

transport

that of energy.

undular

bore,

has been noted, consists of an increase in depth of

fluid

advancing with a series of

waves

on its surface.

Closely

the

'solitary

wave'

which

another shallow-water phenomenon,

i.e.

disturbance

which

high compared with the undisturbed

depth.

solitary wave

not

Figure

1.8

Internal solitary wave moving along an interface

between two fluids in a laboratory tank.

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The

nature of gravity currents

periodic

wave

but consists of a single symmetrical hump which propagates

at uniform velocity without change of form.

Scott Russell in the 1840s investigated solitary waves on the surface of a

canal.

horseback

he was

able to follow examples of such

waves

for several

kilometres and he showed that, with length, depth and amplitude properly

matched, a solitary wave can propagate virtually unchanged, except for small

effects due

bottom friction which reduce the size of the

wave.

Internal solitary waves can exist at an interface between two

fluids

different

density.

Examples occur in the atmosphere, where solitary waves

have

been observed on stable

layers,

moving steadily

away

from the distant

disturbances which generated

them.

What

observed on the ground is

somewhat similar

the arrival of

bore,

with

line of cloud and

gust

wind, but in this

case

with only

temporary increase of surface pressure.

In the laboratory these internal solitary waves

are

very

easy to

create.

Figure 1.8 shows an example of an internal solitary wave formed at

layer

which had been laid down

by a

gravity

current.

When the gravity current

reached the end of the tank

some

of the dense

fluid

ran up the

wall

and

then descended

as a

mass which generated the solitary wave shown, moving

from right to left. When this disturbance reached the other end of the tank,

three metres distant, it

was

reflected and returned with nearly the same

shape and speed.

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