Martian Outflow Channels

Shabari Basu

(Caltech, CA 91125)

Introduction

One of the more dramatic discoveries of the Mariner 9 orbiter was the detection of

extremely large channel like landforms on the Martian surface. These features are

predominantly located to the south and west of Chryse Planitia, a major martian basin,

and together are often called Circum Chryse channel system. Examples of the outflow

channels include Kasei Valley, Maja Vallis, and Tiu Vallis. Other features of similar

characteristics are also found on the Amazonis region of Mars.

Cutts and Blausius (1979) suggested that wind eroded the channels and Schuum (1974)

believes that they have a structural origin. One of the more interesting theories suggested

by Luchchitta (1982) is that these features were formed by the flow of glaciers over the

Martian surface.

However most scientists, such as Baker and Milton (1974), Baker and Kockel (1979),

Carr (1976) and Carr (1979), argue that these features were probably formed due to

catastrophic fluid flow.

The two most probable causes for the Martian floods are massive release of groundwater

and draining of the surface lakes. Both the causes will be analyzed below.

First Probable Cause

Formation of confined aquifers (Carr 1979)

The specific mechanism for forming the flood features proposed here, is as follows. The

rocks within several kilometers of surface are probably volcanic or brecciated by impact

and thus are highly porous. Very early in the planet’s history, water was available at the

surface to dissect the old cratered terrain, as evidenced by the numerous fine channels.

Much of the water was lost to the ground water system. Later the mean annual

temperature fell, and a permafrost layer developed and thickened with time. Ultimately,

the permafrost layer became so thick that it effectively sealed in the underlying

groundwater to form a system of confined aquifers. Pressure within the confined aquifers

would depend on their relief, but in addition, because of the volume increase of water

upon freezing, an increase in depth of the base of the permafrost could add to the pore

pressure within the aquifer.

Model of the proposed flood mechanism. . Water is sealed under high pressure within the brecciated old cratered terrain by a permafrost layer above and compacted nonporous rocks below. Disruption of the permafrost layer in the chaos regions provides access for the water to the surface. Flow into chaos region and out onto the surface causes the draw down of the pore pressure in the region surrounding the chaos. The rapid flow causes undermining of the surface and collapse to enlarge the chaos area.

When the pore pressure reaches the lithostatic pressure, the aquifers become unstable.

Breakout of these aquifers could have been triggered by meteoritic impacts.

Calculation of the discharges

This is to verify whether the model suggested by Carr (1979) – the confined aquifers’

model has discharge rates comparable to those implied by the scale of the channels(10⁶-

10⁹ m³/s). The basic equation for flow through a confined aquifer is the following

Ѳh = (1/n). (¶h/¶t) (1)

where h is the hydrostatic head, t is the time and n is the hydraulic diffusivity

The above equation will be solved for an infinite aquifer of uniform transmissibility and

uniform compressibility which at time t=0 gains access to the surface through a conduit

of radius a . The problem is analogous to that of drilling a well into a confined aquifer.

For this purpose (1) can be restated in terms of draw down around the conduit:

Ѳw = (1/n).(¶w/¶t) (2)

where the draw down w is h₀-h, where h₀ is the hydrostatic pressure at t=0 and h is the

head at any position(x, y) and at time t.

The last equation is exactly analogous to the basic heat flow equation, the thermal

diffusivity being substituted for ν and the temperature being substituted for w. Carlsaw

and Jagger (1959) provide solutions for a heat flow problem analogous to the draw

down of hydrostatic head around a conduit to the surface in a confined aquifer. They give

solutions for an infinite plate, initially at temperature T and bound internally by a hole

maintained at 0 degree C. The solutions were transposed into that for the flow in confined

aquifers .

ν= T/S, S is the storage coefficient and T is the transmissivity

S = ρgb(α+mβ)

Where ρ is the density of water, g is the acceleration due to gravity, b is the thickness of

the aquifer, α is the vertical compressibility of the aquifer skeleton and β is the

compressibility of water, m is the porosity.

For a confined aquifer, flow is relatively insensitive to the value of S, which is likely to

have a narrow range of values as compared to T .

The main uncertainty is in the value of T

T = kgbρ/μ

Where k is the permeability and μ is the viscosity.

Now for finding the discharge the following values for the various variables were taken-

these are reasonable for Mars.

α = 2x10^-13 cm²/dyn

β= 4x10^-11cm²/dyn

m= 0.1

so α+mβ = 4.4x10^-12

k=3000 darcies

A rock density of 3.5gm/cm³ is assumed. Discharge rates depend on time, the diameter

of the chaotic region, the depth of burial, the aquifer thickness and its permeability.

Assuming breakout occurs when the pore pressure equals the lithostatic pressure, for an

aquifer 3km deep and 3km thick with a permeability of 1000 darcies, discharges are

around 10 ⁶ m³/s which is comparable to the data from the channel dimensions

The high artesian pressures could be simply caused by the generally low elevations of the

source regions compared to the water level in the regional aquifer system.

There are however problems with the model suggested by Carr (1979)- the discharges

from the aquifer are pretty high- with such large flows – the aquifer would have been

disrupted and the host rocks carried away in the flood. The flow therefore not be

constrained by the permeability. Collapse of the surface to form the chaotic terrain is

testament to the removal of the aquifer material.

This particular origin of the outflow channel also assumes that there was a massive

release of ground water which cause these floods, but there is evidence for multiple

flooding which suggests that a single gush of groundwater could not have done it all.

Despite the morphological evidence indicating a flood- outflow origin for several of the

large Martian channels, a number of theoretical difficulties persist for the above

hypothesis. Sharp and Malin (1975) have summarized it as follows:

A disparity exists between the dimensions of some channels and the volume of the fluid

that could be released from the probable source areas.

Second Probable Cause

The possible source of origin of some outflow channels by catastrophic release of water

in lakes within the canyons , as suggested by Mc Cauley (1978). Given a global aquifer

system, it is to be expected that water would pool in the Canyons. The Ophir, Candor,

and Melas Chasma in the central section of Valles marines are over 8km deep. At present

the nominal thickness of the cryosphere is 2.3 km at the equator , but it was probably

thinner at the time layered sediments which are the main evidences of former lakes,

accumulated. Thus the canyon floors were well below the expected base of the

cryosphere and water could have leaked into the canyons both while they were forming

and after they formed. Under present climatic conditions , such ponded water would tend

to stabilize at the level of the local water table to form an ice covered lake.

Subsurface seepage out of the lakes might ultimately have led to undermining and

catastrophic release of the ponded water and formation of some outflow channels.

Landforms seen in the outflow channels include streamlined islands, dry and horse shoe

cataracts, anastomosing channels scour around the base of the obstacles, linear grooves

possibly bars and basin and butte topography. Based on their study on similar terrestrial

features, Baker and Milton (1974) suggest that Martian outflow channels were carved out

by the flow of water on a very large scale. The channeled scablands of Washington State

contain most of the landforms seen in the Martian Channels. The Scablands formed

when an ice dammed lake, which existed during the last glacial period, burst through the

ice dam and released large amounts water over a short period of time. The water flowed

down to the pacific, carving an enormous braided channel on its way.

The Channeled Scablands of Eastern Washington

The calculation of flow velocities, discharges and other hydraulic parameters is a useful

exercise in comparing scale of the fluid flows. However accurate calculations are difficult

for Mars – the problem is compounded by the unknown nature of the fluid properties and

by the less precise definition o f the channel geometries involved.

The indirect calculation of flow hydraulics from channel dimensions is usually

accomplished by using the semi- empirical Mannings equation:

V = (1/n) D ^2/3 S ^½ (3)

Where V is the mean velocity, D is the depth of flow in meters and S is the energy slope.

The term n in the equation is the Manning roughness coefficient which requires

estimation for any application of the above equation(e.g. Chow, 1959)

Other considerations applying to the use of this equation include the substitution of the

depth for hydraulic radius and the channel bottom slope for the energy slope.

Due to the difference in the gravity on ear and Mars it is not possible to simply adjust the

above equation hence an approximate formula suggested by Carr is more useful.

V = ( 0.5 / n ) D ^2/3 S^1/2 (4)

The multiplier 0.5 represents an approximate adjustment for the Marian gravity.

A dimension quantity that is useful in comparing flows of different scales is the Froude’s

number F

F = V / ( g D )^1/2

Where g is the acceleration due to gravity.

The preliminary Mars calculations show that Mars channels also have variable Froude

numbers. The Ares and Maja reaches were supercritical in the range F=1.0-2.0,

depending on the chosen. Mangala was subcritical, F=0.5-0.8. The high Froude number

reaches display steep gradients and constricted flow as in the Channeled Scablands.

The immense scale of the proposed Martian flood flows requires an immense scale of

sediment transport. The reduced gravity on Mars means that mean flow velocities for

similarly scaled flows are less on Mars than on the earth. However the lower weight of

the otherwise similar sediment on Mars means that those particles are more easily carried

than on earth.

Maximum width of streamlined forms versus planimetric form area for the Channeled Scabland, Kasei Vallis and Maja Vallis. The plotted equation is a general model (from Baker (1979)

The outflow channels on Mars may be in places over 200 kilometers wide (1980).

The erosional effectiveness of water flows on this scale may be enhanced by fluid flow

phenomena not normally seen in rivers. Baker (1979) describes highly ordered turbulent

behavior , known as macroturbulence , which can exist in deep rapidly flowing fluid. The

best known example of macroturbulent flow is a kolk, which is a turbulent eddy with a

vertical axis. Kolks produce a hydraulic lift or plucking action which acts on the channel

bottom. Kolks have been suggested to be one of the main erosive forces in the formation

of he Channeled Scablands of Washington. Two other types of macroturbulent flow,

rollers and longitudinal vortices, can also form during high rates of flow downstream of

obstacles in the flow . Fluctuating pressures where the flow separates produce large

shear stresses in the channel bed, facilitating erosion.

Another fluid flow action which may enhance the erosive capability of the flow is

cavitation. When vapor bubbles form in a fluid due to high temperature it is called

boiling. When they are produced due to dynamic pressure fluctuations it is known as

cavitation.. Pressure drops large enough to produce cavitation may occur downstream of

an obstruction in the core of a vortex. Erosion occurs due to a shock wave produced in

the collapse of the vapor bubble or by jets of liquid that shoot into the collapsing cavity.

These actions produce pitting of any surface near them.

As a first approximation, cavitation occurs when absolute pressure Pa at some point in a

liquid is reduced below the vapor pressure Pv, generally by the increase in the flow

velocity V according to Bernoulli’s theorem

σ = ( Pa - Pv ) / ½ ρ V² (5)

Where σ is the critical cavitation number and ρ is the fluid density. At points in the flow

field exhibiting critically low σ values, vapor will form the liquid as growing bubbles that

are carried downstream. However, hydraulic experience has shown that the cavitation

parameter above is only a rough guide to the dynamics of the cavitation phenomena

(Knapp, 1970)

The above equation applies only to fluid dynamic pressure effects.

A more generalized statement of the critical cavitation number is that it represents the

ratio of the pressure tending to collapse a cavity to the pressure tending to induce

cavity formation and growth.

Cavitation inception occurs in zones of local pressure drop, such as venturi like flow

constrictions. It also appears at low pressure points along solid boundaries. The transient

bubbles are then carried downstream in this traveling cavitation condition. Vortex

cavitation occurs when cavities develop in zones of high fluid shear. The third variety of

importance is fixed cavitation in which liquid flow detaches from the rigid boundary of

an immersed body. This cavity may then grow downstream from the immersed body, a

condition known as supercavitation.

The actual stress required to create a cavity is the tensile strength of the liquid at various

temperatures. Experiments summarized by Knapp, showed that appreciable tensions

develop at zones of weakness in the liquid caused by various contaminants. For example

suspended solids, bubbles of undissolved air, and other defects in the fluid probably serve

to nucleate cavitation bubbles. Thermodynamic and hydrodynamic characteristics of the

flow are also important. These considerations limit the quantitative precision of the

estimates presented here.

For terrestrial river flow, Barnes (1956) began his estimate of the critical conditions for

cavitation inception by assuming that fluvial bed obstructions will increase local

velocities to about twice the mean flow velocity V. This allows calculation of the critical

mean stream velocity permitting terrestrial cavitation, Ve from Bernoulli’s Theorem

Ve = ( 2g/3 )^1/2 ( ( Pa-Pv )/γ + d )^1/2 (6)

Where g is the acceleration due to gravity, γ is the specific weight of water and d is the

stream depth in meters. For Pa =1atm and Pv =0.024atm (21 deg C) the above equation

reduces to Ve = 2.6 ( 10+d )^1/2 (7)

The extrapolation of the cavitation behavior from one set to another is a complex

problem. The scaling to possible water flow in Mars is thus tentative, but simplifications

were made by Baker (1979). For relatively cold water, thermodynamic properties of the

fluid become minor. Adjusting to the Martian gravity the above equation can be written

as Vm = 1.6 ( ( Pa-Pv ) /4000 + d )^1/2 (8)

Where Vm is the critical mean flow velocity for cavitating water flow on Mars.

or the present Martian atmosphere with pressures of a few millibar

the above becomes Vm = 1.6 ( d )^1/2 (9)

Critical conditions for cavitation in flood flows on Mars and earth for various

atmospheric pressures. The critical cavitation velocities are compared to the critical Froude numbers for both planets (from Baker (1979))

For the higher atmospheric pressures of various postulated ancient atmospheric

conditions, the Pa-Pv term will become more important, especially at flow depths less

than 100m. A set of various representative curves of critical cavitation velocities on Mars

at various atmospheric pressure values is presented in the figure above.

These curves assume that vapor pressures for water were always small in comparison to

the absolute pressures of cavitation inception. The important point is that the combination

of lower gravity and lower atmospheric pressure allows Martian fluvial cavitation to

occur at much lower flow velocities than are required in the terrestrial rivers.

Clearly the inception of cavitation in Martian water flows poses no problems. The very

low atmospheric pressure may be thought to pose difficulties for the maintenance of a

coherent liquid flow because of cavitation throughout the entire flow depth. High velocity

water lows in direct contact with the Martian atmosphere would not be able to achieve the

pressures necessary for bubble collapse, thereby maintaining the liquid flow.

Pieri (1980) calculated that Martian cavitation bubble pressures become important for

bedrock erosion only at flow depths of approximately 30m or more. However this is too

simple for the dynamics of fluid flow in the channels.

The alternating constrictions and expansions of the channel cross section (Baker, 1978)

require alternating changes in the flow depth and velocity. In the deep slow moving water

of an expanding reach, the cavitation parameter will be drastically increased because of

lower flow velocities and higher absolute pressures beneath the thick water column. Thus

foaming water flows initiated at the throats of constrictions could revert to coherent

liquid in the adjacent expansion.

The very high flow velocities are associated with great depths (Baker, 1974). The deep

Martian floods could have had very high velocities and merely been the critical point for

cavity inception. An ice cover could also locally increase the cavitation parameter.

Water flows of smaller scale would simply cavitate out of existence, while exceptionally

deep flows could be maintained at high velocities.

The process of cavity collapse and resulting erosion are commonly viewed as results of

pressure shock waves that radiate from the collapse centers of the bubbles.

Conclusion

The Channeled Scabland is the closest terrestrial analog to the outflow channels on Mars.

The bed rock erosional forms are the most comparable and include anastomosing

channels eroded in rock streamlined uplands, cataracts, inner channels scour depressions

and grooves. The same detailed assemblage of landforms characterizes the Martian

outflow channels and the Channeled Scabland.

Repeated flooding from frozen lakes seems to be the cause for the catastrophic floods that

carved out the channels. Fluvial processes involving ice covers, macroturbulence ,

streamlining and cavitation appear likely in the large scale flood flows.

Catastrophic cavitating water flows moving over the irregular Martian surface rapidly

eroded constrictions and expansions with the aid of venturi pressure effects.. Residual

areas were preserved as streamlined uplands that subsequently minimized cavitation

erosion.

While the above can explain many of the features found in the Martian outflow

channels, the above hypothesis is not necessarily synonymous with the truth- this

however seems to be more a reasonable hypothesis compared to the others.

References

Murray B. et al.: Earthlike Planets. W.H.Freeman and Company. 1881

Manning. Trans. Inst. Civil Engrs. Ireland. Vol 20. p. 161 .1890.

Vennard J.K. and Street R.L : Elementary Fluid Mechanics. John Wiley & sons. SI

version. Fifth Edition. 1986.

Schlichting, H.: Boundary Layer theory. McGraw- Hill Book Company. Seventh edition.

1979.

Acosta A.J.: Cavitation inception. Proceedings of the US-Romanian workshop on water

resources engineering. 1989. pp 69-72.

Knapp R. T. et al.: Cavitation. McGraw-Hill Book Company. 1970.

Baker, Victor R.: Channels of Mars. University of Texas Press, Austin, first edition.

Baker, Victor R.: Catastrophic Flooding-Origin of Channeled Scablands, 1981.

Sharp and Malin: Channels on Mars. Geological Society of America Bulletin, vol86.

p593-609.

Carr, Michael H.: Formation of Martian Fluid Features by Release of water from

Confined Aquifers. Journal of Geophysical Research. Vol 84. 1979

Carr, Michael H: Water on Mars. Oxford University Press. First edition. 1996.

.