Jökull - 01.12.1983, Side 62

Since lava fronts are quite steep, it should be possi-
ble to obtain a measure of the thickness. The front
condition based on the conservation of lava volume
and equation (16) reads then
(18)
- (g/3v) (h0 - f)3V2h = (h0 - í)v0((h0 - f),v),
or
- (g/3v) (h0 - f)2V2h = v0((h0 - f),v), (!9)
where the value of V 2h is to be taken ahead of the
front.
As of now, there appear no possibilities ofobtain-
ing meaningful estimates of vD((h-f),v) on the
basis of the mechanical situation at the front and
this quantity will therefore have to be taken to be a
purely empirical condition.
Because of the non-linearities in h(S), equation
(17) with (19) can only be solved by numerical
methods.
DISCUSSION
At this end, it is of interest to briefly discuss the
possible applications of the above results. In this
respect it is important to note that although
equation (17) is supposed to govern the flow of thin
sheet Newtonean lavas, the above problem setting
is incomplete since the front condition (19) has yet
to be quantified. This can only be achieved on the
basis of considerable observational material on
suitable field cases, viz., on a sufficiently large
number of flowing lavas that cover a wide range of
viscosities. Unfortunately, such material is not
available at this time. We are therefore unable to
make full use of equation (17) in given field cases.
However, equation (16) can easily be applied to
estimate the viscosity of flowing lavas. For this pur-
pose, we have only to know the local surface slope
V2h, the actual local thickness (h-f) and the valueof
the integral on the left of (16) that represents the
total volume flow per unit front length. The latter
quantity can be roughly estimated by observing the
thickness and the velocity of the front.
It is of interest to point out that the development
above is closely related to the theory of flow of
ice-sheets. The basic equation for ice-sheets bears a
resemblance to equation (17) (see Bodvarsson, 1955
and Paterson 1969).
ACKNOWLEDGEMENT
This work was partially supported by the National
Science Foundation of the U.S. under Grant EAR 8023850.
REFERENCES
Bodvarsson, G., 1955: On the flow of ice-sheets and
glaciers, Jökull 5:1-8.
Hooper, P.R., 1982: The Columbia River Basalts,
Science 215: 1463-1468.
Hulme, G., 1974: The interpretation of lava flow
morphology, Geoph. J. R. Astr. Soc. 39:361-383.
Paterson, W.S.B., 1969: The Physics of Glaciers, lst
ed., 250 p., Pergamon Press Ltd., London.
Walker, G.P.L., 1973, Length of lava flows, Phil.
Trans. R. Soc. London. A. 274: 107-118.
Accepted for publication 30 Sept. 1982.
ÁGRIP
UM HRAUNRENNSLI
Gunnar Böðvarsson, Oregon State University
I greininni er sett fram stærðfræðilegt líkan af
rennsli hraunstraums, á þeirri forsendu að hraunið
sé vökvi með tiltekinn seigjustuðul. Úr líkaninu má
fá fram ólínulega diffurjöfnu, er ákvarðar lögun yfir-
borðs slíkra hrauna. Unnt er að nota jöfnuna til að
áætla seigju rennandi hrauns, en ýmis vandamál
eru þó óleyst í líkaninu að því er varðar randskilyrði
við hraunjaðarinn.
60 JÖKULL 33. ÁR