Jökull - 01.12.1973, Page 37

TABLE 4.
Critical Rayleigh numbers for a 600 km two-phase layer (based on (mks units)).
h = 6 x 105; A = 5 x 10-12; a = 2 X 10-6; c = 103;
a = 2 X 10-5; g= 10; /3X = 10-3
Critical Critical
Transition Rayleigh No. Rayleigh No. %
W. Phase W/O Phase Difference
Change Change
Mg2Si04 -> Mg2Si04 forsterite -* spinel 1170 2000 -42
Mg2Si04 2MgO + SiOa spinel -> oxides 4000 2000 + 100
Fe2Si04 -» Fe2Si04 fayalite -» spinel 1300 2000 -35
Fe2Si04 -> 2FeO + Si02 spinel -> oxides 2680 2000 + 34
two-phase mantle. The results show that the
known mantle phase transitions are of only
mmor importance with respect to the existence
°f mantle convection. These results are con-
trary to those of Knopoff (1964). Knopoff, how-
ever> has only considered the stabilizing latent
heat effect of the olivine-spinel transition. The
destabilizing effect resulting from the displace-
roent of the phase surface is neglected in liis
treatment. On the other hand, the present
results are, with respect to the effects of the
phase transitions, in good agreement with the
results of Schubert and Turcotte (1971) and
Busse and Schubert (1971) for the case of a
normal phase transition in a fluid layer heated
from below.
ln conclusion we wish to remark that there
are no inherent difficulties in solving equation
0) in the case of variable parameters such as
íhe thermal conductivity K or the density p.
Moreover, equation (8) can be replaced by any
aPpropriate jton-Newtonian flow relation. In
prtnciple, it is therefore possible to apply the
striP model to more complex cases involving
non-homogeneous, non-Newtonian fluids with
'ariable pressure and temperature dependent
properties. A further advantage of the strip
model is that it can furnish an order of magni-
tude estimate of the temperature and velocity
fields in the convecting fluid.
ACKNOWLEDGEMENTS
The work of one of the authors (R.P.L.) on
this research was supported by the office of
Naval Research through contract N00014-67
A-0369-0007 under project NR 083-102.
BIBLIOGRAPHY
Allan, D. W., W. B. Thompson, and N O.
Weiss. 1967: Convection in the earth’s
mantle. In: Mantles of the Earth and Ter-
restrial Planets, edited by S. K. Runcorn,
pp. 507—512, Interscience, New York.
Anderson, D. L. 1967: Phase changes in the
upper mantle. Science, 157, 1165—1173.
— and T. Jordan. 1970: The composition of
the lower mantle. Phys. Earth Planet. In-
teriors, 3, 23—35.
JÖKULL 23. ÁR 35