It is well known
(Gebhart et al. 1988, pp. 728-30; Vest & Arpaci 1969)
that the narrow cavity limit flow in the analogous single fluid problem;
i.e. that reported by Jones & Furry (1946);
is susceptible to both stationary and travelling instabilities.
Thus, while the studies projected in §4.6.1 will define the
aspect ratios for which the present solution is valid, a stability analysis
must still be performed to determine the applicable range of 
and the
other parameters. This lies beyond the scope of the present project.