ROTATION-DRIVEN SHEAR-FLOW INSTABILITIES

A general treatment of stability is considered for an isentropic flow equilibrium against three-dimensional incompressible perturbations by taking into account the difference in the orientations of the system r otation and flow vorticity. It is shown that the aforementioned orient ation difference can indeed generate a coupling that drives instabilit ies at the expense of the rotational energy. Two types of instability are identified, with one growing algebraically and the other growing e xponentially; the parameter regimes for both instabilities are also lo cated. The algebraically growing modes are destabilized more easily th an the exponentially growing modes; for example, the former can be uns table when the angle between the rotation axis and the vorticity is be yond 70 degrees.5, whereas the latter becomes unstable when this angle is greater than 90 degrees. In addition, we find that even in the lim it of small vorticity, the system may still be unstable algebraically at a considerable strength, in contrast to the case of exact zero vort icity, which is absolutely stable. This finding indicates the existenc e of structural instability for a rotating fluid. The present analysis is applied also to examination of the problem of shear mixing interio r of an accreting white dwarf in the context of nova explosions. In or der for the nuclear fuels to be blended deep inside the star and make the explosion, the high angular momentum accreted materials combined w ith the stellar materials should undergo shear flow instabilities. We find that the shear flow instabilities happen when the disk rotation a xis is off by more than 90 degrees from the star rotation axis. The in stability has in general an exponential growth, on a timescale much sh orter than that of the runaway nuclear burning.