Edge modes and short period coherent oscillations in cataclysmic variables

The non-linear growth of non-axisymmetric instability in thin Keplerian discs is followed numerically, using a two-dimensional spectral code. The instability develops at the inner edge of the disc when it is reflective, corresponding to a rigid accreting white dwarf or neutron star. We assume alpha approximate to 0.1 and a Mach number M = upsilon(phi)/c(s) approximate to 40, and find that the m = 2 mode is the dominant one. Its high Q value (> 10(4)) and its period are characteristic of short period coherent oscillations observed in Cataclysmic Variables. In addition, the period of the mode decreases with increasing a, or equivalently with increasing mass accretion rate, and provides an explanation to the 'banana diagram' of the observed coherent oscillations in the period-intensity plane.