  We show the possibility of quasiperiodic waves at the onset of thermal
convection in a thin horizontal layer of slowly rotating zero-Prandtl number
Boussinesq fluid confined between stress-free conducting boundaries. Two
independent frequencies emerge due to an interaction between a stationary
instability and a self-tuned wavy instability in presence of coriolis force, if
Taylor number is raised above a critical value. Constructing a dynamical system
for the hydrodynamical problem, the competition between the interacting
instabilities is analyzed. The forward bifurcation from the conductive state is
self-tuned.
