  Context: Hydrodynamical model of the kappa-mechanism in a purely radiative
case. Aims: First, to determine the physical conditions propitious to
kappa-mechanism in a layer with a configurable conductivity hollow and second,
to perform the (nonlinear) direct numerical simulations (DNS) from the most
favourable setups. Methods: A linear stability analysis applied to radial modes
using a spectral solver and DNS thanks to a high-order finite difference code
are compared. Results: Changing the hollow properties (location and shape) lead
to well-defined instability strips. For a given position in the layer, the
amplitude and width of the hollow appear to be the key parameters to get
unstable modes driven by kappa-mechanism. The DNS achieved from these more
auspicious configurations confirm the growth rates as well as structures of
linearly unstable modes. The nonlinear saturation follows through intricate
couplings between the excited fundamental mode and higher damped overtones.
