  Sharp density features in protoplanetary discs, for instance at the edge of a
magnetically dead zone, have recently been proposed as effective barriers to
slow down or even stop the problematically fast migration of planetary cores
into their central star. Density features on a radial scale approaching the
disc vertical scale height might not exist, however, since they could be
Rayleigh (or more generally Solberg-Hoiland) unstable. Stability must be
checked explicitly in one-dimensional viscous accretion disc models because
these instabilities are artificially eliminated in the process of reducing the
full set of axisymmetric equations. The disc thermodynamics, via the entropy
stratification, and its vertical structure also influence stability when sharp
density features are present. We propose the concept of Rayleigh adjustment for
viscous disc models: any density feature that violates Rayleigh stability (or
its generalization) should be diffused radially by hydrodynamical turbulence on
a dynamical time-scale, approaching marginal stability in a quasi-continuous
manner.
