  We simulate the viscous evolution of an accretion disc around a spinning
black hole. In general any such disc is misaligned, and warped by the
Lense-Thirring effect. Unlike previous studies we use effective viscosities
constrained to be consistent with the internal fluid dynamics of the disc. We
find that nonlinear fluid effects, which reduce the effective viscosities in
warped regions, can promote the breaking of the disc into two distinct planes.
This occurs when the Shakura & Sunyaev dimensionless viscosity parameter alpha
is <~ 0.3 and the initial angle of misalignment between the disc and hole is >~
45 degrees. The break can be a long-lived feature, propagating outwards in the
disc on the usual alignment timescale, after which the disc is fully co- or
counter-aligned with the hole. Such a break in the disc may be significant in
systems where we know the inclination of the outer accretion disc to the line
of sight, such as some X-ray binaries: the inner disc, and so any jets, may be
noticeably misaligned with respect to the orbital plane.
