  It is usually thought that viscous torque works to align a circumbinary disk
with the binary's orbital plane. However, recent numerical simulations suggest
that the disk may evolve to a configuration perpendicular to the binary orbit
("polar alignment") if the binary is eccentric and the initial disk-binary
inclination is sufficiently large. We carry out a theoretical study on the
long-term evolution of inclined disks around eccentric binaries, calculating
the disk warp profile and dissipative torque acting on the disk. For disks with
aspect ratio $H/r$ larger than the viscosity parameter $\alpha$, bending wave
propagation effectively makes the disk precess as a quasi-rigid body, while
viscosity acts on the disk warp and twist to drive secular evolution of the
disk-binary inclination. We derive a simple analytic criterion (in terms of the
binary eccentricity and initial disk orientation) for the disk to evolve toward
polar alignment with the eccentric binary. When the disk has a non-negligible
angular momentum compared to the binary, the final "polar alignment"
inclination angle is reduced from $90^\circ$. For typical protoplanetary disk
parameters, the timescale of the inclination evolution is shorter than the disk
lifetime, suggesting that highly-inclined disks and planets may exist orbiting
eccentric binaries.
