  Rotation contributes to internal mixing processes and observed variability in
massive stars. A significant number of binary stars are not in strict
synchronous rotation, including all eccentric systems. This leads to a tidally
induced and time-variable differential rotation structure. We present a method
for exploring the rotation structure of asynchronously rotating binaries. We
solve the equations of motion of a 3D grid of volume elements located above the
rigidly rotating core in the presence of gravitational, centrifugal, Coriolis,
gas pressure and viscous forces to obtain the angular velocity as a function of
the three spatial coordinates and time. We find that the induced rotation
structure and its temporal variability depend on the degree of departure from
synchronicity. In eccentric systems, the structure changes over the orbital
cycle with maximum amplitudes occurring potentially at orbital phases other
than periastron passage. We discuss the possible role of the time-dependent
tidal flows in enhancing the mixing efficiency and speculate that, in this
context, slowly rotating asynchronous binaries could have more efficient mixing
than the analogous more rapidly rotating but tidally locked systems. We find
that some observed nitrogen abundances depend on the orbital inclination,
which, if real, would imply an inhomogeneous chemical distribution over the
stellar surface or that tidally induced spectral line variability, which is
strongest near the equator, affects the abundance determinations. Our models
predict that, neglecting other angular momentum transfer mechanisms, a
pronounced initial differential rotation structure converges toward average
uniform rotation on the viscous timescale. We suggest that by taking into
account the processes that are triggered by asynchronous rotation, a broader
perspective of binary star structure, evolution and variability may be gleaned.
