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.
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