  Binary stars in eccentric orbits are frequently reported to present
increasing levels of activity around periastron passage. In this paper we
present results of a calculation from first principles of the velocity field on
the surface of a star that is perturbed by a binary companion. This allows us
to follow the orbital phase-dependence of the amount of kinetic energy that may
be dissipated through the viscous shear, dot-E, driven by tidal interactions.
For stars with relatively small stellar radii compared with the orbital
separation at periastron (R/r_per< 0.14), a clear maximum occurs before
periastron passage for sub-synchronous rotation and after periastron for
super-synchronous rotation. For larger stellar radii however, dot-E oscillates
over the orbital cycle and periastron passage does not cause a particularly
greater enhancement in energy dissipation rates than some of the other orbital
phases. Finally, we perform exploratory calculations for a WR/LBV binary system
that in 1993-1994 underwent an LBV-like eruption, HD 5980. Our dot-E
calculations reproduce the oscillations that appear around periastron passage
in HD5980's recent visual light curve. We suggest that the energy dissipation
from tidal flows in asynchronously rotating binary stars may provide a
mechanism by which evolving stars may be driven into an active state. Given the
nature of the tidal perturbations, the resulting mass-loss distribution is
expected to be non-uniform over the stellar surface and highly time-dependent.
