  We study the importance of hydrodynamic effects on the evolution of
coalescing binary neutron stars. Using an approximate energy functional
constructed from equilibrium solutions for polytropic binary configurations, we
incorporate hydrodynamic effects into the calculation of the orbital decay
driven by gravitational wave emission. In particular, we follow the transition
between the quasi-static, secular decay of the orbit at large separation and
the rapid dynamical evolution of configurations approaching contact. We show
that a purely Newtonian hydrodynamic instability can significantly accelerate
the coalescence at small separation. Such an instability occurs in all close
binary configurations containing sufficiently incompressible stars.
Calculations are performed for various neutron star masses, radii, spins, and
effective polytropic indices. Typically, we find that the radial infall
velocity just prior to contact is about 10\% of the tangential orbital
velocity. Post-Newtonian effects can move the stability limit to a larger
binary separation, and may induce an even larger radial velocity. We also
consider the possibility of mass transfer from one neutron star to the other.
We show that stable mass transfer is impossible except when the mass of one of
the components is very small (less than about 0.4 solar mass) and the viscosity
is high enough to maintain corotation.
