  We employ an approximate treatment of dissipative hydrodynamics in three
dimensions to study the coalescence of binary neutron stars driven by the
emission of gravitational waves. The stars are modeled as compressible
ellipsoids obeying a polytropic equation of state; all internal fluid
velocities are assumed to be linear functions of the coordinates. The
hydrodynamic equations then reduce to a set of coupled ordinary differential
equations for the evolution of the principal axes of the ellipsoids, the
internal velocity parameters and the binary orbital parameters. Gravitational
radiation reaction and viscous dissipation are both incorporated. We set up
exact initial binary equilibrium configurations and follow the transition from
the quasi-static, secular decay of the orbit at large separation to the rapid
dynamical evolution of the configurations just prior to contact. A
hydrodynamical instability resulting from tidal interactions significantly
accelerates the coalescence at small separation, leading to appreciable radial
infall velocity and tidal lag angles near contact. This behavior is reflected
in the gravitational waveforms and may be observable by gravitational wave
detectors under construction.
