GLOBAL ASPECTS OF ELLIPTIC INSTABILITY IN TIDALLY DISTORTED ACCRETIONDISKS

Tidally distorted accretion disks in binary star systems are subject t o a local hydrodynamic instability that excites m = 1 internal waves. This instability is three-dimensional and approximately incompressible . We study the global aspects of this local instability using equation s derived under the shearing-sheet approximation, where the effects of the azimuthal variation along distorted orbital trajectories are incl uded in source terms that oscillate with local orbital phase. Linear a nalyses show that the excitation of the instability is essentially loc al, i.e., insensitive to radial boundary conditions. The region of rap id growth feeds waves into the region of slow or negligible growth, al lowing the instability to become global. The global growth rate depend s on the maximum local growth rate, the size of the rapid-growth regio n, and the local group velocity. We present an empirical expression fo r the global growth rate. We note that the local nature of the instabi lity allows the excitation of waves with m not equal 1 when the local growth rate is large.