One of the major challenges in modern astrophysics is the unexplained turbulence of gas-dynamical (nonmagnetic) accretion disks. Such disks, being as they are stable, should not theoretically be turbulent — but observations show they are. The search for instabilities that can develop into turbulence is one of the most intriguing problems in modern astrophysics. In 2004 the presented authors pointed to the formation in accretion disks of binary stars of the so-called ’precessional’ density wave, which produces additional density and velocity gradients in the disc. Linear hydrodynamics stability analysis of an accretion disk in a binary shows that the presence in the disk of a precessional wave produced by the tidal influence of the second binary component gives rise to the instability of radial modes whose characteristic growth times are about one tenth or one hundredth of the binary’s orbital period. The immediate reason for the instability is the radial velocity gradient in the precessional wave, the destabilizing perturbations being those in which the radial velocity variation on the wavelength scale is of order or greater than the sound speed. Unstable perturbations occur in the interior of the disk and make the gas turbulent as they propagates outward. The characteristic turbulence parameters are in agreement with observations (the Shakura—Sunyaev parameter $\alpha \lesssim 0.01$).