STANDARD MODEL

Our standard model has a sound speed of 0.25, a mass ratio of unity, and an initially flat density profile. The Mach number of the rotational flow is of order 12 in the interior of the disk. A two-armed spiral shock quickly develops, and remains relatively steady for a few binary orbits. This evolution is best seen in the animation of this simulation. The left image shown below is of the entire numerical grid, with the binary companion oriented to the right of the disk. The image on the right is an expanded view (a factor of 5). The inner circle is the inner boundary of the numerical grid, at a radius of 0.02.
The evolution of the mass transport during the simulation is illustrated below. The first three lines are from the first few orbital periods, when the double spiral pattern dominated the disk. The dotted line is from the end of the simulation, when other wave modes are interacting with the double spiral.

DEPENDENCE ON MACH NUMBER

We ran additional simulations with colder disks, since CV systems are characterized by relatively high Mach number. Colder disks have more tightly-wound spiral waves that decay faster with decreasing radii. In our coldest disk with an internal Mach number of order 40, the double spiral is gone inside a radius of about 0.1. In its place, one can see a single-armed spiral wave, but this too decays away before reaching the inner radius of the disk. Colder disks are also more unsteady, as seen in the animation. The figure below shows disks with sound speeds of 0.25, 0.125, and 0.0625.
The effective alpha, however, is still of order 0.1 in the outer regions of the accretion disk, where the double spiral is relatively strong.

DEPENDENCE ON MASS RATIO

We ran additional simulations with smaller (q=0.2, on the left) and larger (q=5, on the right) mass ratios. The strength of the spiral waves was relatively constant in all of these models.
The effective alpha is relatively independent of mass ratio. The only significant difference between these models is the location of the outer disk edge, as determined by tidal truncation.