Using a 2.5D time-dependent numerical code we recently developed , we solve the full compressible Navier-Stokes equations to determine the structure of the boundary layer between the white dwarf and the accretion disk in non-magnetic cataclysmic variable systems .
In this preliminary work , our numerical approach does not include radiation .
In the energy equation , we either take the dissipation function ( \Phi ) into account or we assume that the energy dissipated by viscous processes is instantly radiated away ( \Phi = 0 ) .
For a slowly rotating non-magnetized accreting white dwarf , the accretion disk extends all the way to the stellar surface .
There , the matter impacts and spreads towards the poles as new matter continuously piles up behind it .
We carry out numerical simulations for different values of the alpha viscosity parameter ( \alpha ) , corresponding to different mass accretion rates .
In the high viscosity cases ( \alpha = 0.1 ) , the spreading boundary layer sets off a gravity wave in the surface matter .
The accretion flow moves supersonically over the cusp making it susceptible to the rapid development of gravity wave and/or Kelvin-Helmholtz shearing instabilities .
This BL is optically thick and extends more than 30 degrees to either side of the disk plane after only 3/4 of a Keplerian rotation period ( t _ { K } =19s ) .
In the low viscosity cases ( \alpha = 0.001 ) , the spreading boundary layer does not set off gravity waves and it is optically thin .