  The non-axisymmetric features observed in the discs of dwarf novae in
outburst are usually considered to be spiral shocks, which are the non-linear
relatives of tidally excited waves. This interpretation suffers from a number
of problems. For example, the natural site of wave excitation lies outside the
Roche lobe, the disc must be especially hot, and most treatments of wave
propagation do not take into account the vertical structure of the disc.
  In this paper I construct a detailed semi-analytical model of the non-linear
tidal distortion of a thin, three-dimensional accretion disc by a binary
companion on a circular orbit. The analysis presented here allows for vertical
motion and radiative energy transport, and introduces a simple model for the
turbulent magnetic stress. The m=2 inner vertical resonance has an important
influence on the amplitude and phase of the tidal distortion. I show that the
observed patterns find a natural explanation if the emission is associated with
the tidally thickened sectors of the outer disc, which may be irradiated from
the centre. According to this hypothesis, it may be possible to constrain the
physical parameters of the disc through future observations.
