We analyse the variations of the director n and of the scalar order paramet
er S of a nematic liquid crystal in contact with a surface which imposes a
sinusoidal boundary distortion. The amplitude A of the surface profile and
the corresponding wavelength lambda vary in ranges compatible with the elas
tic regime Aq < 1, where q = 2 pi/lambda is the surface wave vector. The an
alysis is carried out by means of a Landau expansion of the free energy whe
re both n and S gradients are taken into account. We obtain an evident coup
ling between S and n in a nematic surface layer of thickness xi(S) of the o
rder of a few hundred Angstroms. Moreover S can vanish close to the surface
if the distortion imposed by the boundary conditions is strong enough. The
numerical approach presented in this paper is based on the finite element
method.