  In the context of resonant absorption, nonlinearity has two different
manifestations. The first is the reduction in amplitude of perturbations around
the resonant point (wave energy absorption). The second is the generation of
mean shear flows outside the dissipative layer surrounding the resonant point.
Ruderman et al. [Phys. Plasmas 4, 75 (1997)] studied both these effects at the
slow resonance in isotropic plasmas. Clack et al. [Astron. Astrophys. 494}, 317
(2009)] investigated nonlinearity at the Alfven resonance, however, they did
not include the generation of mean shear flow. In this present paper, we
investigate the mean shear flow, analytically, and study its properties. We
find that the flow generated is parallel to the magnetic surfaces and has a
characteristic velocity proportional to $\epsilon^{1/2}$, where $\epsilon$ is
the dimensionless amplitude of perturbations far away from the resonance. This
is, qualitatively, similar to the flow generated at the slow resonance. The
jumps in the derivatives of the parallel and perpendicular components of mean
shear flow across the dissipative layer are derived. We estimate the generated
mean shear flow to be of the order of $10{\rm kms}^{-1}$ in both the solar
upper chromosphere and solar corona, however, this value strongly depends on
the choice of boundary conditions. It is proposed that the generated mean shear
flow can produce a Kelvin--Helmholtz instability at the dissipative layer which
can create turbulent motions. This instability would be an additional effect,
as a Kelvin--Helmholtz instability may already exist due to the velocity field
of the resonant Alfven waves. This flow can also be superimposed onto existing
large scale motions in the solar upper atmosphere.
