  We perform numerical simulations of a turbulent channel flow over an
hyper-elastic wall. In the fluid region the flow is governed by the
incompressible Navier-Stokes (NS) equations, while the solid is a neo-Hookean
material satisfying the incompressible Mooney-Rivlin law. The multiphase flow
is solved with a one-continuum formulation, using a monolithic velocity field
for both the fluid and solid phase, which allows the use of a fully Eulerian
formulation. The simulations are carried out at Reynolds bulk $Re=2800$ and
examine the effect of different elasticity and viscosity of the deformable
wall. We show that the skin friction increases monotonically with the material
elastic modulus. The turbulent flow in the channel is affected by the moving
wall even at low values of elasticity since non-zero fluctuations of vertical
velocity at the interface influence the flow dynamics. The near-wall streaks
and the associated quasi-streamwise vortices are strongly reduced near a highly
elastic wall while the flow becomes more correlated in the spanwise direction,
similarly to what happens for flows over rough and porous walls. As a
consequence, the mean velocity profile in wall units is shifted downwards when
shown in logarithmic scale, and the slope of the inertial range increases in
comparison to that for the flow over a rigid wall. We propose a correlation
between the downward shift of the inertial range, its slope and the wall-normal
velocity fluctuations at the wall, extending results for the flow over rough
walls. We finally show that the interface deformation is determined by the
fluid fluctuations when the viscosity of the elastic layer is low, while when
this is high the deformation is limited by the solid properties.
