  In this paper, we prove the global well-posedness and interior regularity for
the 2D Navier-Stokes equations driven by a fractional noise acting as an
inhomogeneous Dirichlet-type boundary condition. The model describes a vertical
slice of the ocean with a relative motion between the two surfaces and can be
thought of as a stochastic variant of the Couette flow. The relative motion of
the surfaces is modeled by a Gaussian noise which is coloured in space and
fractional in time with Hurst parameter greater than 3/4.
