  We study the so-called homogeneous model of wind-driven ocean circulation,
also known as the single-layer quasigeostrophic model. Our attention focuses on
performing a complete asymptotic analysis that highlights boundary layer
formation along the coastal line. We assume rough coasts without any particular
structure, resulting in the study of a nonlinear PDE system for the western
boundary layer in an infinite domain. As a consequence, we look for the
solution in nonlocalized Sobolev spaces. Under this hypothesis, the eastern
boundary layer exhibits a singular behavior at low frequencies far from the
rough boundary leading to issues with convergence. The problem is tackled by
imposing ergodicity properties. We establish the well-posedness of the
governing boundary layer equations and the approximate solution. Our results
generalize the ones in the paper of Bresch and G\'erard-Varet (Commun. Math.
Phys. (1) 253: (2005), 81-119) in the context of periodic irregularities.
