  Oceanic geostrophic turbulence is mostly forced at the surface, yet strong
bottom-trapped flows are commonly observed along topographic anomalies. Here we
consider the case of a freely evolving, initially surface-intensified velocity
field above a topographic bump, and show that the self-organization into a
bottom-trapped current can result from its turbulent dynamics. Using
equilibrium statistical mechanics, we explain this phenomenon as the most
probable outcome of turbulent stirring. We compute explicitly a class of
solutions characterized by a linear relation between potential vorticity and
streamfunction, and predict when the bottom intensification is expected. Using
direct numerical simulations, we provide an illustration of this phenomenon
that agrees qualitatively with theory, although the ergodicity hypothesis is
not strictly fulfilled.
