  Realistic computational simulations in different oceanic basins reveal
prevalent prograde mean flows (i.e. in the direction of topographic Rossby wave
propagation along isobaths; a.k.a. topostrophy) on topographic slopes in the
deep ocean, consistent with the barotropic theory of eddy-driven mean flows.
Attention is focused on the Western Mediterranean Sea with strong currents and
steep topography. These prograde mean currents induce an opposing bottom drag
stress and thus a turbulent boundary-layer mean flow in the downhill direction,
evidenced by a near-bottom negative mean vertical velocity. The slope-normal
profile of diapycnal buoyancy mixing results in down-slope mean advection near
the bottom (a tendency to locally increase the mean buoyancy) and up-slope
buoyancy mixing (a tendency to decrease buoyancy) with associated buoyancy
fluxes across the mean isopycnal surfaces (diapycnal downwelling). In the upper
part of the boundary layer and nearby interior, the diapycnal turbulent
buoyancy flux divergence reverses sign (diapycnal upwelling), with upward
Eulerian mean buoyancy advection across isopycnal surfaces. These near-slope
tendencies abate with further distance from the boundary. An along-isobath mean
momentum balance shows an advective acceleration and a bottom-drag retardation
of the prograde flow. The eddy buoyancy advection is significant near the
slope, and the associated eddy potential energy conversion is negative,
consistent with mean vertical shear flow generation for the eddies. This
cross-isobath flow structure differs from previous proposals, and a new
one-dimensional model is constructed for a topostrophic, stratified, slope
bottom boundary layer. The broader issue of the return pathways of the global
thermohaline circulation remains open, but the abyssal slope region is likely
to play a dominant role.
