  To close the overturning circulation, dense bottom water must upwell via
turbulent mixing. Recent studies have identified thin bottom boundary layers
(BLs) as locations of intense upwelling, yet it remains unclear how they
interact with and shape the large-scale circulation of the abyssal ocean. The
current understanding of this BL--interior coupling is shaped by 1D theory,
suggesting that variations in locally produced BL transport generate exchange
with the interior and thus a global circulation. Until now, however, this
picture has been based on a 1D theory that fails to capture the local evolution
in even highly idealized 2D geometries. The present work applies BL theory to
revised 1D dynamics, which more naturally generalizes to two and three
dimensions. The BL is assumed to be in quasi-equilibrium between the upwelling
of dense water and the convergence of downward buoyancy fluxes. The BL
transport, for which explicit formulae are presented, exerts an influence on
the interior by modifying the bottom boundary condition. In 1D, this BL
transport is independent of the interior evolution, but in 2D the BL and
interior are fully coupled. Once interior variables and the bottom slope are
allowed to vary in the horizontal, the resulting convergences and divergences
in the BL transport exchange mass with the interior. This framework allows for
the analysis of previously inaccessible problems such as the BL--interior
coupling in the presence of an exponential interior stratification, laying the
foundation for developing a full theory for the abyssal circulation.
