The influence of the bottom topography on the large-scale ocean circulation is discussed and illustrated with a simple model based on the ideal-fluid thermocline equations. The requirement that fluid remains in linear vorticity balance while conserving its density leads to a coupled problem, but one that can be reduced to a single characteristic equation under an assumption of uniform potential vorticity on density surfaces. The characteristics are intermediate between the f/H contours found in a homogeneous ocean and the f contours found in an ocean with a motionless abyss.
The extent to which topography influences the circulation in upper layers is quantified and is shown to depend on both the strength of the bottom currents and on the vertical profile of stratification. In a realistic limit, in which the abyssal waters are sluggish and weakly stratified, the circulation in surface layers is relatively indifferent to the topography beneath.
The direction in which a current deflects around a topographic obstacle of finite amplitude differs significantly from previous results for small amplitude obstacles. The path of the bottom streamlines is uniquely determined by the bottom density gradient upstream of the obstacle: if the topography shallows, then the abyssal streamlines deflect up the bottom density gradient; conversely if the topography deepens, then the abyssal streamlines deflect down the bottom density gradient. Streamlines for the depth-integrated flow follow a path determined by linear vorticity balance.
The model is generalized in study the interaction of a wind-driven gyre with a midocean ridge. Internal jets, embedded within the large-scale circulation, are found when the topography protrudes sufficiently into the main thermocline of the gyre.