The effects of stratification, planetary rotation and a sloping bottom combine to produce an asymmetric response in which the characteristics of an oceanic bottom boundary layer depend on the direction, in addition to the magnitude, of the along-isobath velocity in the inviscid interior. The asymmetric response is examined theoretically under idealized conditions in which the motion begins from rest, the flow is uniform in the along-isobath and cross-isobath directions, and the water column is initially uniformly stratified. The analysis is based on an integrated model, in which the bottom stress is determined from a quadratic drag law, and the height of the boundary layer is determined from a Pollard–Rhines–Thompson mixing criterion. The model indicates rapid mixing at the onset of forcing to a height limited by planetary rotation and interior stratification, followed by evolution in which the height of the boundary layer may either increase or remain fixed near its initial value, depending on the behavior of the buoyancy within the boundary layer and the shear across the top of the layer. The model indicates reduction of the velocity within the boundary layer with increasing time, as a result of increasingly important buoyancy forces acting in opposition to the forcing by the dynamic pressure gradient. Model results compare favorably with previous turbulence closure computations, and the model reproduces the qualitative asymmetric behavior apparent in observations of boundary layer height.