A simple two-dimensional model is developed for the perpendicular flow dynamics of boundary layers located on closed magnetic field lines in the equatorial magnetosphere. In addition to viscous damping in the equatorial region, nonlocal dissipation associated with the closure of field-aligned currents in the ionosphere and field-aligned potential drops is included and is shown to have two consequences: (1) coupling to the ionosphere causes large-scale disturbances to decay anisotropically and (2) field-aligned potential drops promote long-lived fluctuations at scale lengths that can be comparable to the ''inverted V'' scale but which vary with the local Hartmann number (a measure of the ratio of ionospheric resistive friction to magnetospheric viscous friction). Depending on the degree of anisotropy, the combined effect is a tendency for the two-dimensional flow to organize into either relatively isotropic eddies or essentially one-dimensional striations. The limiting case of a one-dimensional flow is considered with applications to the low-latitude boundary layer and internal magnetospheric shear layers. A particular boudary layer equilibrium state is compared with observations of an ionospheric boundary layer region and is found to be in fair agreement with the observed properties for reasonable values of the model parameters. It is also shown, under certain conditions, that a monotonically varying internal shear layer can form paired oscillations in the electric field, which are characteristic of the so-called ''V shocks'' that occur in and above the auroral acceleration region. ¿ American Geophysical Union 1987