During the last two solar minima in the distant heliosphere the equatorial heliospheric plasma velocity oscillated perpendicular to the ecliptic plane with an approximately 26-day period in the distant heliosphere. Two explanations have been proposed: compressive interactions between streams and velocity shear interactions that produce a K¿rm¿n vortex street. The latter interpretation has been challenged on the basis that the velocity jumps are supersonic, thereby suppressing the Kelvin-Helmholtz (K-H) instability. Here we examine this issue using a time-dependent compressible magnetohydrodynamics code solved in spherical coordinates in the two-dimensional r-&thgr; plane. We conclude that supersonic flow does suppress small-scale instabilities and that the classic K¿rm¿n vortex street cannot be excited. Both velocity shear layers and stream interactions can, however, produce signatures in density, velocity, and magnetic field that resemble the observations. In particular, we find north-south variations of the flow velocity with a period that is approximately half that of the period of the variation in flow speed: a result insensitive to the thickness of the velocity shear layers. A depletion in density (and magnetic field magnitude) relative to the expected Parker value is predicted by the simulations that generate the north-south flow via velocity shear. The Voyager spacecraft observed a similar depletion in the outer heliosphere during the last two solar minima. When the effective tilt of the plasma sheet is increased, corotating interaction regions produce shock waves and other complex time-dependent evolution. We conclude that at solar minimum the observed north-south oscillations are a robust phenomenon that can form from either the interaction of fast and slow solar wind streams or from velocity shear. Which mechanism dominates is a consequence of the degree of tilt of the heliospheric current sheet, the magnitude of the velocity shear, and other physical parameters. However, the depletions seen in density and magnetic flux in the Voyager data suggest that velocity shear in the outer heliosphere at solar minimum may be the dominant cause of the observed north-south flow patterns. ¿ 2001 American Geophysical Union