Here we consider a new effect, the rotation of the system. In addition to the gravity body force, the fluid is now also subjected to the action of the centrifugal body force. However, the more important effect is that of the Coriolis accelerations which appear in the direction perpendicular to that of the speed (in the rotating system). Rotating fluids are a complicated topic even for homogeneous fluid (see Greenspan 1968; Ungarish 1993) and hence we shall consider only some simple systems which, nevertheless, provide useful insights and illustrate the power of the available theory. These are: (1) the axisymmetric current which spreads out radially in a cylindrical geometry, and (2) the current in a rotating channel which propagates mostly in the longitudinal direction in a Cartesian geometry. In both cases the propagation is over (or under) a horizontal boundary, the rotation is about a vertical axis with constant angular velocity Ω, viscous effects are negligible, and the Boussinesq simplification is valid.