Sure it can. In an incompressible flow (e.g. water under anything resembling normal circumstances), there is no net flow into or out of any given volume, i.e.

Sure it can. In an incompressible flow (e.g. water under anything resembling normal circumstances), there is no net flow into or out of any given volume, i.e. a 3-D box or other shape. But the surface is 2-D! So you can look at a little box with its top at the surface and its bottom slightly below the surface. If there is downward flow out the bottom (and zero flow out the top, of course), there must be net inward flow in the sides. Nothing wrong with that. This could happen if the river has constant speed and constant cross-sectional area everywhere but gets progressively narrower and deeper. The water moves inward because it has to get away from the encroaching banks and moves down to fill the deepening channel. If this is abrupt enough even in the absence of turbulence, the downward current a foot or so below the surface will be substantial.