[OAB 74] It is pointed out that "the meandering serpentine course of many rivers and canyons cut through many layers of strata." However, it is not completely clear what conclusion is intended to be drawn from this observation, so I will cover two different possibilities. One argument that I have heard is that meandering riverbeds will not maintain the same channel long enough to dig deep serpentine canyons, such as the San Juan River in Utah, because periodic flooding will break through to a straighter course, creating oxbow lakes, as happens with the lower Mississippi River. In fact there are two reasons why the riverbed of the lower Mississippi is not stable, and these two reasons are not necessarily present for all meandering riverbeds. The first is that the Mississippi floods rather frequently, and the second is that the lower Mississippi riverbanks are made of relatively soft material (soil and shale). In Utah, flooding is not as frequent, so the river will have time to cut a deeper canyon. Also, the riverbanks in Utah are made of hard sandstone, not soft shale. Both of these factors will make it much harder for floods to break through to a straighter course.
Not only are serpentine canyons easy to explain from an Old-Earth standpoint, they are virtually impossible within the Young-Earth model. A canyon formed in a short period of time by a huge torrent of water could not possibly be serpentine, because the flood would overflow the shallow meandering channel and form a more straight canyon. The only way for a river to be serpentine is for it to be flowing slowly (like the lower Mississippi River today), therefore a serpentine canyon can only be formed by a slow-flowing river. Since a slow-flowing river would take at least many tens of thousands of years to dig a deep canyon, these canyons cannot possibly be any younger than that.
Another possible argument simply notes that many present rivers are cutting into sedimentary strata (A.W. Mehlert, Creation Research Society Quarterly, v.25, no.3, pp.121-123 (Dec 1988), as cited in OAB). Of course, since rivers change their course relatively frequently, especially near their deltas, I see nothing implausible in the theory that a river flowed through a certain area, laying down sedimentary deposits, then changed course to a different area, and finally returned sometime later to erode its own sediment.