The river-of-time metaphor symbolises the flow of time as the steady movement of a current along with all the flotsam it carries—and the events we experience are depicted by the particular pieces of flotsam being carried along past us by this current. Unfortunately, the movement of such a current can be understood only as a process which itself takes time to happen in; a certain movement of a piece of flotsam which has moved from a particular position to a new position somewhat further downstream can be understood only as a change of position plotted against time. That is, the supposed movement of the current and the flotsam it bears can only be understood as movement if it is given time in which to take place. The flow of the river of time cannot he conceived at all unless we introduce a second-order time against which the flow can be measured. If we introduce a second-order time, to be consistent we must picture this new time on the model of a flowing river, and if we do this, the same problem arises in that the movement of flotsam down this second river can he conceived only if we supply still another time in which it occurs. And of course, maintaining consistency dictates that this third time be interpreted as the flow of a river. Clearly the regress is vicious, and the only way to avoid it is to give up the belief that time flows like a river.
—Keith Seddon: Time: A Philosophical Treatment (1987)
Snapshot, likely of Long Beach Boulevard in Long Beach, California, completely submerged by floodwaters in February, 1916. (source)