Thinking of time as a river is an interesting concept to me as there are many characteristics of time that are synonymous with that of a river. For example time as far as we are aware of it moves in one continuous direction, and yes while a river may not take the most direct route to the sea there is still a final destination in mind. (Although we have no knowledge of an end to time so this model doesn't fully fit)
Another example would be that a river is effected by many different currents/flows (turbulent, streamlined etc.) much the same way that relative movement effects time (the faster one moves, the closer they get to the speed of light, the more space time begins to break down) I feel this is synonymous with the turbulent flow of a river.
The flow is constantly accelerating as the flow is continuously changing direction, and as such (without any outward interference, such as the river bank in this example) the flow exponentially begins to become more chaotic/begins to break down more.
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