Water is flowing from one point to the next because of gravity. This seems very logic, but gravity has quite some impact on river features. Change in slope causes current speed differentials, having effects we want to take in account when paddling a river.

River sides

Naming river sides can be confusing. Is river right the right side of the one who's calling, the one who's watching, looking upstream, downstream, ... ?

The convention is easy, river right is the right side of the stream, when looking or paddling downstream. River left is the left side of the stream, looking or paddling downstream. So even when you're looking upstream and talking about the river bank on your left, you should name it river-right. Confusing? Maybe, until you get used to it.

Current differentials

As I mentioned earlier, current differentials can be caused by a change in slope of the river bed. But a cross section of a river, without obstacles, also has current differentials.

These differentials are present across the stream, but also from surface to the bottom.

The thickness of the lines in this image indicate the speed of the current.

As you can see the fastest current is in the middle of the stream, the closer you get to the borders the slower the water is moving in comparison to the water in the middle of the stream.

These differentials exists because of the nature of the river. The river is, in a classic, normal situation, the deepest in the middle, the shallowest at the sides. Water that is flowing over and between rocks and sand, is subject to breaking action. The greater the distance to the bottom, the smaller the effect of the breaking action and thus the faster the water is flowing.

We see the same kind of behaviour when watching a river flow top-down.

As mentioned next to the above picture, water flowing over rocks and sand suffers a breaking action. The greater the distance to the bottom the faster the water is flowing.

You do notice though that the thickest line is not at the surface, but just beneath. There is another, slightly slower flowing part of the water at the surface.

Water is flowing best on water. This effect causes the gradual speeding up of the flow when moving to the surface. Since water is the best option to flow on, air is less interesting to be in contact with. Air is having a slight but present breaking effect on the current. That's why a thin layer of surface flow is a bit slower and the fastest current is just beneath the surface.

The knowledge of the presence of these current differentials is important. Did you ever think of using those current differentials for a ferry or any other river manoeuvre? Or did you ever gave it a thought why your throwline is moving downstream slower then your swimmer you're trying to hit? More details will be present in the appropriate articles.

Bent current

When a river is moving around the corner, a bent is present. This bent creates a special situation for the current. Physics laws dictate that an object that is moving in a given directory, it keeps on moving in that given directory. That is exactly what water is doing.

Water keeps on moving straight forward until it gets stopped by the river bank on the outside of the bent. This changes the river behavior as described above. The fastest current is no longer in the middle of the stream, but is moving to the outside of the river.

Often, but not always, the river is the deepest at the outside and the shallowest at the inside.

The other effect of bents is that the water that is flowing at the inner side of the river, is relatively much slower then it is at the same side of a straight flowing river. Often, but not always, there is an eddy present on the inner side of a bent.

What an eddy is, I'll explain right away, but first I'll show a real life image of a bent current:

The yellow line is approaching the main current.

Eddies

Eddies exist behind obstacles in the river. When water is flowing down and an obstacle is in the way, water is flowing past it. At the first instance leaving a void behind the obstacle. We all know though that liquids try to equalize their level when the volumes are in connected with each other. This causes water to flow in a direction we'd call upstream, to fill that void.

Here is a diagram that shows such a behavior:

As you can see in the diagram, the water is gradually moving back towards the center of the river, using all the space again. The combination of these factors define the nature of the eddy: the size, the shape, the strength.

Important to notice here in this diagram is the fact that the lines are moving closer to each other when coming closer to the rock. In this diagram the distance between the lines is indicating how fast the current is flowing.

As you can see here, water is being blocked by a rock and thus pushed together to bypass that stone. The water flowing close by that rock is moving remarkably faster because more water has to pass through that channel in the same time. This is also a property you should take in account when approaching eddies on the river.

This image is showing an eddy next to the river bank. Again we see that water is speeding up (lines closer to each other) close to the rock.

This diagram is showing more though. Here the concepts: eddy line, eddy zone and current line are introduced.

The eddy line is clear, that's the border of the eddy, the light blue line in this diagram.
When we know that, the current line must be the dark blue line next to the red zone, indicating the border of current.
Then the red zone must be the eddy zone.

What's all the fuss about those colored lines and red zone? For now you only have to know that there is not just one line, but 2 with eventually a zone in between. Why these lines and zone are important, are explained in the section about approaching eddies. Do also remember that the eddy zone, the red one in this diagram, is a very unreliable zone. Water is flowing everywhere and nowhere. The presence of such a current zone is defined by the nature of the river, the nature of the obstacle and how fast the water is flowing.
The faster the water is flowing, the smaller the chance you encounter an eddy zone. An eddy behind a tree and/or tree roots is having a bigger chance of an awkward eddy zone. Slow moving rivers generally also have larger eddy zones.

A natural example:

The upper line is indicating the eddy line, the lower the current line. The mainstream is flowing from left to right at the bottom of the image. 

Downstream V 's

A downstream V indicates the area where you want to be, where the river is deepest and water moving through the easiest.

A downstream V is formed by 2 obstacles in the river.

Water is hitting an obstacle and being forced to move aside. When this happens on two sides, a channel is formed where the water can pass through. The borders of that channel are defined by faster moving water due to the obstacle being hit.

Notice that on this diagram only the current lines have been drawn. Behind the rocks eddies are present. The fact that you have an eddy zone, how close the eddy line and current line are to each other, is depending on the river.

Do also take in account that not every downstream-V is indicating an eddy on either side. Downstream-V's can also be formed when the river is getting narrower and thus having no eddies present.

Some images of natural downstream-V's: