Please explain why do long rivers ( such as the Nile ) flow along serpentine paths rather than straight?
There are two processes at work that cause rivers to become serpentine, erosion and sedimentation. At a given point in time, if a river is in a steady state, these two processes are in equilibrium, the rate of erosion, or soil being removed from the riverbed is equal to the rate of sedimentation, or silt being deposited on the riverbed. But this is not a stable point. If any disturbance causes the speed of the water on one side of the river to go faster (or slower) than the water on the other side of the river, this equilibrium is broken. On the side of the river that temporarily moves faster, erosion increases and the river becomes deeper and wider. On the other side where the water temporarily moves slower, sedimentation increases, and the river becomes shallower and narrower. These effects compound the original disturbance and the process accelerates, and the first curve in the river is created and will continue to grow.
It is this first curve that causes the forces to build the corresponding second curve. As discussed above, the water flowing on the outside of the first curve has a greater velocity than the water flowing on the inside of the first curve. As the first curve grows, this faster moving outside water enters the straight section of the river at an increasing angle, which directs a greater volume of water at the riverbank opposite the first curve. This greater volume of faster moving water is in essence an original disturbance to a stable, straight river as above, except it occurs on the opposite side. Hence, in this case the opposite bank erodes faster where as sedimentation increases along the inner bank creating a second curve that forms the shape of an S.
Jim Aspell, M.S., Gradient Consulting Group
It isn't only long rivers that are prone to the serpentine shape, it's actually every moving body of water. When considering rivers, however, you must take into account a number of factors. These are gradient, soil density, soil composition, and the characteristics of rainfall.
When it rains, if the ground is tilted in any direction, a portion of the water will immediately run off, and a portion will stay in the soil. The part that runs off follows the direction of the highest gradient, that is, the steepest path downhill. The remainder gets absorbed by the soil. This is determined by the soil density and composition. Dry clay, for example, will run off almost all of the water in a hard, fast rain, but in a slow soaking rain will gradually turn into mud. The soil density and composition also affect the percolation of the soil, ie - the rate at which it can absorb water. Returning to our earlier point when water runs across the ground, it erodes the ground it's on. This creates a small depression which is more likely to divert water flow in the future. You can see that this is an accelerating path. Even if the ground is perfectly flat, the soil is probably not uniform all the way across, and will still sink differently, causing a flow.
No matter which mechanism causes the water to flow, gradient or composition or both, once the flow starts, it continues in an accelerating spiral of development, so long as the waterflow is reliable. When you look at the larger pattern of streams and rivers in a country or continent, you can see that they work from smaller to larger, and transport water to the oceans.
Rivers don't form in straight lines, because they always follow the steepest gradient, and they usually follow the softest soils. This process can continue for thousands of years as a river gouges down into the rock, leaving something like the Grand Canyon behind if conditions are right.
Frank DiBonaventuro, B.S., Air Force officer, Physics grad, The Citadel
What causes a river to meander is flat / low gradient terrain. When a stream reaches relatively flat terrain / a plain, it slows up because the ground slope cannot sustain the velocity the stream had at steeper topography ( ground profiles).
As it slows the stream spreads because of the continuity of flow requirement i.e. that the volume rate of flow from the steeper zone must be maintained at the flat zone.
Further, in spreading, the water along the horizontal perimeter of the flow flows faster than that along the middle path of flow since the former has a greater distance to travel. This hydrodynamic phenomenon is similar to the phenomenon that causes uplift in airplanes in which the air flowing over the upper surface of the plane flows faster than that flowing beneath.
Two factors then come into play:
(i) sediment drops out of the middle path of the stream more readily than out of the perimeter zones causing the build up of an embankment that impedes further flow
(ii) the faster moving perimeter flow scours the channel more than the middle stream flow.
After a flood say therefore, the subsiding waters will find an easier path along the perimeter of flow of retarded flow zones than along their original direction. The water will therefore tend to divide into two downstream channels.
These perimeter paths will never be equally fluent and so the stream of water further chooses the more fluent of the two resulting in a meander.
Meanders therefore develop in rivers flowing through relatively flat areas as opposed to long rivers.
Roger Yearwood, B.S., BSc CE, UWI, Trinidad & Tobago
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'