Potential and Kinetic Energy:
A river follows the path of least resistance as it flows downhill under the influence of gravity. A river possesses potential energy, and tries to maximise the rate of flow by reducing the amount of energy it loses through friction by taking the path of least resistance. Most friction happens along the bed and banks, but there is also internal and air friction.
The deep side will be more efficient, and near the surface the flow will be slower because of the air resistance. The river wants to change it's potential energy to kinetic energy and flow along a graded profile.
Laminar Flow is the horizontal movement of water but it's impossible basically.
Turbulent flow consists of a series of erratic eddies both vertical and horizontal in a downstream direction. It varies with the velocity of the river, which depends on the amount of energy it has after it has overcome friction.
Symmetrical vs Asymmetrical Channels
Where the river is straighter the channel will be more symmetrical.
Asymmetrical channels are usually found in meanders in a river.