The Principle of Gradient Selection
Flows of mass and energy occur along the steepest gradients of potentials or concentrations. The principle of gradient selection is simply that features associated with these gradients persist and grow. Take, for instance, the redistribution of excess (i.e., more than the ground can absorb or retain) surface water. Hydraulic selection principles favor the most efficient paths, which we can generally interpret as the fastest pathways. Thus the steepest slopes and/or the routes with the lowest resistance to flow attract more water. The most efficient paths persist and prevail; less efficient options dry up. For example:
Standard flow resistance equations are of the general form
V = f(RaSbf-c)
where R is hydraulic radius (cross-sectional area divided by wetted perimeter; typically roughly equal to mean depth), S is slope (hydraulic gradient), and f is a roughness or frictional resistance factor. The exponents a, b, c < 1. For example, the D’Arcy Weisbach equation is
V = 8g R0.5 S0.5 f-0.5