Dimensionless Stream Advance in Sloping Borders

The optimum choice of characteristic reference variables used to put the zero-inertia governing equations of continuity and momentum with boundary condition, into dimensionless form is not obvious. The effect of different choices is noted, as are the effects of choosing different formulas for field roughness and infiltration. The choice of normal depth for characteristic dept, a characteristic distance equal to the quotient of normal depth and bottom slope, and characteristic time equal to the time to travel the characteristic distance at normal velocity leads to a useful two-parameter set of dimensionless curves for advance prior to cut off in a border of indefinite length. These are presented for a series of Kostiakov-infiltration-formula dimensionless coefficients and exponents. It proves possible to present virtually all practical field and laboratory combinations of input variables—inflow rate and border slope, Manning roughness, and infiltration—in ten graphs, each spanning 3 log cycles.