Dimensionless Solutions of Border-Irrigation Advance

The equations of border-irrigation flow are written in dimensionless form and solved numerically at three different levels of mathematical approximation. For the advance phase three independent parameters exist: the Froude number based on normal depth, the dimensionless exponent of the Kostiakov infiltration equation, and a dimensionless parameter determining the deviation of flow conditions from normal. It is shown both by order of magnitude analysis and from the results of the numerical computation that the inertia terms in the governing equations are unimportant for border flow (Froude number approximately zero). The model governed by the remaining two parameters, the zero-inertia model, is used to generate dimensionless advance trajectories and related information for all practical combinations of these two parameters. An additional advance trajectory is computed for each value of the dimensionless infiltration exponent using the normal-depth model to show the range of applicability of the latter.