Finite element analysis of finite gravity surges

Stable finite gravity surges in confined channels are investigated analytically using perfect-fluid theory, and the resulting Laplace equation is solved numerically by a finite-element method employing linear triangular elements. An iterative algorithm is developed which satisfies the nonlinear interface condition resulting from cross-interface pressure balance and momentum conservation in the direction of flow. The results are presented graphically and discussed. The overall Richardson number of the flow field, equal to 4 for an infinite surge (Benjamin, 1968), is found to increase as surge length and thickness decrease. Downstream receding flow can be either subcritical or supercritical, depending on Richardson number. The gravity-surge phenomenon occurs in the atmosphere, in saltwater/freshwater locks, in avalanches, and in sea-surface oil spills.