Shallow Free-surface Flows Research Articles

Mechanism of structure formation in circular hydraulic jumps: numerical studies of strongly deformed free-surface shallow flows

We studied numerically circular hydraulic jumps of moderate Reynolds number to clarify the structure formation in circular hydraulic jumps. The numerical model has been constructed based on the CIP–CUP (cubic interpolated propagation–combined unified procedure) method, the level set method and the CSF (continuum surface force) model. The model can simulate strongly deformed interfaces as those found in hydraulic jump phenomena. In this study, we found that the pressure deviation from the hydrostatic equilibrium around the hydraulic jump is essential for the structure formation and that the surface tension plays an important role for the establishment of the pressure deviation.

Depth averaged and moment equations for moderately shallow free surface flow

The classical depth averaged St. Venant equations for shallow free surface flow are extended to treat problems with nonhydroslatic pressure and nonuniform velocity distributions. The equations required to solve for the additional degrees of freedom are derived by a moment weighted residual method from the fundamental Reynolds equations. The new equations are derived in detail in one horizontal dimension and evaluated for the basic problems of uniform flow and small amplitude waves. With further study and application, these new equations may offer a means for obtaining greater detail over a wider range of problems than is presently practical.