# Hydrodynamics of Undular Free Surface Flows

## Abstract

In this study, the hydrodynamics of three types of steady undular free surface flow problems are theoretically analyzed. These flows are governed by the steady-state equations of conservation of mass and momentum developed by Bose and Dey in 2007 (J Hydraul Eng 133:1074–1079) and 2009 (Phys Rev E 80:036304). The first type of flow is an undular hydraulic jump on a plane smooth boundary when the approach flow Froude number marginally exceeds its critical value of unity. Here, it is established that the undular hydraulic jump phenomenon can be treated as an instability of the free surface flow being described by the instability principle. The results reveal that the threshold of an undular hydraulic jump is represented by a monotonic increase of approach flow Froude number with boundary inclination. The elevation of the undular free surface increases, as the boundary inclination increases. However, the amplitude of the free surface waves decreases with downstream distance. The second type of flow is that over a submerged hemi-cylindrical boss (inverted semi-circular section) placed on the channel bottom with its horizontal diameter lateral to the flow direction. The steady-state flow analysis shows that there is a drop in the free surface elevation on the downstream end of the cylinder with an undular free surface profile. The third type of flow is that over a continuous sinusoidal boundary of a channel. A numerical experiment shows that there exists a phase lag between the free surface profile and the boundary profile. Also, it is revealed that if the flow depth is reduced, an accumulation of heaved wave occurs indicating an onset of chocking.

## Keywords

Free Surface Flow Depth Wave Crest Hydraulic Jump Free Surface Elevation## References

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