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Hydraulic jump in a rectangular channel, also known as classical jump, is a natural phenomenon that occurs whenever flow changes from supercritical to subcritical flow. In this transition, the water surface rises abruptly, surface rollers are formed, intense mixing occurs, air is entrained, and often a large amount of energy is dissipated.
In the mild reach, the hydraulic jump occurs downstream of the gate, but in the steep reach, the hydraulic jump occurs upstream of the gate. It is important to note that the gradually varied flow equations and associated numerical methods (including the standard step method) cannot accurately model the dynamics of a hydraulic jump. [6]
Figure 4: An undular front on a tidal bore. At this point the water is relatively deep and the fractional change in elevation is small. A tidal bore is a hydraulic jump which occurs when the incoming tide forms a wave (or waves) of water that travel up a river or narrow bay against the direction of the current. [16]
The momentum equation for open-channel flow may be found by starting from the incompressible Navier-Stokes equations : ⏟ + ⏟ ⏞ = ⏟ + ⏟ ⏟ + ⏟ where is the pressure, is the kinematic viscosity, is the Laplace operator, and = is the gravitational potential.
The coefficient, 3.1 varies for different entrance conditions. The value of the coefficient is slightly higher if the conveyance channel has a greater width than the inlet. The value 3.1 is based on the assumption that H e and v a are measured at a location that exhibits subcritical flow conditions.
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The shallow-water equations in unidirectional form are also called (de) Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant (see the related section below). The equations are derived [ 2 ] from depth-integrating the Navier–Stokes equations , in the case where the horizontal length scale is much greater than the vertical ...
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