**2.2.3 Other topics**

In addition to the general aspects mentioned above, a list of specific items is also presented here. The first item, cavitation, is among them, being one of major relevance for spillway flows. It is known that the air/water mixture does not damage the spillway for void fractions of about 5% to 8% (Peterka, 1953). For this reason, many studies were performed aiming to know the void fraction near the solid boundary and to optimize the absorption of air by the water. Additionally, the risk of cavitation was analyzed based on instant pressures observed in physical models. Some specific topics are show below:


10. Use of spaced steps;

244 Hydrodynamics – Natural Water Bodies

(a) (b)

The sketch of Figure 6b emphasizes the existence of rolls downstream from the inception position of the aeration. Further experimental studies, such as Chamani & Rajaratnam (1999a, p.363) and Ohtsu et al. (2001, p.522), showed that the incorporated air flow distributes along the depth of the flow and reaches the cavity below the pseudo-bottom,

The mentioned studies of multiphase flows in spillways (among others) thus generated predictions for: (1) the position of the inception point of aeration, (2) profiles of void fractions (3) averages void fractions over the spillways, (4) characteristics of the bubbles. As mentioned, frequently the conclusions obtained for smooth spillways were used as basis for studies in stepped spillways. See, for example, Bauer (1954), Straub & Anderson (1958), Keller & Rastogi (1977), Cain & Wood (1981), Wood (1984), Tozzi (1992), Chanson (1996),

In addition to the general aspects mentioned above, a list of specific items is also presented here. The first item, cavitation, is among them, being one of major relevance for spillway flows. It is known that the air/water mixture does not damage the spillway for void fractions of about 5% to 8% (Peterka, 1953). For this reason, many studies were performed aiming to know the void fraction near the solid boundary and to optimize the absorption of air by the water. Additionally, the risk of cavitation was analyzed based on instant pressures

Boes (2000), Chanson (2002), Boes & Hager (2003b) and Wilhelms & Gulliver (2005).

observed in physical models. Some specific topics are show below:

4. Characteristics of hydraulic jumps downstream of stepped spillways;

6. Recommendations for the design of the height of the side walls;

7. Geometry of the crest with varying heights of steps;

Reference: (a) Sorensen (1985, p.1467) and (b) Peyras *et al.* (1992, p.712).

where large eddies are maintained by the main flow.

Fig. 6. Illustration of the flow

**2.2.3 Other topics** 

1. Cavitation;

5. Plunging flow;

2. Channels with large steps; 3. Stepped chutes with gabions;

8. Aerators for stepped spillways;

9. Baffle at the far end of the stepped chute;


As can be seen, stepped chutes are a matter of intense studies, related to the complex phenomena that take place in the flows along such structures.
