2. Literature Review
2.1 Introduction
Research into the components of the hydraulic characteristics found at low-head dam structures has taken place as far back as about a half century ago. Early investigations on the subject were chiefly concerned with the characterization of the submerged hydraulic jump which forms at most of these low-head dam sites. The initial investigations on this subject do not seem to acknowledge the life-threatening nature of these structures. They simply try to characterize the phenomena occurring in these locations.
In the last two decades attention has been drawn to the dangers that exist at low-head dams throughout the country. State governments have published several brochures and papers warning recreational users of the dangers. Newspaper articles show up all too often detailing the tragic drownings that take place at low-head dams every summer; yet, to date little has been done to rectify the problem. Some states, such as Minnesota, have started documenting low-head dam accidents. During the 29-year period ending in 2002,
The Boat and Water Safety Section of the Minnesota Department of Natural Resources reported 53 deaths and 50 injuries at low-head dams throughout the state (Tschantz
2003). While this is an alarming figure, many states do not keep such specific statistics, so the aggregate effect of these dangerous hydraulic structures can not be adequately quantified. Though the effects can not be positively identified it is clear that safety concerns at low-head dams must be addressed.
This section focuses on detailing previous research on hydraulic jumps and the recirrculating currents produced at low-head dams. Attempts will be made to outline

previous research and present pertinent equations used in the understanding and control of these hydraulic characteristics. Furthermore, five existing retrofits or alteration plans are illustrated using the information presented by the source.
2.2 Hydraulic Jump
Hydraulic jumps occur most commonly in man-made channels as a way to dissipate energy, usually gained from dropping over an overflow structure. A hydraulic jump occurs when flow changes from supercritical to subcritical levels. According to Hwang and Houghtalen (1996), critical flow is the flow at which a flow rate, [Q], can be passed with minimum energy. This occurs at the critical depth. Therefore, it follows that if the water level in the structure drops, the velocity must increase in order to convey the same flow. This situation is called supercritical flow. When the water depth is greater than the critical depth the flow is called subcritical, which results in a lower velocity necessary to handle the same Q. The flow regime can be characterized by a comparison of the unit inertial reaction to the unit gravitational force or Froude number, F , (Forester & Skrinde
1949). It is defined by Foster & Skrinde (1949), Leutheusser & Birk (1991), and
Leutheusser & Fan (2001) as follows:
F

V
1 gd
1
(1)
By definition when F =1 the flow is critical, when F >1 supercritical flow has developed, and when F <1 the flow is subcritical. The water levels before and after the hydraulic jump, or, the change from super critical to subcritical flow, is defined by the Belenger

equation (Foster & Skrinde (1949), Leutheusser & Birk (1991), and Leutheusser & Fan
(2001) : d
2 d
1

1
2
1

8 F
1
2 
1

(2)
The flow rate per unit width of overflow [q] can be determined using the head on the overflow (Leutheusser & Birk (1991), and Leutheusser & Fan (2001) : q

2
3
C w
2 g H
3
2
(3) where C w

.
611

.
075
H
P
(4)
According to Foster & Skrinde (1949) and Leutheusser & Birk (1991) a hydraulic jump will form when the downstream depth [ d
2
] satisfies equation 2 meaning that the downstream velocity and subcritical Froude number are the important characteristics in determining the structure height and optimal hydraulic jump location (Leutheusser &
Birk 1991). From this equation it can be seen that there is an ideal manner for the jump to form. In reality these conditions do not occur readily in the field.
2.3 Submerged Hydraulic Jump
The ideal situation does not usually occur at low-head dams. The phenomenon which takes place at these structures is referred to as a submerged hydraulic jump. When the tail water [ d
2
] raises to become higher than the ideal condition would require in eq.2 the

jump becomes submerged. A submerged hydraulic jump sweeps back on itself and creates a vortex (Leutheusser & Fan 2001). According to Leutheusser and Fan this vortex swirls on a horizontal axis creating a strong upstream surface velocity, pushing whatever it comes in contact with back into the dam (2001). Rajaratnam (1965) and
Leutheusser and Fan (2001) have the described the behavior in terms of submergence of the jump using the relationship:
S
 d t
 d
2 d
2
(5)
The optimal jump occurs when S = 0, the jump is swept downstream if S < 0, and the dangerous submerged jump happens when S > 0 (Leutheusser & Fan 2001). This relation illustrates the fact that the submerged jump occurs if the tailwater depth downstream of an overflow structure exceeds the subcritical depth of the hydraulic jump (Leutheusser &
Fan 2001).
The horizontal surface velocity of the upstream directed wave was first modeled by
Leutheusser and Birk (1991). With their initial investigation they developed a rough estimate for the surface velocity. In accordance with predicted results the velocity directed upstream decreased as the tailwater increased (Leutheusser and Birk 1991).
They also state that the maximum human swimming velocity is about 2m/s, which will be used for comparison wherever necessary. It is also important to remember that a 2m/s swimming velocity is only achievable by Olympic class athletes and would probably not be possible over the extended period of time necessary to escape the recirculating current.

In 2001 Leutheusser and Fan developed a more comprehensive way to predict the maximum upstream directed velocity. The velocity can be predicted using the equation:
V s
V
1




 
S

1

16

E 
1
 dm
8 F
1
2 d
1

1

F
1
2



1
3
(6)
The experimentation of Leutheusser and Fan supports their statement that the maximum upstream velocity, [ V s
], is about one-third the unsubmerged jump supercritical inflow velocity V
1
(2001). Using general hydraulic methods as well as the relationships determined by previous research it should be possible to quantify the dangerous hydraulic features occurring at low-head dam structures.
2.4 Alternatives/Solutions
Increased Spillway Elevation
According to Leutheusser and Birk (1991) many overflow structures are constructed too low to produce a hydraulic jump that effectively dissipates the increased kinetic energy of the flow. Although the operational requirements of the low-head dams were satisfied, he claimed that engineers failed to notice that the low overflow structures did not allow the flow to go through the optimal, free hydraulic jump. The faulty hydraulic condition, therefore, posed great danger. His suggestion for eliminating the dangerous rollers, produced at the base of low-overflow structures, was to simply elevate the height of the dam. He claimed that by using the combination of tailwater depth and the rate of flow at the downstream end of the roller it is possible to determine the required height of the overflow structure that will produce the optimal hydraulic jump. However, Leutheusser

and Birk , realized that the required height in many cases would be so great that this design option would become impractical (1991).
Baffled Chutes
Leutheusser and Birk suggested an alternative retrofit which would eliminate the
“hydraulic” of overflow structures completely (1991). See Figure 1. He claimed that the
“baffled chute spillways” feature “continuous energy dissipation by cascade action”
(Leutheusser & Birk 1991). Hotchkiss and Comstock (1992) did an experiment involving the baffled chutes described by Leutheusser and they found the claim to be flawed. The authors argued that while the baffled chutes did dissipate energy by creating turbulence, they presented a new safety hazard for boaters navigating through the baffles.
The float used in their experiment often got trapped among the baffled chutes.
Furthermore, the collected floating and suspended debris may result in the overtopping of the basin and damage to the baffle blocks (Anonymus). This occurrence would require regular cleaning of the blocks.
Figure 1. Baffled Chute Basin. (Dam Safety 1999)

Labyrinth Weir
Hauser et. al. (1991) proposed an alternative design, called a labyrinth weir (Figure 2), for low-head hydropower dams. The new structure increases minimum flow between generating periods. Hauser et. al. claim that high discharge per unit width may develop rollers. They pointed out that by enlarging the crest length of the labyrinth weir the discharge per unit width would reduce. This effect would therefore limit the chance of roller formation. In his conclusion, Hauser et. al. list a few disadvantages of this design.
The disadvantages include the difficulty of increasing the crest length and the nonnavigable nature of the labyrinth.
Figure 2. Labyrinth Weir. (Physical Hydraulic 2005)
Stepped Spillways
Stepped Spillways are also used as energy dissipaters for low overflow structures (Figure
3). The flow over the steps can be categorized as nappe flow or skimming flow. In the

nappe flow, water hits each step as a “falling jet, with the energy dissipation occurring by jet breakup in air, jet mixing on the step, with or without the formation of a partial hydraulic jump on the step” (Rajaratnam 1990). In the skimming flow, the flow from each step travels as a consistent stream, “skimming” over each step creating recirculating vortices. The momentum transfer to these vortices enhances the energy dissipation over the structure. Christodoulou (1992) conducted experiments to validate Rajaratnam’s estimates on the energy loss over stepped spillways. He determined that the amount of energy lost is mainly governed by the ratio of the critical depth of the water flow passing over the spillway to the step height ( d c
/h) , and the number of steps N. He also found that a greater number of steps and decreasing values of d c
/h result in increased energy dissipation over the spillway. With further experimentation Chamani and Rajaratnam
(1994) were able to present a method to estimate the energy loss within the nappe region flow and find a relationship for the variation of energy loss at each step. To retrofit a low head dam, Freeman and Garcia (1996) constructed a four- and a six-step spillway. They concluded that even though the six-step spillway performed better, the four-step arrangement is more cost effective and a more feasible solution.
Figure 3. Four-step spillway. (Freeman 1996)

Rock Arch Dam Conversion
There is ongoing investigation on the effectiveness of a new retrofit for low-head dams, called rock arch rapids. Dr. Luther Aadland, who designed the retrofit, is currently taking data at multiple locations where the design has been implemented. The retrofit design uses 3 different sized field stones, which are placed as seen in Figure 4. The downstream end of the rock arch rapids curves and then becomes flat as it approaches the dam crest.
The slope of the rapid is approximately 5%, which allows fish to swim upstream. The slope of the weirs varies to match the grade. “Weirs are integrated into the bank and gaps between the large boulders near the bank are filled with smaller stones to reduce leakage and create pools” (Aadland 2005). The weirs add stability to the rapids and direct flow down toward mid-channel; consequently, the flow velocity and stress on the river banks is reduced. Aadland claims that the retrofit completely eliminates the “hydraulic” and provides a pathway for migrating fish. The varying sized stones are necessary since each size serves a specific purpose. The size of the field stones or boulders range between three and six feet in diameter. They are set 1 foot above the grade and are spaced according to the slope for a maximum of one foot head loss per weir (Aadland 2005).
The size of the smaller field stones change from one foot to three feet depending on the shear stress exerted on the rocks due to the varying flow rates. Finally, “cobble” is used for filling voids near the crest. The size of a cobble can be between one and six inches in diameter. Because this design has not been fully examined, only one of its likely disadvantages, its permanence, was expressed.

FLOW 5% slope or lower
R
E
S
T
D
A
M
C
SLOPE
Figure 4 . Rock Arch Dam Conversion (Aadland 2005).
Notation:
The following are used in the paper: g = acceleration due to gravity
F = Froude number
F
1
= Froude number at jump inflow d
1
= supercritical depth d
2
= subcritical depth d c
= critical depth
N = number of steps h = step height
H = head on weir q = flow rate per unit width
S = submergence d t
= local tailwater depth of channel
V s
= surface velocity

E dm
= change in energy defined in Leutheusser & Fan 2001

= Experimental constant found in Table 1 of Leutheusser & Fan 2001

References
Aadland, Luther (personal communication, June 9, 2005)
Chamani, M.R. and Rajaratnam, N. (1994), “Jet Flow on Stepped Spillways,” Journal of
Hydraulic Engineering , ASCE, Vol. 120, No. 2, pp 245-259.
Christodoulou, G. C. (1993), “Energy Dissapation on Stepped Spillways,”
Journal of
Hydraulic Engineering , ASCE, Vol. 119, No. 5, pp 644-650.
Leutheusser, H. J. and Birk, W.M (1991), “Downproofing of Low Overflow Structures,”
Journal of Hydraulic Engineering , ASCE, Vol. 117, No. 2, pp 205-213.
Freeman, J.W. and Garcia, M.H. (1996), “Hydraulic Model Study for the Drown
Proofing of Yorkville Dam, Illinois,” (Hydraulic Engineering Series No. 50).
University of Illinois, Civil Engineering Studies.
Hauser. G. E., Shane, R. M and Brock, W.G. (1991), “Innovative Reregulation Weirs for
Dam Releases, “ Proc. 1991 Nat. Conf. on Hydr. Eng., ASCE, Jul. 29- Aug 2, pp
178-183.
Hoctkiss, R. and Comstock, M. (1992), Discussion of “Downproofing of Low Overflow
Structures,”
Journal of Hydraulic Engineering , ASCE, Vol. 118, No. 11, pp
1586-1588.
“Physical Hydraulic Modeling of the Dam,”
City of Waco, Water Utility Services ,
Retrieved on June 20, 2005 from http://www.waco-texas.com/brazosdesign.htm.
Rajaratnam, Nallamuthu. (1990), “Skimming Flow in Stepped Spillways,” Journal of
Hydraulic Engineering , ASCE, Vol. 116, No. 4, pp 587-591.
Rajaratnam, Nallamuthu. (1965), “Submerged Hydraulic Jump”.
Journal of Hydraulics.
ASCE Vol. 91, pp. 71-96.
Forester, J.W. and Raymond A. Skrinde. (1949). “Control of the Hydraulic Jump by
Sills”. Transactions of the American Society of Civil Engineers. Vol. 115, pp.
973-1022.
Leutheusser, Hans J. and Jerry J. Fan. (2001). “Backward Flow Velocities of Submerged
Hydraulic Jumps”. Journal of Hydraulic Engineering. ASCE, Vol. 129, pp. 514-
517.