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11.1 SURFACE WAVES
Surface waves are unsteady open-channel flow features typically occurring under high Froude-number flows.
Figure 11-1 shows a surface wave on the Hassayampa river,
near Morristown, Arizona (Phillips and Ingersoll, 1998).
The disturbance is a wave propagating slowly downstream, and it is indicative of
hydraulic characteristics in alluvial channels under upper-regime flow conditions
Figure 11-3 shows the Santa Catarina river, at Monterrey, Nuevo Leon, Mexico, during the passage of Hurricane Gilbert, on September 17, 1988. The observed large surface waves are an indication of the high Froude-number flows which most likely prevailed during the passage of the flood.
Surges are perturbations created by sudden gate closures or rapid changes in stage or flow depth. Typically, a surge does not attenuate readily, traveling along the channel for a considerable distance. Surges are avoided by opening gates slowly, to minimize the possibility of sudden stage or depth changes. Surge attenuation increases as the dimensionless wavenumber decreases from that corresponding to a true dynamic wave (with constant celerity, i.e, to the right side of the wavenumber spectrum) to that corresponding to a mixed dynamic wave (with variable celerity, i.e., along the upper falling side of the S-curve) (Fig. 11-4).
Based on the above criterion, a first approximation to the time of opening To of a canal gate, to avoid a surge, is (Ponce et al., 1999):
in which uo = flow velocity, So = channel slope, g = gravitational acceleration, and k = a constant varying with Froude number as shown in Table 11-1.
11.3 KINEMATIC SHOCKS
Kinematic shocks are kinematic waves that have steepened to the point where they become, for all practical purposes, a wall of water, with a near vertical face. Actually, the shock is not a perfect discontinuity; however, its thickness is relatively small compared to the wavelength of the disturbance (Lighthill and Whitham, 1955).
Kinematic waves travel downstream, and may either steepen or flatten out, depending on their interaction with the cross-sectional geometry. Only kinematic waves that steepen can develop into kinematic shocks. While kinematic waves are gradually varied, kinematic shocks are rapidly varied.
The development of a kinematic shock is a function of the following flow conditions (Ponce and Windingland, 1985):
Thus, kinematic shocks will develop in field situations involving: (a) a kinematic wave, (b) an ephemeral channel (zero baseflow), (c) a high flow rate (a flood), and (d) a hydraulically wide channel. This may be the case of a major cloudburst rapidly concentrating flow through a canyon in a semiarid region.
A well-documented flash flood, which was in all probability a kinematic shock, occurred July 26, 1981 in Tanque Verde Creek, a tributary of the Santa Cruz river, in eastern Arizona. The flood, which killed eight people, was, by all accounts, only a 2-yr flood. However, the suddenness of the flood which, according to survivors' reports amounted to a "wall of water," resulted in substantial loss of life (Hjalmarson, 1984).
Kinematic shocks have been observed with certain frequency in laboratory overland flow computations. These computations are known to be conducive to kinematic shock development (Kibler and Woolhiser, 1970). The shock presence is attributed to the prescribed spatial regularity which is necessary to make the problem more tractable.
11.4 ROLL WAVES
Roll waves develop in open-channel flow when the Vedernikov number V > 1 (Craya, 1952; Chow, 1959). In natural channels, the condition V > 1 is seldom, if ever, met (Jarrett, 1982). Thus, roll waves are restricted to artificial channels lined with either concrete or masonry. Typically, roll waves appear as a train of waves that move downstream, as shown in Fig. 1-7 (Chapter 1).
The Vedernikov is defined as the ratio of relative kinematic wave celerity to relative dynamic wave celerity (Ponce, 1991):
in which β = exponent of the discharge-area rating (Eq. 10-52), u = mean velocity, h = flow depth, and g =
gravitational acceleration. Roll waves occur when the relative kinematic wave celerity exceeds the relative dynamic wave celerity.
Since kinematic waves transport mass, and (true) dynamic waves transport energy, roll waves occur at the threshold where mass and energy are being transported
at the same speed.
In practice, roll waves occur in steep artificial canals when the Vedernikov number
A curious and somewhat extreme example of roll waves in a steep urban channel is seen in this video of an event on the Huayñajahuira river, La Paz, Bolivia, on February 25, 2016, at 5:30 pm.
11.5 TIDAL WAVES
Tidal bores are rapidly varied unsteady free-surface flow features which take place in certain rivers in the proximity of their estuaries. A tidal waves occurs in an estuary for a large tidal range on or around either of the equinoxes (March 20 and September 22). Whether the tidal wave is able to move upstream into the river proper and develop into a recognizable bore of finite depth, depends largely on the cross-sectional geometry of the estuary. Tidal bores are more likely to form in smooth, hydraulically wide channels of relatively constant depth.
Large tidal bores have been observed on the Araguari river, in Brazil (Fig. 11-7), on the Chien Tang river, in China (Fig. 11-8), and in other selected estuaries around the world. Chow (1959) described the Hangchow bore at Haining on the Chien Tang river, China. The wavefront was about 16 ft high, traveling at high velocity. Seven miles after it could first be distinguished on the horizon, the wave had passed. The water reached a final height of about 28 ft within 30 minutes. The width of the river at the observation point was about 1 mile.
11.6 DEBRIS FLOWS
Debris flows are sudden accumulations of runoff containing great quantities of sediment particles, usually boulder size and above. Debris flows travel downstream at great speeds, destroying everything in their path and threatening life and property (Fig. 11-9).
Debris flows are induced by intense rains, but they can also be triggered by earthquakes. In Southern California, along the base of the San Gabriel Mountains, east of Los Angeles, rain-induced debris flows recur with predictable regularity. The factors leading to the formation of these debris flows are:
The steep slopes covered with chaparral vegetation, followed by a sequence of wind, fire, and rain, is what triggers the debris flows in the Southern California region. During fire, the waxlike substances vaporize at the surface and recondense at a depth of 10 to 50 mm from the surface, below which the soil is non-wettable, i.e., hydrophobic. The accumulation of intense rainfall, exceeding 25 mm per hour, immediately below the surface and above the non-wettable layer, leads to the entrainment of large quantities of sediment which go on to constitute the debris flows. A typical rain-induced debris flow in Southern California may carry away 10-50 mm of soil in a few hours. By way of comparison, normal erosion rates are typically less than 1 mm per year.
Massive debris flows can also be triggered by earthquakes. Such was the case of the Huascaran slide on May 30, 1970, in Peru, which buried the town of Yungay, killing more than 20,000 people (Fig. 11-13). The town has since been rebuilt at a location just north of the ill-fated site.
Lahars are debris flows triggered by snowmelt, following a volcanic eruption and subsequent sudden melting of the snowcap. The word lahar originated in Indonesia, where the phenomenon is common. Lahars have the consistency, viscosity, and approximately the same density as concrete; fluid when moving, and solid when stopped (Fig. 11-14).
Lahars can be massive and deadly, as shown by the November 13, 1985 eruption of the Nevado del Ruiz volcano, in Colombia. Four lahars came down the river valleys on the volcano flanks. The largest of them virtually destroyed the town of Armero, burying it under 5 m of mud and debris, and killing more than 75% of its 28,700 inhabitants (Fig. 11-15).
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