Geoscience Reference
In-Depth Information
7.1
TWO EXTREME CASES OF LARGE FLOOD
WAVE PROPAGATION
In Chapter 5 it was shown how different types of wave can result from small disturbances
of the water surface, depending on which terms are important and which terms can be
omitted in the momentum equation. Special types of large wave can also be simulated,
again depending on which are the main factors controlling the momentum budget of the
flow.
7.1.1
Surge or dynamic shock
Under certain conditions the water surface exhibits an obvious and visible disturbance,
also variously called an abrupt wave, a surge, a bore or a moving hydraulic jump. Similar
phenomena occur in other situations in the environment as well, and they constitute the
front of what are broadly referred to as gravity currents (Simpson, 1997). For instance,
in Chapter 3 analogous surges were seen to occur as the gust front of thunderstorms (see
Figures 3.8 and 3.9).
Any such disturbance may be interpreted, if not as a discontinuity, at least as a
point where the water depth
h
is not a smooth function; this interpretation means that the
derivative (
x
) is discontinuous, i.e. indeterminate. In general, it depends on the nature
of the flow around such a wave, whether it will amplify or decay. As already noted in
Chapter 5 on the basis of the solution of the linear case, the criterion for bore formation
is Fr
∂
h
/∂
a
−
1
2.
However, the instantaneous speed of propagation
c
s
of such a wave depends solely on
the magnitude of the discontinuity itself, as will now be shown.
>
(where
a
is the power in Equations (5.39) and (5.43)), or Fr
>
1.5
∼
Types of abrupt wave
In general, there are four different types of abrupt wave. A simple way of visualizing
them makes use of a thought experiment illustrated in Figure 7.1. Consider a sluice
gate under well-established steady flow conditions, whose opening is suddenly changed.
If the gate is raised, the downstream flow can be seen to develop situation A and the
upstream flow develops situation C. If the sudden change is downward, situations B and
D develop, respectively upstream and downstream from the gate. Waves in class A move
downstream as positive surges; these types of bore are the ones of primary interest in
hydrology, as they can transport large amounts of water and have caused some major
flooding events in the past. Waves of type B are also positive surges, but in contrast
to A, they advance upstream. They are typical for tidal bores, which are observed in
some estuaries and rivers affected by tidal action. Such bores can be formed when the
rising tide reverses the river flow and the tidal water enters into a gradually narrowing
and shallowing channel, usually with a small bed slope; this narrowing environment
slows down the leading edge of the tide, and allows it to be overtaken by the deeper and
faster traveling water of the continually rising tide coming up from the rear. Although
the survey was not totally exhaustive, at last count (Bartsch-Winkler and Lynch, 1988),
