2.5 UNSTEADY FLOW
Unsteady flows of interest to the designer of waterway crossings and encroachments are: (1)
waves resulting from disturbances of the water surface by wind and boats; (2) waves resulting
from the surface instability that exists for flows with Froude numbers close to 1.0; (3) waves
resulting from flow disturbance due to change in direction of flow with Froude numbers greater
than about 2.0; (4) surges or bores resulting from sudden increase or decrease in the flow by
opening or closing of gates or the movement of tides on coastal streams; (5) standing waves and
antidunes that occur in alluvial channel flow; and (6) flood waves resulting from the progressive
movement downstream of stream runoff or gradual release from reservoirs.
Waves are an important consideration in bridge hydraulics when designing slope protection of
embankments and dikes, and channel improvements. In the following paragraphs, only the basic
one-dimensional analysis of waves and surges is presented. Other aspects of waves are
presented in other sections.
2.5.1 Gravity Waves
The general equation for the celerity c (velocity of the wave relative to the velocity of flow) of a
small amplitude gravity wave (ao << λ) is
2π y o
c = tan h
where the terms are defined in Figure 2.14.
Figure 2.14. Definition sketch for small amplitude waves.
For deep water waves (short waves) defined as