EM 1110-2-1100 (Part II)
30 Apr 02
to the change in coastal datums that may result from sea (or lake) level rise and/or land subsidence or
rebound.
(5) Parts II-5-5 through II-5-7 describe nontidal variability in water surfaces. These fluctuations can be
storm-generated, as in the case of tropical and extratropical storms; atmospheric- and geometry-related, as
in the case of seiches or tidal bores; or be due to responses stemming from earthquake-generated tsunamis
or other rapid changes in the environment.
(6) The primary goal of this chapter is to define tidal and storm-generated fluctuations in the water
surface and describe the datums to which they are referenced. Seiches will only be briefly discussed and
tsunamis are not addressed because a special report on tsumanis has been prepared by the Coastal and
Hydraulics Laboratory (CHL) (Camfield 1980). In addition to Camfield, Engineer Manual 1110-2-1414,
"Water Levels and Wave Heights for Coastal Engineering Design," addresses the propagation of tsunamis.
However, because both seiches and tsunamis are classified as long waves, the numerical modeling techniques
discussed in Part II-5-7 are an appropriate means of analysis.
II-5-2. Classification of Water Waves
a. Wave classification.
(1) The long wave descriptions that follow are based on small-amplitude wave theory solutions to the
governing equations. This theory places certain criteria on the physical shape of the wave. For example,
from Figure II-5-1, the amplitude is assumed small with respect to the depth (i.e., η/h ratio is small, and the
surface slope dη/dx is assumed small).
(2) Although wave amplitude is assumed small with respect to depth, the manner in which the wave
propagates is a function of just how small this ratio is. The propagation of small-amplitude waves in water
can now be described as a function of the wave length and the depth of water in which the wave is
propagating. In fact, waves can be classified according to a parameter referred to as the "relative depth,"
defined as the ratio of water depth h to wave length L. When this ratio is less than approximately 1/20, waves
can be classified as long waves or "shallow-water waves." Figure II-5-1 shows typical long wave geometry
for a wave whose length L is large with respect to the depth of water h.
(3) Astronomical tides represent one important example of long waves. In Chesapeake Bay, for example,
the M2 primary lunar tidal constituent is contained completely within the Bay at a given instant in time,
producing a wavelength of approximately 300 km. The mean depth of flow in the Bay is approximately 10
m; therefore, the relative depth is 3.3 10-5. Long waves are not limited to what is normally considered
shallow water because the relative depth is a function of wavelength. In fact, most tides are long waves over
the entire ocean because their wavelengths are on the order of 1,000 km and depths are on the order of
kilometers. Similarly, seismic-forced phenomena such as tsunamis propagate across the Pacific Ocean in
depths of up to 20 km but have wavelengths on the order of hundreds of kilometers.
(4) Waves are classified as short waves, also referred to as "deepwater waves," when the relative depth
is greater than approximately 1/2. Coastal waves described in Part II-2 are generally of this class. The
geometry of short waves implies wave steepness great enough to cause them to break. The class of waves
between short (deep) and long (shallow) are referred to as "intermediate waves." Table II-5-1 (Ippen
II-5-2
Water Levels and Long Waves
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