EM 1110-2-1100 (Part II)
30 Apr 02
Figure II-5-1.
Long wave geometry (Milne-Thompson 1960)
Table II-5-1
Wave Classification (Ippen 1966)
Range of h/L
Range of kh=2πh/L
Types of waves
0 to 1/20
0 to π/10
Long waves (shallow-water wave)
1/20 to 1/2
π/10 to π
Intermediate waves
1/2 to 4
π to 4
Short waves (deepwater waves)
1966) summarizes wave classification criteria according to relative depth and the wave parameter kh defined
below.
(5) Applying the relative depth and wave number parameter to the characteristics of long waves can be
seen in the simplification to progressive small-amplitude wave theory solutions. For example, from Part II-1,
the wave celerity, wave length, horizontal (x-direction) and vertical velocities can be written as
g
C2 '
tanh (k h)
(II-5-1)
k
gT 2
tanh (k h)
L'
(II-5-2)
2π
a g k cosh k (h % z)
u'
(II-5-3)
sin (k x & σ t)
σ
cosh k h
a g k sinh k (h % z)
w'&
(II-5-4)
cos (kx & σt)
σ
cosh k h
where k is the wave number (2π/L), σ is the angular frequency (2π/T where T is the period of the wave), a is
the amplitude of the wave, g the acceleration of gravity, h is the total depth, and z is the depth measured
downward from the quiescent fluid surface. A schematic diagram of the variation of velocity as a function
of depth is shown in Figure II-5-2.
Water Levels and Long Waves
II-5-3
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