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

tanh (*k h*)

(II-5-1)

tanh (*k h*)

(II-5-2)

2π

(II-5-3)

sin (*k x *& σ *t*)

σ

cosh *k h*

(II-5-4)

cos (*kx *& σ*t*)

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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