(c) The ratio

2π(*z *% *d*)

cosh

(II-1-43)

2π*d*

cosh

is termed *the pressure response factor*. Hence, Equation II-1-41 can be written as

(II-1-44)

(d) The pressure response factor *K *for the pressure at the bottom when *z *= -d,

1

(II-1-45)

2π*d*

cosh

is presented as function of *d/L*0 in the tables (SPM 1984); see also Figure II-1-5. This figure is a convenient

graphic means to determine intermediate and shallow-water values of the bottom pressure response factor *K*,

the ratio *C/C*0 (=*L/L*0 = k0 /k ), and a number of other variables commonly occurring in water wave

calculations.

(e) It is often necessary to determine the height of surface waves based on subsurface measurements of

pressure. For this purpose, it is convenient to rewrite Equation II-1-44 as

η'

(II-1-46)

ρ *g K*z

where *z *is the depth below the SWL of the pressure gauge, and *N *a correction factor equal to unity if the

linear theory applies.

(f) Chakrabarti (1987) presents measurements that correlate measured dynamic pressure in the water

column (*s *in his notation is the elevation above the seabed) with linear wave theory. These laboratory

measurements include a number of water depths, wave periods, and wave heights. The best agreement

between the theory and these measurements occurs in deep water. Shallow-water pressure measurements for

steep water waves deviate significantly from the linear wave theory predictions. The example problem

hereafter illustrates the use of pertinent equations for finding wave heights from pressure measurements based

on linear theory.

(8) Group velocity.

(a) It is desirable to know how fast wave energy is moving. One way to determine this is to look at the

speed of wave groups that represents propagation of wave energy in space and time. The speed a group of

II-1-22

Water Wave Mechanics

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