Table 1.1. Basics of linear wave theory.
RELATIVE DEPTH
WAVE PARAMETER
SHALLOW WATER
d
1
Z < 20
TRANSITIONAL WATER
1
d
1
20 < Z < 2
DEEP WATER
d
1
Z > 2
1. Wave profile
Same as —»
H
F 27rx
2?rt
77 — — cos--------------2
L
L .
H
— — cos 0
2
«— Same as
2. Wave celerity
c=ÿ = Vgd
C — — — -— tanh
T
2tv
L
gT
C^Co = - = ^1
Ztv
3. Wavelength
L = Tyfgà = CT
T
gT2
, /27rd\
L = ----- tanh 1 ------ )
2tt
\ L J
gT2
l = lo = ^—- = cot
2tv
4. Group velocity
Cg=C= y/gd
C, = „C = 1[1+ . gTJc
2
sinh(47rd/L)_
2
4tt
5. Water particle velocity
a) Horizontal
b) Vertical
H [g
.
U = ---y — COS 0
2 V d
Htt C
z\ . n
w —
I 1 H
sm 9
T \
d)
H gT cosh[27r(z + d)/L]
u =-------------- -—?----- ——- cos 9
2 L
cosh(2-7rd/L)
H gT sinh[27r(z + d)/L] .
w =---------------—7----- —— sin 0
2 L
cosh(27rd/L)
TtH 2ttz
u = ----- e l cos 0
T
tvH
w = -----e l sm#
T
6. Water particle accélération
a) Horizontal
b) Vertical
f~g .
ax = — C-sm9
az = —2H
cos#
givH cosh[27r(z + d)/L] . .
ax =------------------;
sm 9
L
cosh(27rd/L)
gnH sinh[27r(z + d)/L]
CLz —
/
.
COS v
L
cosh(27rd/L)
/ 7T \ 2 2-n-z
ax = 2H 1 — j e l sin 0
/ 7T \ 2 2-n-z
az = —211 Ç—j e l cos 9
7. Water particle displacement
a) Horizontal
b) Vertical
H
o
■ “
J L
H b i
ùq p x— z
!
tq 1
1 1
I I
uz
1 1
H cosh[27r(z + d^/L} .
ç —
z
.
sin. 0
2
sinh(27rd/L)
H sinh[27r(z + d)/L]
Q
2
sinh(27rd/L)
H 2'kz t
t =----- e l sin y
2
H 2irz
Ç = —e l cos 9
2
8. Subsurface pressure
P = P9 cosh[27r(z + d)/L]
p^pg'n
,
,/rx
pgz
cosn(27ra/L)
2tvz
p = pgrje l -pgz
Coastal Engineering: Theory and Practice