Ecoinformatics Problems of the World Ocean - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 346

The following approximation is valid for plain progressive waves spreading in
direction x without barriers

ux ðÞ ¼Ax ; ð exp ik ðÞ ; 4 : 54 Þ

The function ( 4.54 ) is solution of equations

u þ k 2 u ¼ 0 D ; ð 4 : 55 Þ

@ A i

2k

@

2 A

x 2 þ @

2 A

x ¼ @ @ @ y 2

The diffraction coef cient is

K d ¼ Ax j ðÞ ; j

2 A @ x 2

@ 2 A @ y 2 when @ the following relation takes place

@

2k @

2 A
@

A i A

2r ; r ¼ l 2

@

ʸ ʸ

where l=r and relation A/(2r)re fl ects wave front crookedness, and r are polar

coordinates.
Seiche oscillation takes place in the port zone, due to the penetration of low-
frequency oscillations from the open sea to the port zone. This oscillation stimulates
a very dangerous phenomenon called as harbor oscillation that leads to disagreeable
consequences for the ship. Cycles of harbor oscillations range from 0.5 s to 4 min
with an amplitude of horizontal oscillations equal to 4 m. According to the theory of
formation of low-frequency oscillations two systems of wind-induced waves exist
in the sea. One of them is a resonance system with phase speed equal to the wind
speed. The second system is under-resonance with smaller phase speed that steadily
increases. Two maxima correspond to these systems in the energetic spectrum of
wind-induced sea roughness. The origin of such a situation is impossible under long
strong stable wind above vast aquatory (linear range about 100 km). The calculation
of low-frequency oscillations in coastal zone can be realized using the following
formula (Krylov 1966):

;

3 = 2 h 2
g

H
g

h lf ¼ 2 p

2 f 2

ð 4 : 56 Þ

s s

2

where H is the aquatory depth; g is the acceleration of gravity; h is the height of
wind-induced wave;

˄ is the time period of wind-induces wave. Function f 2 is

de ned empirically and its view is given in Fig. 4.35 (Krylov 1981).