Environmental Engineering Reference
In-Depth Information
coastal currents parallel with the line of the coast is to estimate the design velocity
(U
surf
) in the surf zone as follows:
p
g
H
B
U
surf
¼
2
s
where
H
B
height of breaking wave
s
slope of seabed near the shore
We can choose the same power law equation for the vertical profile of the wave-
generated current as for the tidal current.
Superposition of currents
The flow velocity resulting from all three components generally has to be combined
with the sea state. For simplicity and to remain on the safe side, they are assumed to act
in the same direction:
1
=
7
;
1
=
7
d
þ
z
d
d
0
þ
z
d
o
d
þ
z
d
U
c
ðÞ¼
U
c
;
sub
þ
Max
:
U
c
;
wind
0
þ
U
c
;
surf
Depending on the location, further types of current, such as the velocity constant over the
depth due to a permanent current, may need to be added into the equation.
2.5.2 Natural sea state
The term “natural sea state” is understood to be the totality of the observed wave events.
This irregular mechanism can only be described with the help of the theory of
stochastic processes.
The mathematical concept can be considerably simplified if we are allowed to assume
that an observed stochastic process is stationary and ergodic. A process is stationary
when the statistical means (moments) of the random variables are time-invariant. A
process is ergodic when the generation of means from sampling (ensemble) can be
replaced by a temporal averaging from a representative ensemble function, that is from
the evaluation of a time series.
The natural sea state may be considered to be approximately stationary for short
periods of time. Within the range of validity of this assumption, the sea state can be
described as the result of the superposition of an infinite number of low-steepness
harmonic waves with various directions, heights, periods and phase positions.
The central limit theorem of statistics can be used to verify that this superposition
model leads to a random variable that exhibits a normal (or Gaussian) distribution.
Consequently, individual short-term sea states are described by a Gaussian process that
is stationary and ergodic. Every sea state, that is the associated Gaussian process, is
described unambiguously in the frequency domain by the sea state spectrum, which
specifies the distribution of the energy of the sea state by means of frequency and
direction of movement.
