142
4 How to Determine Wave Parameters
order of one, for K > 100, wave-induced force on a body is totally dominated
by drag force, and the oscillatory character of the flow can be neglected in
calculation of forces.
When exploring wave-induced forces on submerged objects, another spatial
scale has to be taken into account. This is the wavelength and its relation
to the characteristic length of the object. When an object spans a significant
fraction of a wavelength, the incident waves undergo significant scattering or
diffraction. The Morison equation is not applicable in such a situation because
this equation is based on the assumption that the kinematics of the undisturbed
flow close to the object do not change in the incident wave direction. Since flow
velocity and acceleration do in fact vary with a wavelength, L, the assumption
implicit in the use of the Morison equation is that the ratio Lb/ L is small.
For marine plants and animals, even as large as whales, the condition L b/ L «
1 is usually satisfied. Therefore, we will not proceed further with the problem
of calculating wave forces on large bodies when this condition is violated. Let
us only note here that for offshore concrete gravity petroleum structures, with
typical diameter of the order of 200 m and columns with diameters of the order
of 20 m, wave scattering becomes important when determining wave forces. For
example, for a vertical column when D / L > 0.2 (D is column diameter, and L is
wavelength), K does not exceed 2.2 and usually is less than 1. This means that
for large bodies, inertia force dominates over drag force (see Eq. 4.79). Special
numerical techniques, known as diffraction techniques, have been developed to
deal with objects of large dimensions.
For further details, the reader should consult Sarpkaya and Isaacson (1981)
and Massel (1981).
4.3 Statistical and Spectral Properties of Waves
4.3.1 A Brief Orientation
Looking at ocean surface waves, one can notice both their randomness and
their quasi-regularity. Wave profiles are constantly changing with time and
in a random fashion. Consequently, the properties of waves are not readily
defined on a wave-by-wave basis. The fundamental property of surface waves
induced by wind is their irregularity. The prediction of wave parameters can
be achieved through stochastic analysis only, which can be developed in two
basic domains, i.e. probability and frequency domains.
In the probability domain, particular wave parameters, such as surface displacement at a given time, wave height, wave period, etc. are considered as
elementary random events. This approach is easy to understand when dealing
with digitized data. The digitized data of a particular parameter forms a set
of random realizations of a random variable, when the time sequence of the
parameter is not taken into account. The final results in this approach are
expressed in terms of probability density functions, distributions functions and
some statistical values.
4 How to Determine Wave Parameters
order of one, for K > 100, wave-induced force on a body is totally dominated
by drag force, and the oscillatory character of the flow can be neglected in
calculation of forces.
When exploring wave-induced forces on submerged objects, another spatial
scale has to be taken into account. This is the wavelength and its relation
to the characteristic length of the object. When an object spans a significant
fraction of a wavelength, the incident waves undergo significant scattering or
diffraction. The Morison equation is not applicable in such a situation because
this equation is based on the assumption that the kinematics of the undisturbed
flow close to the object do not change in the incident wave direction. Since flow
velocity and acceleration do in fact vary with a wavelength, L, the assumption
implicit in the use of the Morison equation is that the ratio Lb/ L is small.
For marine plants and animals, even as large as whales, the condition L b/ L «
1 is usually satisfied. Therefore, we will not proceed further with the problem
of calculating wave forces on large bodies when this condition is violated. Let
us only note here that for offshore concrete gravity petroleum structures, with
typical diameter of the order of 200 m and columns with diameters of the order
of 20 m, wave scattering becomes important when determining wave forces. For
example, for a vertical column when D / L > 0.2 (D is column diameter, and L is
wavelength), K does not exceed 2.2 and usually is less than 1. This means that
for large bodies, inertia force dominates over drag force (see Eq. 4.79). Special
numerical techniques, known as diffraction techniques, have been developed to
deal with objects of large dimensions.
For further details, the reader should consult Sarpkaya and Isaacson (1981)
and Massel (1981).
4.3 Statistical and Spectral Properties of Waves
4.3.1 A Brief Orientation
Looking at ocean surface waves, one can notice both their randomness and
their quasi-regularity. Wave profiles are constantly changing with time and
in a random fashion. Consequently, the properties of waves are not readily
defined on a wave-by-wave basis. The fundamental property of surface waves
induced by wind is their irregularity. The prediction of wave parameters can
be achieved through stochastic analysis only, which can be developed in two
basic domains, i.e. probability and frequency domains.
In the probability domain, particular wave parameters, such as surface displacement at a given time, wave height, wave period, etc. are considered as
elementary random events. This approach is easy to understand when dealing
with digitized data. The digitized data of a particular parameter forms a set
of random realizations of a random variable, when the time sequence of the
parameter is not taken into account. The final results in this approach are
expressed in terms of probability density functions, distributions functions and
some statistical values.