Page 45 - Marine Structural Design

22 Part I Structural Design Principles

a =Wave amplitude
k = 2w/ A : wave number
A =Wavelength
w = 2w/ T : wave ferquency
T = Wave period
8 =Phaseangle
Pierson, Neumann, and James (1955) also proposed that the surface elevation h(x,t) of an
irregular sea could be represented as:

A number of different procedures exist on to how to describe a sea surface. Jensen (2001)
provides a detailed analysis for the description of surface waves.
2.2.3 Ocean Wave Spectra
A vast amount of data regarding ocean waves has been collected and measured throughout the
years. This data is needed in order to define the sea-state where the ship is likely to sail. One
of the most comprehensive collections of data regarding ocean waves was published by
Hogben, Dacunha, and Olliver (1986). It tabulates the data from 104 ocean areas, known as
Marsden areas, covering all major shipping routes.
The representation of the ocean data may be carried out in a number of different ways.
Bretschneider (1 959) proposed that the wave spectrum for a given sea-state could be described
in terms of two parameters: the significant wave height @IS) and the modal wave frequency
(OM). The modal wave frequency is the peak frequency at which the wave spectrum's
maximum height occurs. One of the most popular spectra in use is given by Pierson and
Moskowitz (1964). This spectrum assumes a deep sea and a fully developed sea-state. For
coastal waters, the Joint North Sea Wave Project (JONSWAP) spectrum is used as described
by Hasselman (1 973) and Ewing (1976).
Chakrabarti (1987) gave the mathematical descriptions for the various wave spectrums, such
as
Phillips
Neumann Spectrum
Pierson-Moskowitz Spectrum
Bretschneider Spectrum
ISSC Spectrum
ITTC Spectrum
Unified Form
JONSWAP Spectrum
Scott Spectrum
LiuSpectnun