6-Seakeeping - Ship Motions in Irregular Waves (2012)

Seakeeping – Motions in Irregular Waves SEAKEEPING – SHIP MOTIONS IN IRREGULAR WAVES MODULE Note: These notes are drawn from those issued by Dr Jonathan Duffy to students of JEE329 Seakeeping & Manoeuvring at the Australian Maritime College Dr Duffy has used edited extracts from the main reference books for the subject and which are listed at the end of the module Irregular Waves Ocean waves are not regular and are usually rather complex and extremely irregular The shape of the ocean surface will constantly be varying as the wave velocity is a function of the wave length Therefore, the longer waves will be overtaking the shorter ones producing a continually varying surface There is a large body of measured ocean wave data, including wind speed, wind direction, wave height and wave length This data has been collected by oceanographic institutions and meteorological departments and various summaries have been produced for all oceans around the world For example, Global Wave Statistics Online provides worldwide coverage of wave climate in 104 sea areas, and an additional database providing a higher spatial resolution for the North European Continental Shelf The constantly varying ocean surface is not amenable to an exact mathematical definition Therefore statistical concepts are used to define an irregular seaway An example of an irregular wave is given in Figure H Figure (a) Irregular seaway plotted to a base of time (b) Irregular seaway plotted to a base of x (Bhattacharyya 1978) Seakeeping – Motions in Irregular Waves Due to the random nature of irregular waves we need to establish a suitable method of describing the wave height and wave period Some of these parameters are explained below: ζ ζ𝑎 𝐻 Tz Tc is the instantaneous wave elevation from the reference line is the apparent wave amplitude, i.e the distance from the reference line to the crest of the wave is the apparent wave height, which is the vertical distance between a successive wave crest and wave trough is the apparent zero-crossing period, which is the time between two upward or downward zero crossings is the apparent period, which is the time between two successive peaks (sometimes called the peak to peak period and denoted as Tp ) The mean zero-crossing period is the average of the apparent zero-crossing periods for multiple observations The mean apparent period is the average of the apparent periods for multiple observations The mean values of several readings are usually signified by a bar, e.g Tz The average wave height of an irregular seaway is the arithmetic mean of the heights of all the waves, for multiple observations When investigating ship motions we are often most interested in the largest waves rather than the average, as these are the ones most likely to cause problems A simple way of describing waves in this manner is to calculate the average height of the highest waves that make up 1/3rd of the total number of waves recorded This is called the significant wave height and is denoted H1/3 Sometimes the highest 1/10th waves are averaged and this is denoted H1/10 1.1 Histogram A histogram can be used to describe the properties of an irregular seaway at a given time or at a given place An example histogram is shown in Figure This histogram pertains to wave elevations for a collection of wave measurements Here the wave elevation has been split into bands of 1m For example, all records with a wave elevation between 0.5m and 1.5m are grouped together and the sum of records within this band are presented as a percentage of the entire population This is repeated for all other wave elevation bands Experience has shown that a histogram of the wave elevations takes the shape of a Gaussian or normal distribution, as shown by the dotted line in Figure Figure Example of a wave elevation histogram (Bhattacharyya 1978) Seakeeping – Motions in Irregular Waves A histogram may also be produced based on wave period An example is shown in Figure Figure Example of a wave period histogram From wave measurements it has been found that a very irregular seaway will produce a low, relatively wide histogram, whereas a more regular seaway will produce a high, narrow histogram The location of the centre of gravity of the histogram in relation to the y axis gives the average value of the wave period (see Figure 3) It has been found from many ocean wave measurements that the theoretical Rayleigh curve fits the histograms for double amplitude (wave height) very well The Rayleigh distribution is given by Equation 𝑝 𝐻𝑖 = 2𝐻𝑖 𝐻2 𝑒 −𝐻𝑖 𝐻2 (1) Where 𝑝 𝐻𝑖 is the probability density per metre or the percentage of times that any particular wave height 𝐻𝑖 will appear, with 0