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Regular Airy Wave

Theory

A single regular wave travelling in the direction of anticlockwise relative to the global Y direction, results in a water surface elevation at a point in the wave field which is represented by the equation

               (1)

where:        

• is the wave amplitude (MWL to crest or trough)

• is the wave number

• is the wavelength

• is the horizontal distance from vertical axis (Y=Z=0) to point in question  

• is the horizontal distance from vertical axis to point in question in global Y direction

• is the horizontal distance from vertical axis to point in question in global Z direction

The wave spacial origin can be specified via the *WAVE-GENERAL keyword such that S becomes where ŷ & ẑ are the specified y and z offsets from the origin.

• is the wave circular frequency

• is the wave period

• is the present solution time

Water particle velocities and accelerations at any point through the depth in the horizontal and vertical directions are calculated using Airy wave theory via the following expressions:

               (2)

               (3)

               (4)

               (5)

where:

• is the water particle velocity in vertical (global X) direction

• is the gravitational constant

• is the vertical distance from mudline to point in question

• is the water depth

• is the water particle velocity in horizontal direction of wave travel

• is the water particle acceleration in vertical (global X) direction

• is the water particle acceleration in horizontal direction of wave travel

Where several regular Airy waves are specified, the above five Equations are replaced by the following summations:

               (6)

       (7)

       (8)

       (9)

       (10)

where:

• is the amplitude of nth regular wave

• is the wave number of nth regular wave

• is the horizontal distance from vertical axis to point in question in direction of travel of nth regular wave

• is the angle of approach of nth regular wave relative to global Y axis (positive anticlockwise

• is the circular frequency of nth regular wave

• is the phase of nth regular wave relative to some datum

• is the number of user-specified regular Airy waves

Relevant Keywords

•*WAVE-REGULAR is used to specify regular Airy wave loading.

If you would like to see an example of how this keyword is used in practice, refer to C02 - Multi-Line Flexible System.