Wave spectrum can be calculated using above formulas if significant height of wave and period are known. There are a lot of factors to generate wave, wind is one of the most usual factors. The wave generated by wind is called surface gravity wave. The elements of wave are determined by wind speed, standing time of wind and the size of wind area. Generally, the wave arisen from wind is very irregular. In deep water area, this kind of wave is called irregular long crest wave. Table 2 lists the wave scales defined by China Ocean Bureau.

　

 Table 2 indicates the relation of wave scale and wind scale with wave height, but does not list the relation of wave scale and wind scale with wave period. Table 3 lists the relation of wave scale, wind with wave height, wave period referring to wave scale defined by department of Russia Ocean and the wave height, wave period adopted by simulation algorithm.

　

　

　

　

 Irregular long crest wave can be composed by multiple regular long crest waves with different amplitude and length. The instantaneous height of wave is calculated using following formula:

　

　

Here:

HTide: Tide height

　

　

, the wave number of i-th wave unit

　

g: g=9.81m/s², acceleration of gravity

t: time

φi: phase angle of i-th wave unit(Rad)

0 : spreading direction of wave , θ∈[0.2π]

　

 The key problem of calculating instantaneous height of wave is how to calculate the amplitude ζui, angle frequency ωi and phase angle□i of wave unit.

　

 Wave spectrum S ζ(ω) can be calculated if significant wave height and average period T1 are known as Tabel1 listed,. Denote wave spectrum for simulated Sζ(ω), the most part of energy is between ω1〜ω2(see Fig.1). During simulating, ω1,ω2 are calculated after precision being inputted. If precision denotes □ , then

　

　

　

 If □ and Sζ(ω) are known, □1, □2 can be calculated. Then the section [□ 1, □ 2] can be discretized adaptively according to the number n of wave unit input.

　

 Suppose the total energy of section [□1, □2] is E, the frequency in the peak of spectrum is □P, the energy of section [□1,, □P] is E1,the number of wave units is n1, the energy of section [□P, □2] is E2, the number of wave unit is n2,then

　

　

 The frequency intervals of section [□1,□P],[□P,□2]

are respectively:

　

Δω1 = (ωP - ω1)/n1

Δω2 = (ω2 - ωP)/n2　(8)

　

 After calculating the intervals Δω1 and Δω2, the representing frequency of each section can be calculated by following formula:

　

　

 The value of wave spectrum Sζ(i) corresponding to frequency i can be calculated by spectrum formula listed in Table 1, the corresponding amplitude can be calculated using formula (3)

　

　

 The wave number is

　

　

 Fig. 2 is the flow chart for calculating angle frequency ωi and wave amplitude ζai of one wave unit. Table 4 lists the discrete angle frequency and amplitude of P-M spectrum corresponding to each wave scale. Fig. 3 shows the simulated P-M spectrum of different wave scales (Precision=O.O1, ten wave units)

　

　

　

 Formula (6) is used for calculating the instantaneous wave height of position (x,y) in time t. Unique mesh model and texture mapping technology are adopted for real-time simulation.

　

(1) Mesh model

　

 In visual system, the simulated sea with MxN (m²) is divided to dynamic area and static area for implementing real-time simulation of irregular long crest wave (shown in Fig. 4). The dynamic area consists of mXn meshes and static area covers the remains beyond .dynamic area.

　

 When visual system is getting started, the coordinates (xj,yj) of each node in the above mesh are calculated firstly. Assuming (Sx,Sy) is the world coordinates of ship at time t, the world coordinates of mesh nodes are obtained by moving the origin of coordinate system to ownship's position