z = 77(water surface) 



z^w 



y////////////////////}///////////////////////////////////////////////////////^^^ 



Figure 1.3: Coordinate system for Lambrakos-Baldock-Swan method. 



only a single free mode, with all other included components being bound modes 

 traveling with the wave at the same phase speed, thus representing an asymmetric 

 wave of permanent form. A solution that does not allow a change in form is unlikely 

 to accurately capture waves in deep water, where frequency dispersion can lead to 

 transient extrenae waves, or, indeed, in shallow water where shoaling effects cause a 

 change in form as the waves progress. 



Seeking to improve on global methods, Lambrakos (1981) developed a method for 

 determining the kinematics of two dimensional irregular waves that includes many 

 free modes, and thus unsteady motion. Baldock and Swan later refined Lambrakos' 

 method, applying it specifically to large transient waves, first in deep water (Baldock 

 and Swan 1994), and then in shallow water (Baldock and Swan 1996). Baldock 

 and Swan's method adopts the following potential function that is a double Fourier 

 expansion in space and time: 



AT M 



(f){x, z, t) = y^ y^ cosh (nkz) (An.m COS {nkx — mut) + Bn,m sin [nkx — mut)) 



n=l m=l 



(1-8) 



where fc, w, An^m^ Bn,m are global constants, and 2 = at the bed (Fig. 1.3). 

 In this potential function each frequency component {mui) has a corresponding set 

 of wavelengths (nk), allowing each component to travel at distinct phase speeds. 



