Archive image from page 16 of Directional irregular wave kinematics (1998) Directional irregular wave kinematics directionalirreg00bark Year: 1998 z = 77(water surface) zw y////////////////////}/////////////////////////////////////////////////////// Figure : 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 wate
Archive image from page 16 of Directional irregular wave kinematics (1998) Directional irregular wave kinematics directionalirreg00bark Year: 1998 z = 77(water surface) zw y////////////////////}/////////////////////////////////////////////////////// Figure : 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) ( COS {nkx — mut) + Bn,m sin [nkx — mut)) n=l m=l (1-8) where fc, w, Anm Bn,m are global constants, and 2 = 0 at the bed (Fig. ). In this potential function each frequency component {mui) has a corresponding set of wavelengths (nk), allowing each component to travel at distinct phase speeds.
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