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#    sinhk(z + D)
                             ! = "   $               cos(kx " #t)
                                    k  0   sinhkD
                                                                                              (10.4.38)
                                   #        sinhk(z + D)
                                = "  $(x,t)
                                    k         sinhkD


                   This is a good example  of the streamlines not being particle trajectories. The streamlines,

                   shown in Figure 10.4.4 give the direction of the instantaneous velocity field but since the
                   motion is time dependent and the streamlines keep changing with time the fluid elements

                   do not follow the streamline paths on their trajectories.





                                                                                      c




























                   Figure 10.4.4 The instantaneous stream line pattern for a propagating gravity wave. In the
                   figure kD=1. The (exaggerated) free surface has been drawn in by hand.


                   The fluid velocities can also be used to solve for the fluid trajectories.











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