Formation of threedimensional surface waves on deepwater using elliptic solutions of nonlinear Schrödinger equation
Abstract
A review of threedimensional waves on deepwater is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these threedimensional waves is given through cubic nonlinear Schrödinger equation. The periodic solutions of the cubic nonlinear Schrödinger equation are found using Weierstrass elliptic $\wp$ functions. It is shown that the classification of solutions depends on the boundary conditions, wavenumber and frequency. For certain parameters, Weierstrass $\wp$ functions are reduced to periodic, hyperbolic or Jacobi elliptic functions. It is demonstrated that some of these solutions do not have any physical significance. An analytical solution of cubic nonlinear Schrödinger equation with wind forcing is also obtained which results in how groups of waves are generated on the surface of deep water in the ocean. In this case the dependency on the energytransfer parameter, from wind to waves, make either the groups of wave to grow initially and eventually dissipate, or simply decay or grow in time.
 Publication:

arXiv eprints
 Pub Date:
 November 2014
 arXiv:
 arXiv:1412.0318
 Bibcode:
 2014arXiv1412.0318S
 Keywords:

 Physics  Fluid Dynamics;
 Mathematics  Analysis of PDEs
 EPrint:
 20 pages, 14 figures