EHD ENVELOPE SOLITONS OF CAPILLARY-GRAVITY WAVES IN FLUIDS OF FINITE DEPTH

We consider the nonlinear electrohydrodynamic stability of wave packet s of capillary-gravity waves in fluids of any depth; they travel predo minantly in one direction, however the wave amplitudes are modulated s lowly in both horizontal directions. The method of multiple time scale s is used to obtain a nonlinear Schrodinger equation describing the be haviour of the perturbed system. The envelope solutions of steady form are obtained in terms of the Jacobian elliptic functions. It follows that various types of envelope solutions of the modulated Stokes waves may exist depending on the relative signs of terms representing dispe rsive and nonlinear effects; the solitary and periodic envelope soluti ons for the general case of any liquid depth are described. It is also shown that the evolution of the envelope is governed by two coupled p artial differential equations with cubic nonlinearity. The stability o f solitons with respect to transverse perturbations is investigated It is found that such wave packets are stable to short waves, and unstab le to long disturbances, and the envelope solitons and the waveguides are always unstable, and the stability of the system depends on the va lues of the dielectric constant ratio, the electric held the wavenumbe r, and the depth of the fluid.