| Abstract: |
| We investigate the effect of constant vorticity background shear on the properties of wavetrains in deep water. We derive a higher-order nonlinear Schr\{o}dinger equation in the presence of shear and surface tension. We show that the presence of shear induces a strong coupling between the carrier wave and the mean surface displacement. The effects of the background shear on the modulational instability of plane waves is also studied, where it is shown that shear can suppress instability, though not for all carrier wavelengths in the presence of surface tension.
Using a modification of the Generalized Lagrangian Mean theory, explicit, asymptotic approximations for the Stokes drift velocity are obtained for plane-wave and Jacobi elliptic function solutions of the nonlinear Schr\odinger equation. We show that background currents have significant effects on the mean transport properties of waves. In particular, certain combinations of background shear and carrier wave frequency lead to the disappearance of mean surface mass transport. These results provide possible explanations for a several
still puzzling oceanographic measurements. |
|