Speaker 2 :  Christopher Curtis  (San Diego State University)
    Date & Time : January 21st (Fri.), 2022 / 9:50-10:30AM (Tokyo (JST)) 
                  (--> January 20th (Thu.), 2022 / 4:50-5:30PM (San Diego (PDT)) )
    Title : Nonlinear waves over deep water shear currents and Stokes drift
    Abstract : 
         We investigate the effect of constant vorticity background shear on the properties of 
       wavetrains in deep water. We derive a higher-order nonlinear Schroedinger 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 
       Schrödinger 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 several still puzzling oceanographic 
       measurements.