Speaker 1 :  Sunao Murashige  (Ibaraki University)
    Date & Time : July 16th (Fri.), 2021 / 10:00-10:40PM (Tokyo (JST))
    Title : Effects of a linear shear current on surface waves in deep water
    Abstract : 
         The interaction of surface waves with a vertically sheared current plays
       an important role in the ocean. The aim of this talk is to show some effects 
       of a linear shear current on the two kinds of nonlinear phenomena, 
       (i) instabilities of steady gravity waves progressing in permanent form and 
       (ii) parasitic capillary waves produced on the forward face of progressive 
       gravity waves. We numerically investigated these two phenomena using 
       unsteady conformal mapping which maps the flow domain into the complex plane 
       where the time-varying water surface is always mapped onto the real axis. 
       This formulation allows us to obtain accurate solutions for the wider range
       of parameters than the previous methods developed in the physical plane. 
       Numerical examples demonstrate that, in the presence of a linear shear current, 
       these nonlinear phenomena can be generated at relatively small-amplitude waves.
       This is a joint work with Wooyoung Choi.