Speaker 1 :  Christian Kharif  (Institut de Recherche sur les Phénomènes Hors Equilibre 
                                     (IRPHE), France)
                                   (Ecole Centrale Marseille, France)
    Date & Time : December 17th (Fri.), 2021 / 10:00-10:40PM (Tokyo (JST)) 
                  (--> December 17th (Fri.), 2021 / 2:00-2:40PM (Paris (CET)) ) 
    Title : Modulational instability of surface waves on water of finite depth
            with constant vorticity
    Abstract : 
         A nonlinear Schrödinger equation for the envelope of two dimensional
       surface waves on finite depth with non-zero constant vorticity derived
       by Thomas et al (2012) and Hsu et al (2018) within the framework of gravity
       waves and gravity-capillary waves respectively, is considered to investigate
       the influence of constant vorticity on the stability properties of weakly nonlinear
       wave packets. It is found that vorticity modifies significantly the modulational
       instability properties of weakly nonlinear plane waves, namely the growth rate 
       and bandwidth. At third order, we have shown the importance of the nonlinear coupling 
       between the mean flow induced by the modulation and the vorticity. Furthermore, 
       it is shown that gravity plane wave solutions may be linearly stable to modulational 
       instability for an opposite shear current independently of the dimensionless parameter
       kh, where k and h are the carrier wavenumber and depth, respectively. 
       The combined effect of vorticity and surface tension is to increase the rate of growth 
       of modulational instability of short gravity waves influenced by surface tension, 
       namely when the vorticity is negative. The rate of growth of modulational instability of
       capillary waves is amplified by negative vorticity and attenuated by positive vorticity.