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Stokes Drift for Inertial Particles Transported by Water Waves

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We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. Using appropriate
asymptotic expansions, we perform an analytical calculation which allows us to predict the dynamics of such particles. Numerical simulations
based on the velocity field resulting from the second-order Stokes theory for the surface elevation have been performed, and an
excellent agreement with the analytical predictions is observed. Such an agreement seems to hold even beyond the formal applicability
of the theory. We find that the presence of inertia leads to a correction to the well-known horizontal Stokes drift; moreover, we find that
the vertical velocity is also affected by a non-negligible drift (up to 20%). The latter result may have some relevant consequences on
the rate of sedimentation of particles of finite size.

Author(s):

Francesco Santamaria    
Dipartimento di Fisica, Universita' di Torino
Italy

Guido Boffetta    
Dipartimento di Fisica, Universita' di Torino
Italy

Marco Martins Afonso    
Institut de Mathématiques et de Modélisation de Montpellier
France

Miguel Onorato    
Dipartimento di Fisica, Universita' di Torino
Italy

Andrea Mazzino    
Dipartimento di Ingegneria Civile, Chimica e Ambientale, Universita' di Genova
Italy