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Stokes drag of oscillation sphere

  1. Jul 12, 2011 #1
    If we consider a sphere oscillates in viscous fluid with frequency w,
    then sphere has velocity u=[itex]u_0*e^{-iwt}[/itex]

    In Laudau's book, he defined the velocity of fluid is:
    v=[itex]e^{iwt}*F[/itex]
    where F is a vector with only spatial variable involved.
    The boundary condition then becomes [itex]u=v[/itex] at [itex]|x|=R[/itex],
    where R is radius of sphere and origin is center of sphere.

    My question is that this is a non-inertial frame, but Landau didn't introduce any
    extra periodic force. Why is this true? Thank you!
     
  2. jcsd
  3. Jul 13, 2011 #2
    I figured it out.
    First, use non-inertial frame, write down the NS equation with velocity w.
    Then let [itex]u=w+u_0[/itex]
    where [itex]u_0[/itex] is velocity of sphere.
     
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