1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Kinematics of surface integrals question

  1. Jul 10, 2011 #1
    This is a continuum mechanics/fluid dynamics question concerning the time rate of change of a surface integral of a vector field, where the surface is flowing along in a velocity field (like in a fluid). (Gauss's law is for fixed surfaces.) This integral goes by various names in different applications, like "Faraday's law for moving media" in electromagnetism, or "Zorawski's criterion" in fluid dynamics (when the integral vanishes). (Truesdell, "Kinematics of Vorticity" page 55). We have two vector fields, one is the velocity vector field, and the other is some other specified vector field, like the magnetic field in E-M. Most of the derivations are based on a surface patch flowing along in the fluid (or more generally a velocity field), this patch surrounded by a closed curve. When the integral vanishes, it means that the integral of the given vector field dotted into the moving surface element of the (velocity) vector-tube (the tube swept out by the flowing surface patch) for the given vector field remains the same during the motion, and we end up with an elegant vector equation (called sometimes Zorawski's criterion). My question is this: Is this also true for closed moving surfaces (instead of a surface patch) like for example a deformed sphere flowing along? Nowhere in the literature can I find this important case of a closed moving surface.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Kinematics of surface integrals question
  1. Kinematics GCSE question (Replies: 16)

  2. Integration question (Replies: 4)

Loading...