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Gradient of a vector

  1. Mar 25, 2013 #1
    Hey guys,
    I'm not sure how to interpret euler's fluid equations

    [tex] \rho (\partial / \partial t + {\bf U} \cdot ∇) {\bf U} + ∇p = 0[/tex]

    I'm not sure what the meaning of [tex]{\bf U} \cdot ∇ {\bf U}[/tex] is.
    am I able to simply evaulate the dot product as [tex] U_{x}\partial_{x} + U_{y}\partial_{y}+ U_{z}\partial_{z}[/tex], and then use this to scale the vector U?
     
  2. jcsd
  3. Mar 26, 2013 #2

    tiny-tim

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    hey stormyweathers! :smile:
    (i'm not sure what you mean by "scale", but …)

    yes, (U.)A = (Uxx + Uyy + Uzz)A, for any vector A :smile:
     
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