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!

Vector calculus

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data
    For a fluid flow of velocity u and vorticity w=∆ x u, show that:

    (u. ∆ )u=-u x w + ∆(1/2|u|²)

    Sorry the triangles should be the other way up!




    2. Relevant equations

    ∆(u.v)=(u.∆)v + (v.∆)u +u x (∆ x v) + v x (∆ x u )



    3. The attempt at a solution
    I need to show this using subscipt notation, but am really stuck, any help?
     
  2. jcsd
  3. Oct 18, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    here's how you write it correctly in tex - click it on the tex to see the expression
    [tex] (u \cdot \nabla )u=-u \times w + \nabla (\frac{1}{2}|u|^2) [/tex]

    i would start by trying to expanding one of the expressions in your equation, use the equations and product rule expansions

    by subscript notation do you mean like:
    [tex] \textbf{u} \cdot \textbf{w} = u_i v_i [/tex]

    [tex] \textbf{u} \times \textbf{w} = u_i v_j \epsilon_{ijk} [/tex]
     
    Last edited: Oct 19, 2009
  4. Oct 18, 2009 #3
    I don't know how to expand the expression....Sorry im really not very good at this area of maths.

    but yes that is what i mean by subscript notation.
     
  5. Oct 19, 2009 #4

    lanedance

    User Avatar
    Homework Helper

    have a crack, i'm not just going to do it for you - how about starting with u x w?
     
    Last edited: Oct 19, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Vector calculus
  1. Calculus on vectors (Replies: 14)

  2. Vector calculus (Replies: 12)

  3. Vector calculus -.- (Replies: 5)

  4. Vector calculus (Replies: 6)

  5. Vector Calculus (Replies: 1)

Loading...