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Lagrangian description of fluid motion

  1. Nov 16, 2015 #1
    1. The problem statement, all variables and given/known data
    Find velocity, acceleration, stream function and vorticity. Prove that velocity is equal to the acceleration. Functions given:
    [tex]X_1(t,e_1,e_2)= (e^\lambda)^t[e_1cos\omega t+e_2sin(\omega t)][/tex]
    [tex]X_2(t,e_1,e_2)= (e^-\lambda)^t[-e_1sin\omega t+e_2cos(\omega t)][/tex]

    2. Relevant equations
    [tex]v(t,e_1,e_2)=\frac{d}{dt} x(t,e_1,e_2)[/tex]
    [tex]a(t,e_1,e_2)=\frac{d}{dt} v(t,e_1,e_2)[/tex]
    [tex]\psi(t,e_1,e_2)=\lambda x_1 x_2[/tex]
    3. The attempt at a solution
    Calculations of velocity:
    [tex]V_1(t,e_1,e_2)= e_1[(e^\lambda)^t\lambda cos\omega t-(e^\lambda)^t \omega sin\omega t]+e_2[(e^\lambda)^t\lambda sin\omega t+(e^\lambda)^t \omega cos\omega t][/tex]
    [tex]V_2(t,e_1,e_2)= e_1[(e^-\lambda)^t\lambda sin\omega t-(e^-\lambda)^t \omega cos\omega t]+e_2[(-e^-\lambda)^t\lambda cos\omega t-(e^-\lambda)^t \omega sin\omega t][/tex]
     
  2. jcsd
  3. Nov 21, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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