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VM524 – Q1. From the momentum equation of the fluctuating velocity, derive the following two-point correlation equation: Solved
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where D(i)Rij ≡ u0j(~x(1),t(1))Ni{~x,t} and D(j)Rij ≡ ui0(~x,t)Nj{~x(1),t(1)}, in which Ni{~x,t} is the momentum equation of u0i(~x,t).
Q2. For the pure shear turbulence case, derive the kinetic energy equation of each velocity component, i.e. and . Estimate the magnitude of each term.
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