10. (*, 20 marks) Consider the motion pla, t) given by pla, t) = ((1 + t)a1, a2 + ta3,--ta2 + a3) and let f(x, t) = tx:
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10. (*, 20 marks) Consider the motion pla, t) given by pla, t) = ((1 + t)a1, a2 + ta3,--ta2 + a3) and let f(x, t) = tx:
10. (*, 20 marks) Consider the motion pla, t) given by pla, t) = ((1 + t)a1, a2 + ta3,--ta2 + a3) and let f(x, t) = tx: +32 be an Eulerian scalar field. Compute the material time derivative off in two ways: Df_af Df d + (v.)/ and en (pla,t), )) law (2,1) DI DE Conclude that these quantities agree but that Bf(x, t) + (6,t). ar dt
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