1. Given the three-dimensional Eulerian flow field u(x,y,z,t) = (y,-x,0.1z).
(i) Write down the equations satisfied by the particle paths.
(ii) Sketch the trajectory of the fluid particle initially located (at t = 0) at position (0,1,1). What is its long time asymptotic (behavior as t----> oo)?
(iii) Compute the Eulerian and the Lagrangian accelerations.

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