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An unsteady fluid flow has velocity field $$\mathbf{u} = (u,v) = t^2(x^2y, -y^2x).$$ Find the limit as $t \to \infty$ of $\displaystyle \frac{1}{t^3} \ln D(t)$, where $D(t)$ is the distance between $P_1,P_2$ as a function of time.

I have that for $P_1$ the particle path is $y = 2-x$, for $P_2$ the particle path is $y = 6-(3/2)x$, at $t=0$, $P_1$ is at $(1,1)$ and $P_2$ is at $(2,3)$, stream function is $\psi = t^2x^2y^2/2$.

I am not sure how to go about finding the function $D(t)$.

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    Write properly mathematics in this site. After being a member for more than 1 year I think it is about time...And this question seems more appropiated for physics than for mathematics. – 2017-01-02
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    @DonAntonio maybe, however i do a mathematics degree and this is applied mathematics so – 2017-01-02
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    Call it as you wish: one needs to know "stream function" and its role in this, and only someone with some minimal working knowledge of this stuff in fluids can help you (I, for one, have no idea what to do with that, and I am lecturing right in this semester in vectorial calculus...). I think in the physics section of exchange it is more likely someone will know. – 2017-01-02

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