Why advection equation is time reversible?

Question

I have advection equation stated in materials provided by professor as follow:

$$ \frac{\delta u}{\delta t} = \nabla \cdot (Vu) $$

According to Why heat equation is not time-reversible? (Time arrow in mathematics) I think that equation is not time reversible due to having odd derivative of t. But my professor stated that the equation is time reversible.

So my question is as follow:

Is this equation time reversible or not?

Maybe V also changes under a change $t\rightarrow -t$ if it is a velocity type variable — Triatticus, Jun 28 '17 at 19:45

score 1 · Accepted Answer · answered Jun 28 '17 at 20:38

1

As noted in the comment, in the advection equation $u$ is a scalar field, as the temperature in the heat equation, but $V$ is a velocity field that change sign when the time $t$ is changed to $-t$.

answered Jun 28 '17 at 20:38

Emilio Novati

64,377

Why advection equation is time reversible?

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