In Terence Tao's piece on Kolmogorov's Law (http://terrytao.wordpress.com/2014/05/15/kolmogorovs-power-law-for-turbulence/) he uses the notation for the fluid velocity
$$u: \mathbb{R} \times \mathbb{R}^3/\mathbb{Z}^3 \to \mathbb{R}^3 $$
What is the meaning of the over $\mathbb{Z}^3$ in this context?
This is notation for the quotient group. If you haven't seen this concept, $\mathbb{R}^3/\mathbb{Z}^3$ can be pictured as a unit cube $[0,1)^3$ in which you add "modulo 1", that is, add as you would in $\mathbb{R}^3$ and then cut off the integer part. Another important way to visualize this group is as $(S^1)^3$, the product of three circles.