notation question: What is $\nabla^{l}$ where $l\in \mathbb{N}$

Question

Does $\nabla^{l}$ where $l\in \mathbb{N}$ mean anything?

Could it mean dimension?

We do have $\nabla^{2}=\Delta$, but I've never seen $\nabla^{3}$ .

Found it in page 17

http://arxiv.org/pdf/1304.0926v2.pdf

thank you