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Let $(M,g)$ be a smooth compact Riemannian surface with no boundary. Given asmooth vector field $V$ with finitely many zeroes on $M$, we study thedistribution of the number of tangencies to $V$ of the nodal components ofrandom band-limited functions. It is determined that in the high-energy limit,these obey a universal deterministic law, independent of the surface $M$ andthe vector field $V$, that is supported precisely on the even integers $2\mathbb{Z}_{> 0}$.

Direction distribution for nodal components of random band-limited functions on surfaces