If we think of a given Riemannian surface S as a vibrating membrane the set of stagnation points on the membrane is called the nodal set. Specifically the nodal sets are zero sets of eigenfunctions of the scalar Laplacian on S . In this talk I will present a result which shows that any set of smooth curves, which divides the surface into two pieces, may be realised, up to isotopy, as a nodal set in a suitably chosen Riemannian metric. In the context of the previous talk I will also show how to use this result to construct overtwisted energy-minimizing curl eigenfields (which gives a negative answer to the conjecture posed by Etnyre and Ghrist in their work on hydrodynamics).