  We consider Berry's random planar wave model (1977), and prove spatial
functional limit theorems - in the high-energy limit - for discretized and
truncated versions of the random field obtained by restricting its nodal length
to rectangular domains. Our analysis is crucially based on a detailed study of
the projection of nodal lengths onto the so-called second Wiener chaos, whose
high-energy fluctuations are given by a Gaussian total disorder field indexed
by polygonal curves. Such an exact characterization is then combined with
moment estimates for suprema of stationary Gaussian random fields, and with a
tightness criterion by Davydov and Zikitis (2005).
