  Completing the study initiated by Mounaix and Collet [J. Stat. Phys. {\bf
143}, 139-147 (2011)], we investigate the realizations of a Gaussian random
field in the limit where a given (general) quadratic form of the field is
large. Concentration in $L^2$ and in probability is proved under mild
conditions and the resulting quasi-deterministic behavior of the field is
given. Applications to a large {\it local} quadratic form are considered in two
specific cases. In particular, the quasi-deterministic structure of a Gaussian
random flow with a large local helicity at some given point is determined
explicitly.
