  We study the two-dimensional Navier-Stokes equations forced by random noise
with a diffusive term generalized via a fractional Laplacian that has a
positive exponent strictly less than one. Because intermittent jets are
inherently three-dimensional, we instead adapt the theory of intermittent form
of the two-dimensional stationary flows to the stochastic approach presented by
Hofmanov$\acute{\mathrm{a}}$, Zhu $\&$ Zhu (2019, arXiv:1912.11841 [math.PR])
and prove its non-uniqueness in law.
