We investigate the Navier-Stokes turbulence driven by a stochastic random
Gaussian force. Using a field-theoretic approach, we uncover an anomaly that
brings hidden structure to the theory. The anomaly is generated by a
non-self-adjoint operator of the Jacobian and it follows the symmetries of the
stochastic Navier-Stokes equation. We calculate the anomaly and demonstrate
that by forcing the anomaly to vanish, the velocity field is constrained and a
monopole-type object with a constant charge is formed. When the viscosity is
zero, the anomaly can be interpreted as the Brownian damping coefficient of a
random fluid particle. We provide the Brownian particle equation and its
solution in the presence of a pump and viscosity. Our results suggest that the
anomaly is an inherent feature of stochastic turbulence and must be taken into
account in all stochastic turbulence calculations. This constitutes an
additional law for the original set of stochastic Navier-Stokes equations.Comment: 16 pages. One more additio