Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations

We propose a novel approach to induce anomalous dissipation through advection driven by turbulent fluid flows. Specifically, we establish the existence of a velocity field v satisfying randomly forced Navier-Stokes equations, leading to total dissipation of kinetic energy in finite time when advecting a passive scalar. This dissipation phenomenon is uniform across viscosity parameters and initial conditions, representing a case of anomalous dissipation. We further explore dissipation induced by individual realizations of v. Our results extend to scenarios where the passive scalar is replaced by solutions to two or three-dimensional deterministic Navier-Stokes equations advected by v.