  Dissipation anomaly, a phenomenon predicted by Kolmogorov's theory of
turbulence, is the persistence of a non-vanishing energy dissipation for
solutions of the Navier-Stokes equations as the viscosity goes to zero.
Anomalous dissipation, predicted by Onsager, is a failure of solutions of the
limiting Euler equations to preserve the energy balance. Motivated by a recent
dissipation anomaly construction for the 3D Navier-Stokes equations by Bru\`e
and De Lellis (2023), we prove the existence of various scenarios in the limit
of vanishing viscosity: the total and partial loss of the energy due to
dissipation anomaly, absolutely continuous dissipation anomaly, anomalous
dissipation without dissipation anomaly, and the existence of infinitely many
limiting solutions of the Euler equations in the limit of vanishing viscosity.
We also discover a relation between dissipation anomaly and the discontinuity
of the energy of the limit solution. Finally, expanding on the obtained total
dissipation anomaly construction, we show the existence of dissipation anomaly
for long time averages, relevant for turbulent flows, proving that the
Doering-Foias (2002) upper bound is sharp.
