  In this paper, we consider the recently introduced EMAC formulation for the
incompressible Navier-Stokes (NS) equations, which is the only known NS
formulation that conserves energy, momentum and angular momentum when the
divergence constraint is only weakly enforced. Since its introduction, the EMAC
formulation has been successfully used for a wide variety of fluid dynamics
problems. We prove that discretizations using the EMAC formulation are
potentially better than those built on the commonly used skew-symmetric
formulation, by deriving a better longer time error estimate for EMAC: while
the classical results for schemes using the skew-symmetric formulation have
Gronwall constants dependent on $\exp(C\cdot Re\cdot T)$ with $Re$ the Reynolds
number, it turns out that the EMAC error estimate is free from this explicit
exponential dependence on the Reynolds number. Additionally, it is demonstrated
how EMAC admits smaller lower bounds on its velocity error, since {incorrect
treatment of linear momentum, angular momentum and energy induces} lower bounds
for $L^2$ velocity error, and EMAC treats these quantities more accurately.
Results of numerical tests for channel flow past a cylinder and 2D
Kelvin-Helmholtz instability are also given, both of which show that the
advantages of EMAC over the skew-symmetric formulation increase as the Reynolds
number gets larger and for longer simulation times.
