Exclusion of zero modes in hydrodynamic turbulence

Previous studies of hydrodynamic turbulence have shown that it is not possible to totally exclude infrared divergences due to the transport of small vortices by a large-scale velocity field. In the present paper, it is shown that this situation is a consequence of the loss of generalized solutions of ballistic-mode type, having a continuous spectrum and concentrated near k = 0. These solutions (termed zero modes) describe the free motion of Lagrangian particles. It is shown that the arbitrary spectral parameter in these modes can be chosen in such a way that the contribution from the interaction of near harmonics to the k = 0 region can be compensated, thereby reducing the infrared divergences.