Non-linear amplification in hydrodynamic turbulence*

Using Direct Numerical Simulations performed on periodic cubes of various sizes, the largest one being $8192^3$, we examine the nonlinear advection term in the Navier-Stokes equations in fully developed turbulence. Flow regions with depleted nonlinearity are not found to be correlated with low dissipation, in contrast to theoretical claims (Moffat $\&$ Tsinober, Annu.~Rev.~Fluid Mech.~{\bf 24} 281-312 (1992)). With increasing Reynolds number ($R_\lambda$), the Navier-Stokes dynamics amplifies the solenoidal (divergence free) part of the nonlinear term, in contrast to the nonlinear suppression observed in past studies (Kraichnan $\&$ Panda, Phys.~Fluids {\bf 31} 2395-2397 (1988); Shtilman, Phys.~Fluids A {\bf 4} 197-199 (1992)), at low $R_\lambda$. With increasing $R_\lambda$, the nonlinear amplification makes the vortex stretching mechanism more intermittent, with the vortex stretching spectrum displaying a scaling anomaly similar to other small-scale quantities commonly examined in turbulence. At higher $R_\lambda$, the vortex tubes are passively advected for much of the time, with the intense stretching of the vortex tubes occurring rarely, but accounting for much of the forward cascade dynamics.