Nonlinear amplification in hydrodynamic turbulence

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being 8192(3), we examine the nonlinear advection term in the Navier-Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier-Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Automated summary

Through direct numerical simulations, it is found that the nonlinear advection term in the Navier-Stokes equations amplifies with increasing Reynolds number, making the vortex stretching mechanism more intermittent. Previous findings of global suppression of nonlinearity are restricted to low Reynolds numbers.