On the mechanism of the reduction of nonlinearity in the incompressible Navier–Stokes equation

The mechanism of the reduction of nonlinearity recently observed in simulations of decaying isotropic turbulence by Kraichnan and Panda [Phys. Fluids 31, 2395 (1988)] is investigated. It is shown that although the alignment of velocity and vorticity in physical space is not the sole source of the effect, it can enhance the effect significantly. Another source of the reduction seems to be a tendency of the Lamb vector v×ω in Fourier space to align with the wave vector k. The ordering of the energy transfer is suggested to be a dynamically generic effect driving the reduction.