Dynamic Phase Alignment in Navier-Stokes Turbulence

In Navier-Stokes turbulence, energy and helicity injected at large scales are subject to a joint direct cascade, with both quantities exhibiting a spectral scaling proportional to k(-5/3). We demonstrate via direct numerical simulations that the two cascades are compatible due to the existence of a strong scale-dependent phase alignment between velocity and vorticity fluctuations, with the phase alignment angle scaling as cos alpha(k) proportional to k(-1).