Phase Alignment and Finite-Time Blow-Up in a GOY Shell Model of Turbulence

The paper investigates how Fourier-phase alignment influences the formation of finite-time singularities in turbulent cascades within the GOY shell model. As stated in the abstract, “we impose a perfect alignment of the phases across all interacting shells” and observe that “the forced system exhibits a robust finite-time blow-up, with enstrophy diverging while energy remains bounded.” The study shows that perfect constructive interference across triads triggers a clean finite-time singularity, while even small phase offsets suppress the blow-up. The mechanism does not transfer directly to the full Navier–Stokes equations, where geometric frustration prevents coherent phase alignment across all triads.