High resolution simulations reveal the impact of frequency bandwidth on a one-dimensional model for wave turbulence

Wave turbulence theory studies the nonlinear interaction between weak waves. It has important applications in many systems in physics, including the internal wave activity in the ocean. In 1997, Courant researchers Andrew Majda, David McLaughlin, and Esteban Tabak proposed the MMT model as a convenient one-dimensional toy model in which to explore the predictions of WTT using high-resolution numerical simulations. However, up until now, the simulations of the MMT system have not agreed with the theoretical prediction and there have been no satisfying explanations. Recently, CAOS PhD student Ryan Shìjié Dù and professor Oliver Bühler have published a paper bridging the theory and simulation gap. Using the NYU supercomputing resources, they were able to simulate the MMT system with higher resolution than ever before over a large parameter space. They discovered that the distances between the forcing and dissipation frequencies affect the equilibrium turbulence dynamics. The theoretical result is recovered in the limit where the distances are infinite. Their discoveries in this toy model of wave turbulence could have crucial implications for the application of wave turbulence theory for the ocean internal wave, where the frequency is limited to a finite range.