Atmosphere Ocean Science Friday Seminar

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Turbulent spectra of the Majda-McLaughlin-Tabak (MMT) model: theory and numerical experiment

Speaker: Ryan Shijie Du, CAOS

Location: Warren Weaver Hall 1314

Date: Friday, February 25, 2022, 4 p.m.

Notes:

The Majda-McLaughlin-Tabak (MMT) equation was proposed as a 1D testbed for the validity of the wave turbulence theory. But since the original 97 paper, it has been a mystery why the numerical simulations of the MMT equation do not exhibit the turbulence spectra slopes predicted by the wave turbulence theory. We explore this problem using theory and numerical experiments. Using a scaling symmetry group argument, we found a family of possible spectra slopes that the MMT equation could exhibit. High-resolution numerical simulations do not agree with the theory, but exhibit dependence of the spectra slopes on the locations of dissipation. This is a factor that neither the wave turbulence theory nor our scaling symmetry argument accounts for. Our result suggests the need for further theoretical development on the Majda-McLaughlin-Tabak (MMT) equation.