We study wave turbulence in systems with two special properties: a large number of fields (large $N$) and a nonlinear interaction that is strongly local in momentum space. The first property allows us to find the kinetic equation at all interaction strengths—both weak and strong, at leading order in $1/N$. The second allows us to turn the kinetic equation—an integral equation—into a differential equation. We find stationary solutions for the occupation number as a function of wave number, valid at all scales. As expected, on the weak-coupling end, the solutions asymptote to Kolmogorov-Zakharov scaling. On the strong-coupling end, they asymptote to either the widely conjectured critical balance scaling or a Kolmogorov-like scaling exponent.

Close

PrevNext

View figure in article

• Large-N expansion in field theory
• Turbulence
• Weak turbulence