Time Scale of Resonant Wave Interactions in Incompressible Hall MHD Turbulence

Wave interactions determine the spectral distribution of energy and other quantities in a turbulent system. In particular, resonant interactions have been shown to determine the long-time behavior of incompressible Hall MHD. Fifteen numerical examples of resonant three-wave systems are constructed with a variety of angles between the interacting wavenumbers. These systems are studied in a Fourier pseudospectral simulation of incompressible Hall MHD to determine their formation of a turbulent state. The power spectrum of each nonlinearity is found to determine which effects are dominant. The energy of the waves in the triplet system is analyzed to determine a characteristic time scale of energy transfer. This allows correlations to be found with the predicted time for the Jacobi-elliptic function solution of the three-wave system.