Quantification of the discretization effects in the representation of key inertial-wave interactions in rotating turbulence

The Navier-Stokes equations in a rotating frame lead to solutions characterized by interactions between wave modes. In asymptotic and weak-turbulence theories, resonant and near-resonant interactions between those modes are expected to be dominant. It is imperative to sufficiently resolve the near- resonant interactions that are thought to be important in the strong rotation limit. When rotating turbulence is studied in a finite-size domain, discrete effects are introduced. We investigate the discretization effects on the capture of exact and near-resonant interactions by numerical simulations. This was done by quantifying the finite-size effect on the number of exact and near- resonant interactions resolved by a given computational domain over a range of rotation rates. A counting of these interactions was done as a function of the nonlinear broadening. The intricate effects of the numerical domain mesh and its truncation are estimated.