Generation of imbalance from balanced initial conditions in rotating stratified turbulence

In the regime of rotating stratified flows, we investigate how a high-order nonlinear balance breaks down, at what scale and after how long. To that end, we perform non-hydrostatic Boussinesq simulations where the initial data is balanced using the Baer-Tribbia nonlinear normal mode initialization scheme, which is accurate to second order in the Rossby number, as the next-order improvement to first-order QG theory. This nonlinear initialization procedure yields an ageostrophic contribution to the energy spectrum that has a very steep slope. If the Rossby and Froude numbers are small enough, this steep spectrum is maintained in the range of the resolved scales for a limited period of time. However, if the Rossby number is increased, a shallow range emerges in the tail of ageostrophic spectrum in time. This shallow range is shown to be the unbalanced part of the dynamics which dominates the total energy spectrum at small scales. By comprehensive investigation of balanced and unbalanced transfer spectra, it is found that the imbalance receives its energy from the balanced part of the flow at relatively large scales near the low-wave number end of the shallow spectral range. Unbalanced energy then cascades to small scales where it is efficiently dissipated. The mechanism that describes this forward cascade is similar to that of previous studies starting from unbalanced initial conditions.