Predictability of decaying stratified turbulence

Abstract

Predictability of geophysical fluid dynamics at various scales remains a crucial challenge for accurate weather and climate forecasting. Following the pioneering framework established by Lorenz, numerous studies on homogeneous and isotropic turbulence have demonstrated that flows characterized by diverse scales may exhibit limited predictability. This limitation arises from the inevitable amplification of errors in the initial conditions from small scales to larger scales, even if the initial error is confined to small scales. This research investigates the predictability of freely decaying homogeneous stratified turbulence, which serves as a representative model for small-scale geophysical turbulence where rotational effects are negligible. Direct numerical simulations are employed to assess predictability by analyzing the growth of errors introduced in pairs of simulations with near-identical initial conditions; errors are modeled as the difference field of the pair. Previous studies have established a connection between the finite range of predictability and the slope of the kinetic energy spectrum. In the context of stratified turbulence, the shape of the energy spectrum exhibits a dependence on the buoyancy Reynolds number (Reb), particularly at lower values of Reb. This work conducts a comparative analysis of both the energy spectra and the error growth behavior across different regimes of stratified turbulence, encompassing a range of Reb values from O(1) to O(10)⁠. The sensitivity of the obtained results to the introduced error is investigated. Modifying the geometrical shape of the error (spherical vs cylindrical complement) and the cutoff wavenumber while maintaining the initial error kinetic energy did not significantly alter the error dynamics. The results are robust to variations in the method of error introduction.