Predictability of Stratified Turbulence

Abstract

In the study of geophysical fluid dynamics, predictability of dynamics at different scales still stands in the foreground of interest as one of the primary challenges. Following Lorenz's pioneering framework, several results from homogeneous and isotropic turbulence have suggested that flows with many scales of motion present limited predictability due to the inevitable contamination of error from small to large scales, even if initially confined to small scales. In this work, we investigate the predictability of freely decaying stratified turbulence, which is representative of small-scale geophysical turbulence where rotational effects are neglected.

Predictability of stratified turbulence is studied using direct numerical simulations by analyzing the error growth in pairs of realizations of velocity fields departing from almost identical initial conditions. Previous studies have indicated that the finite range of predictability is determined by the slope of the flow's kinetic energy spectrum. In stratified turbulence, the shape of the energy spectrum depends on the buoyancy Reynolds number (Reb), at least when Reb is not too large. We perform a comparative analysis of spectra and perturbation upscale growth behaviour in different regimes of stratified turbulence from O(10) to unitary order of buoyancy Reynolds number.

Furthermore, we explore the sensitivity of our experimental outcomes with respect to error introduction. There were no discernible changes between the behavior of the systems and their associated error dynamics while modifying the geometrical shape of the error introduction, going from a spherical domain complement to a cylindrical complement. Likewise, the experiments were insensitive to adjusting the cutoff wavenumber (kc) at which the error is introduced while keeping the same initial error kinetic energy, obtaining similar results for kc = 20,40,60,80.