Uncertainty Growth in Stably Stratified Turbulence

TL;DR

This study quantifies how stratification affects chaos and predictability in turbulence, showing that increased stratification suppresses chaos but preserves universal uncertainty growth patterns, with anisotropic spread along stratification direction.

Contribution

It provides the first systematic analysis of how stratification influences uncertainty growth and chaotic dynamics in three-dimensional turbulence using decorrelator diagnostics.

Findings

Increasing stratification reduces the Lyapunov exponent, indicating less chaos.

Uncertainty growth follows a universal sequence: decay, exponential growth, saturation.

Uncertainty spreads more slowly along the stratification direction, increasing anisotropy.

Abstract

We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. We systematically examine how this exponent depends on stratification strength, quantified by the Brunt--V\"{a}is\"{a}l\"{a} frequency and the Froude number, in a parameter regime relevant to oceanic flows. We find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence -- initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. Our results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows.