In a well-known metaphor for the sensitivity of chaotic systems to initial conditions, a butterfly’s wing flap is imagined to influence the development of a storm. In a dynamically unstable stratified shear layer, small disturbances grow exponentially through various competing instabilities, indicating a similar process in a high-dimensional yet relatively simple system. The objective was to determine whether the primary instability, transition to turbulence, and overall mixing efficiency are sensitive to initial condition details. Using ensembles of nearly identical direct numerical simulations (DNS), we discovered that slight variations in initial random perturbations can lead to significantly different turbulence and mixing outcomes. The figure on the left illustrates the evolution from the initial perturbation, showing the growth and development of KH billows through a horizontal cross-section of Reynolds stress and the turbulent kinetic energy time series. Different initial perturbations result in varied timing of instability growth and kinetic energy levels. This has crucial implications, particularly for initial value problems, as a single simulation may not be representative, suggesting broader implications for the predictability of oceanic and atmospheric movements.
