In a turbulent flow, like a raging river, energy constantly cascades from large whirlpools to small ones. Occasionally, particularly powerful bursts occur, resembling sudden waves crashing against the shore. Scientists asked: can we know in advance when such a "wave" will strike? It turns out the answer depends on which vortices are present in the flow at that moment.

Stochastic modeling of a two-dimensional flow (flat, like the surface of water) showed that each extreme energy burst has its own predictability horizon. Some bursts can be foreseen one chaos period ahead — the time it takes for the flow to completely "forget" its initial state. Others can be foreseen more than four such periods ahead. The deciding factor is the longevity of large vortex structures, which scientists call quadrupolar vortex packets. These structures resemble four connected whirlpools that rotate together.

When such vortex packets live long, they "organize" the flow and make its behavior more predictable. When they quickly decay, the flow becomes chaotic, and the prediction horizon sharply shortens. This conclusion was obtained using a neural network trained on thousands of numerical experiments. The neural network learned to predict energy bursts, and then scientists measured how far into the future its predictions remained accurate.

This approach is like forecasting weather by observing clouds: you don't need to solve complex equations; you just need to recognize the type of clouds and know how long they typically last. This opens a path to estimating predictability limits from real observations — without expensive computations.