  Predicting and perhaps mitigating against rare, extreme events in fluid flows
is an important challenge. Due to the time-localized nature of these events,
Fourier-based methods prove inefficient in capturing them. Instead this paper
uses wavelet-based methods to understand the underlying patterns in a forced
flow over a 2-torus which has intermittent high-energy burst events
interrupting an ambient low energy quiet flow. Three methods are examined to
predict burst events: (1) a straightforward energy tracking approach which acts
as the benchmark; (2) a wavelet proper orthogonal decomposition (WPOD) which
uncovers the key flow patterns seen in the quiet regions and the bursting
episodes; and (3) a wavelet resolvent analysis (WRA) that reveals the forcing
structures that amplifies the underlying flow patterns. Both the wavelet-based
approaches succeed in producing better (earlier) predictions than a simple
energy criterion, with the WRA-based technique always bettering WPOD. However,
both also produce false positives and the improvement of the WRA approach over
WPOD is not as substantial as anticipated. We conjecture that this is because
the mechanism for the bursts in the flow studied is found to be largely modal
associated with the unstable eigenfunction of the Navier-Stokes operator
linearized around the mean flow. The forcing approach should deliver much
better improvements over the WPOD approach for generically non-modal bursting
mechanisms where there is a lag between the imposed forcing and the final
response pattern.
