Anomalous Statistics and Large Deviations of Turbulent Water Waves past a Step

TL;DR

This paper employs large deviation theory to analyze the non-Gaussian, asymmetric statistical features of turbulent water waves passing over a step, revealing the most influential wave patterns responsible for extreme events.

Contribution

It introduces a novel computational approach combining large deviation theory with the truncated KdV equation to accurately predict rare, high-amplitude wave events in turbulent water flows.

Findings

Accurately captures non-Gaussian wave height distributions

Identifies spatio-temporal patterns of anomalous waves

Demonstrates potential for broader nonlinear Hamiltonian systems

Abstract

A computational strategy based on large deviation theory (LDT) is used to study the anomalous statistical features of turbulent surface waves propagating past an abrupt depth change created via a step in the bottom topography. The dynamics of the outgoing waves past the step are modeled using the truncated Korteweg-de Vries (TKdV) equation with random initial conditions at the step drawn from the system's Gibbs invariant measure of the incoming waves. Within the LDT framework, the probability distributions of the wave height can be obtained via the solution of a deterministic optimization problem. Detailed numerical tests show that this approach accurately captures the non-Gaussian features of the wave height distributions, in particular their asymmetric tails leading to high skewness. These calculations also give the spatio-temporal pattern of the anomalous waves most responsible for these non-Gaussian features. The strategy shows potential for a general class of nonlinear Hamiltonian systems with highly non-Gaussian statistics.