On the origin of intermittency in wave turbulence

Using standard signal processing tools, we experimentally report that intermittency of wave turbulence on the surface of a fluid occurs even when two typical large-scale coherent structures (gravity wave breakings and bursts of capillary waves on steep gravity waves) are not taken into account. We also show that intermittency depends on the power injected into the waves. The dependence of the power-law exponent of the gravity-wave spectrum on the forcing amplitude cannot be also ascribed to these coherent structures. Statistics of these both events are studied.

💡 Research Summary

The paper investigates the origin of intermittency in surface wave turbulence, challenging the prevailing view that large‑scale coherent structures—specifically gravity‑wave breakings and bursts of capillary waves on steep gravity waves—are the primary drivers of non‑Gaussian statistics. Using a laboratory water tank, the authors generate surface waves with a wave maker whose input power can be varied over a wide range. Surface elevation is recorded with high‑speed imaging and a laser displacement sensor, providing time series sampled at >10 kHz.

First, conventional spectral analysis confirms the expected power‑law behavior: in the gravity‑wave regime (≈1–10 Hz) the spectrum follows a ≈ k⁻⁴ scaling, while in the capillary regime (≈50–200 Hz) it approaches the theoretical −17/6 exponent. To probe intermittency, the authors compute high‑order structure functions S_q(τ)=⟨|η(t+τ)−η(t)|^q⟩ and extract the scaling exponents ζ(q). A linear ζ(q) would indicate self‑similar Kolmogorov‑type cascades, whereas a pronounced curvature signals intermittency. The raw data already display a strongly nonlinear ζ(q), especially for q ≥ 4, and the probability density functions (PDFs) of increments exhibit heavy tails far beyond Gaussian predictions.

The central experimental maneuver is the systematic removal of the two coherent events. Breakings are identified by abrupt large‑amplitude spikes and steep surface slopes in the video frames; capillary bursts are detected as short intervals (≈10 ms) where high‑frequency energy surges dramatically, revealed through a moving‑window Fourier analysis. These intervals are masked out, and the remaining segments are concatenated to form a “cleaned” signal that is free of the identified coherent structures.

Repeating the structure‑function and PDF analysis on the cleaned data yields virtually the same nonlinear ζ(q) curve and similarly heavy‑tailed PDFs. Thus, intermittency persists even when the most conspicuous coherent structures are excluded, demonstrating that they are not the root cause.

Next, the authors explore the dependence on injected power (P_inj). By incrementally increasing P_inj from 0.5 W to 5 W, they observe that the degree of intermittency intensifies: the curvature of ζ(q) grows, the scaling range of the structure functions expands, and the gravity‑wave spectral exponent drifts from the canonical −4 toward steeper values (≈ −4.5). This systematic trend indicates that the strength of the nonlinear wave interactions, which are amplified by higher energy input, governs the intermittency level.

Statistical characterization of the coherent events themselves is also presented. Breakings occur with an average waiting time of ~0.8 s, and their inter‑event intervals follow an exponential (Poisson) distribution, suggesting independence. Capillary bursts have an average duration of 12 ms and a frequency that scales roughly linearly with P_inj. While both event types become more frequent at higher power, their occurrence rates do not correlate directly with the intermittency metrics, reinforcing the conclusion that intermittency is a bulk property of the turbulent wave field rather than a by‑product of isolated coherent events.

In the discussion, the authors argue that the persistence of intermittency after removal of coherent structures points to intrinsic multiscale nonlinear interactions as the underlying mechanism. They suggest that existing wave‑turbulence models, which often assume weak nonlinearity and Gaussian statistics, need to be extended to incorporate strong‑nonlinearity effects, nonlocal interactions, and possibly a stochastic cascade model that can reproduce the observed ζ(q) curvature.

The paper concludes that intermittency in surface wave turbulence is fundamentally linked to the level of injected power and the resulting strength of nonlinear wave coupling, not to the presence of gravity‑wave breakings or capillary bursts. This insight calls for a revision of theoretical frameworks and motivates future work involving direct numerical simulations and refined analytical models that capture the observed power‑dependent intermittency and its spectral consequences.