Gravity Wave Turbulence in Wave Tanks: Space and Time Statistics

We present the first simultaneous space-time measurements for gravity wave turbulence in a large laboratory flume. We found that the slopes of $k$ and $\omega$ wave spectra depend on wave intensity. This cannot be explained by any existing theory considering wave turbulence as the result of either breaking events or weakly nonlinear wave interactions. Instead, we show that random waves and breaking or coherent structures appear to coexist: The former show themselves in a quasi-Gaussian core of the probability density function and in the low-order structure functions, and the latter in the probability density function tails and the high-order structure functions.

Figure 1

A spectrum in the $k$ domain. The inset shows an image with the detected boundary on the air-water interface.

Figure 2

Slopes of the wave spectra. (a) The $k$ slope as a function of wave intensity. (b) The $k$ slope vs the $\omega$ slope. The linear dispersion relation $\omega =\sqrt{gk}$ is shown by the solid line.

Figure 3

PDFs of the second-order differences: (a) in the $t$ domain, $\tau =30$, 60, 130, 290, and 580 ms (from the top down); (b) in the $x$ domain, $l=54$, 11, 25, 62, 149, and 360 mm (from the top down); (c) SFs of ${\delta }_L^{(2)}$ for $p=1,\dots ,8$.

Figure 4

SF scaling exponents: (a) $\zeta (p)$ in the $t$ domain and (b) $\xi (p)$ in the $k$ domain.