Gravity Wave Turbulence in a Laboratory Flume

We present an experimental study of the statistics of surface gravity wave turbulence in a flume of a horizontal size $12\times 6\mathrm{m}$. For a wide range of amplitudes the wave energy spectrum was found to scale as $E_{\omega }\sim {\omega }^{-\nu }$ in a frequency range of up to one decade. However, $\nu$ appears to be nonuniversal: it depends on the wave intensity and ranges from about 6 to 4. We discuss our results in the context of existing theories and argue that at low wave amplitudes the wave statistics is affected by the flume finite size, and at high amplitudes the wave breaking effect dominates.

Figure 1

Typical results for the energy spectra. △: an experiment with low wave intensity, $\gamma \approx 0.09$; ○: an experiment with high wave intensity, $\gamma \approx 0.25$.

Figure 2

Plot of the spectral slopes vs the wave intensity $J=E_f/f^{-\nu }$ measured within the inertial interval. Here, $\gamma$ varies in the range from 0.08 to 0.25. Inset: Dependence of the spectral intensity $J$ on the energy dissipation rate. $E_f$ is measured in ${\mathrm{cm}}^2\mathrm{s}$, $f$ is in Hz. Solid and open circles correspond to the signals measured simultaneously in two different points separated by a distance of 0.4 m.

Figure 3

PDF of the wave crests for high wave intensity, $\gamma \approx 0.25$.

Figure 4

PDF of the spectral intensity bandpass filtered with frequency window $\Delta f=\pm 1\mathrm{Hz}$ centered at $f=6\mathrm{Hz}$, $\gamma \approx 0.16$. The inset shows the same plot in log-log coordinates.