Gravity surface wave turbulence in a laboratory flume

Abstract

We present experimental results for water wave turbulence excited by piston-like programmed wavemakers in a water flume with horisontal dimensions 6x12x1.5 meters. Our main finding is that for a wide range of excitation amplitudes the energy spectrum has a power-law scaling, $E_ω\sim ω^{-ν}$. These scalings were achieved in up to one-decade wide frequency range, which is significantly wider than the range available in field observations and in numerical simulations. However, exponent $ν$ appears to be non-universal. It depends on the wavefield intensity and ranges from about 6.5 for weak forcing to about 3.5 for large levels of wave excitations. We discuss our results in the context of the key theoretical predictions, such as Zakharov-Filonenko spectrum $ν=-4$, Phillips spectrum $ν= -5$, Kuznetsov's revision of Phillips spectrum (leading to $ν=-4$) and Nazarenko's prediction $ν=-6$ for weak turbulence in finite basins. We measured Probability Density Function of the surface elevation and good correspondence with the Tayfun shapeexcept values near the maximum which we attribute to an anisotropy and inhomogeneity caused by the finite flume size. We argue that the wavenumber discreteness, due to the finite-size of the flume, prevents four-wave resonant interactions. Therefore, statistical evolution of the water surface in the laboratory is significantly different than in the open ocean conditions.