[nlin/0610015] Gravity surface wave turbulence in a (original) (raw)
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Different Regimes for Water Wave Turbulence
Physical Review Letters, 2011
We present an experimental study on gravity capillary wave turbulence in water. By using space-time resolved Fourier transform profilometry, the behavior of the wave energy density j k;! j 2 in the 3D ðk; !Þ space is inspected for various forcing frequency bandwidths and forcing amplitudes. Depending on the bandwidth, the gravity spectral slope is found to be either forcing dependent, as classically observed in laboratory experiments, or forcing independent. In the latter case, the wave spectrum is consistent with the Zakharov-Filonenko cascade predicted within wave turbulence theory.
Gravity surface 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 6 m. For a wide range of amplitudes the wave energy spectrum was found to scale as E ! ! ÿ in a frequency range of up to one decade. However, 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.
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 6 m. For a wide range of amplitudes the wave energy spectrum was found to scale as E ! ! ÿ in a frequency range of up to one decade. However, 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.
SSRN Electronic Journal
The intermittency of gravity wave turbulence on the surface of an infinitely deep fluid has been studied numerically. We estimated the scaling exponent of surface elevation structure-functions directly from the equations of motion, e.g., by numerical solution of the underlying equations of motion, without any additional closure assumptions (e.g., phase randomisation) and reduction to the kinetic equations as in the conventional framework of wave turbulence theory. With our high-resolution numerical methods for accurately modelling the nonlinear water surface, we were able to evaluate the scaling exponents of the structure-function up to relatively high orders (p = 15), which has not been previously reported. We investigated the effect of wave steepness and forcing on intermittency and compared our results with other analytical and numerical studies, including results on the intermittency of wave turbulence of a different nature (turbulence of bending waves on a plate and magnetohydrodynamic turbulence). Our results support the conjecture of universality for intermittency phenomena in wave turbulence.
Discreteness and its effect on water-wave turbulence
We perform numerical simulations of the dynamical equations for a free water surface in a finite basin in the presence of gravity. Wave Turbulence (WT) is a theory derived for describing the statistics of weakly nonlinear waves in the infinite basin limit. Its formal applicability condition on the minimal size of the computational basin is impossible to satisfy in present numerical simulations, and the number of wave resonances is significantly depleted due to the wavenumber discreteness. The goal of this paper will be to examine which WT predictions survive in such discrete systems with depleted resonances and which properties arise specifically due to the discreteness effects. As in [A.I. Dyachenko, A.O. Korotkevich, V.E. Zakharov, Weak turbulence of gravity waves, JETP Lett. 77 (10) (2003); Phys. Rev. Lett. 92 (13) (2004) 134501; M. Onorato et al., Freely decaying weak turbulence for sea surface gravity waves, Phys. Rev. L 89 (14) (2002); N. Yokoyama, Statistics of Gravity Waves obtained by direct numerical simulation, JFM 501 -178], our results for the wave spectrum agree with the Zakharov-Filonenko spectrum predicted within WT. We also go beyond finding the spectra and compute the probability density function (PDF) of the wave amplitudes and observe an anomalously large, with respect to Gaussian, probability of strong waves which is consistent with recent theory [Y. Choi, Y.V. Lvov, S. Nazarenko, B. Pokorni, Anomalous probability of large amplitudes in wave turbulence, Phys. Lett. A 339 (3-5) (2004) 361-369 (also on arXiv: math-ph/0404022 v1); Y. Choi, Y.V. Lvov, S. Nazarenko, Probability densities and preservation of randomness in wave turbulence, India (also on arXiv.org: math-ph/0412045)]. Using a simple model for quasi-resonances we predict an effect arising purely due to discreteness: the existence of a threshold wave intensity above which a turbulent cascade develops and proceeds to arbitrarily small scales. Numerically, we observe that the energy cascade is very "bursty" in time and is somewhat similar to sporadic sandpile avalanches. We explain this as a cycle: a cascade arrest due to discreteness leads to accumulation of energy near the forcing scale which, in turn, leads to widening of the nonlinear resonance and, therefore, triggering of the cascade draining the turbulence levels and returning the system to the beginning of the cycle. (Y.V. Lvov). of statistics to Gaussian or/and to phase randomness (the two are not the same; see ). This closure yields a wave-kinetic equation (WKE) for the waveaction spectrum. Such a WKE for the surface waves was first derived by Hasselmann . A significant achievement in WT theory was to realize that the most relevant states in WT are energy cascades through scales similar to the Kolmogorov cascades in Navier-Stokes turbulence, rather than thermodynamic equilibria as in the statistical theory of gases. This understanding came when Zakharov and Filonenko found an exact power-law solution to a WKE which is similar to the famous Kolmogorov spectrum .
Gravity Wave Turbulence in Wave Tanks
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 ! 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. FIG. 4 (color online). SF scaling exponents: (a) ðpÞ in the t domain and (b) ðpÞ in the k domain.
Role of the basin boundary conditions in gravity wave turbulence
Journal of Fluid Mechanics, 2015
Gravity wave turbulence is investigated experimentally in a large wave basin in which irregular waves are generated unidirectionally. The roles of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. A quasi-one-dimensional field of nonlinear waves propagates towards the beach, where they are damped whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency power law with an exponent that increases continuously with the forcing amplitude up to a value close to −4-4−4. The physical mechanisms involved most likely differ with the boundary condition used, but cannot be easily discriminated with only temporal measurements. We also studied freely decaying gravity wave turbulen...
Wave turbulence and intermittency in directional wave fields
Wave Motion
The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In realistic oceanic sea states, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the effect of wave directionality on wave turbulence. Results show that the occurrence of coherent and intermitted structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes.