Energy flux measurement from the dissipated energy in capillary wave turbulence

We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a fluid by changing its viscosity. We observe that the frequency power law scaling of the capillary spectrum departs significantly from its theoretical value when the dissipation is increased. The energy dissipated by capillary waves is also measured and found to increase nonlinearly with the mean power injected within the fluid. Here, we propose an experimental estimation of the energy flux at every scale of the capillary cascade. The latter is found to be non constant through the scales. For fluids of low enough viscosity, we found that both capillary spectrum scalings with the frequency and the newly defined mean energy flux are in good agreement with wave turbulence theory. The Kolmogorov-Zakharov constant is then experimentally estimated and compared to its theoretical value.Comment: Physical Review E (2013) submitted to PR

Nonlinear waves on the surface of a fluid covered by an elastic sheet

We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the dispersion relation of waves. When the forcing is increased, a significant nonlinear shift of the dispersion relation is observed. We show that this shift is due to an additional tension of the sheet induced by the transverse motion of a fundamental mode of the sheet. When the system is subjected to a random noise forcing at large scale, a regime of hydro-elastic wave turbulence is observed with a power-law spectrum of the scale in disagreement with the wave turbulence prediction. We show that the separation between relevant time scales is well satisfied at each scale of the turbulent cascade as expected theoretically. The wave field anisotropy, and finite size effects are also quantified and are not at the origin of the discrepancy. Finally, the dissipation is found to occur at all scales of the cascade contrary to the theoretical hypothesis, and could thus explain this disagreement.Comment: Journal of Fluid Mechanics (2013

Direct numerical simulations of capillary wave turbulence

This work presents Direct Numerical Simulations of capillary wave turbulence solving the full 3D Navier Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after few forcing periods. Smaller wave scales are generated by nonlinear interactions, and the wave height spectrum is found to obey a power law in both wave number and frequency in good agreement with weak turbulence theory. By estimating the mean energy flux from the dissipated power, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with the exact theoretical value. The time scale separation between linear, nonlinear interaction and dissipative times is also observed. These numerical results confirm the validity of weak turbulence approach to quantify out-of equilibrium wave statistics.Comment: Physical Review Letters (2014) in pres

Decay of capillary wave turbulence

We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent than the one found in the stationary regime, in agreement with weak turbulence predictions. The amplitude of all Fourier modes are found to decrease exponentially with time at the same damping rate. The longest wavelengths involved in the system are shown to be damped by viscous surface boundary layer. These long waves play the role of an energy source during the decay that sustains nonlinear interactions to keep capillary waves in a wave turbulent state

Breaking wave field statistics with a multilayer model

The statistics of breaking wave fields is characterised within a novel multi-layer framework, which generalises the single-layer Saint-Venant system into a multi-layer and non-hydrostatic formulation of the Navier-Stokes equations. We simulate an ensemble of phase-resolved surface wave fields in physical space, where strong non-linearities including wave breaking are modelled, without surface overturning. We extract the kinematics of wave breaking by identifying breaking fronts and their speed, for freely evolving wave fields initialised with typical wind wave spectra. The $\Lambda(c)$ distribution, defined as the length of breaking fronts (per unit area) moving with speed $c$ to $c+dc$ following Phillips 1985, is reported for a broad range of conditions. We recover the $\Lambda(c) \propto c^{-6}$ scaling without any explicit wind forcing for steep enough wave fields. A scaling of $\Lambda(c)$ based solely on the mean square slope and peak wave phase speed is shown to describe the modelled breaking distributions well. The modelled breaking distributions are found to be in good agreement with field measurements and the proposed scaling is consistent with previous empirical formulations. The present work paves the way for simulations of the turbulent upper ocean directly coupled with realistic breaking waves dynamics, including Langmuir turbulence, and other sub-mesoscale processes.Comment: first submissio

Bubble deformation by a turbulent flow

We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier-Stokes equations, considering a low-density bubble in the high density turbulent flow at various Weber number (the ratio of turbulent and surface tension forces) using the air-water density ratio. We discuss a theoretical framework for the bubble deformation in a turbulent flow using a spherical harmonic decomposition. We propose, for each mode of bubble deformation, a forcing term given by the statistics of velocity and pressure fluctuations, evaluated on a sphere of the same radius. This approach formally relates the bubble deformation and the background turbulent velocity fluctuations, in the limit of small deformations. The growth of the total surface deformation and of each individual mode is computed from the direct numerical simulations using an appropriate Voronoi decomposition of the bubble surface. We show that two successive temporal regimes occur: the first regime corresponds to deformations driven only by inertial forces, with the interface deformation growing linearly in time, in agreement with the model predictions, whereas the second regime results from a balance between inertial forces and surface tension. The transition time between the two regimes is given by the period of the first Rayleigh mode of bubble oscillation. We discuss how our approach can be used to relate the bubble lifetime to the turbulence statistics and eventually show that at high Weber number, bubble lifetime can be deduced from the statistics of turbulent fluctuations at the bubble scale

Role of the basin boundary conditions in gravity wave turbulence

Gravity wave turbulence is studied experimentally in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite to the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. Quasi-one dimensional field of nonlinear waves propagate before to be damped by the beach 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, which is the value predicted by the weak turbulence theory. The physical mechanisms involved are probably different according to the boundary condition used, but cannot be easily discriminated with only temporal measurements. We have also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation that highlights the important role of a large scale Fourier mode. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with a recent theoretical value.Comment: Journal of Fluid Mechanics, Cambridge University Press (CUP), 2015, in press in JF

Data set for "Role of contamination in optimal droplet production by collective bubble bursting"

Data set for Role of contamination in optimal droplet production by collective bubble bursting.This work has been supported by NSF Grant 1849762, and the Cooperative Institute for Earth System modeling between Princeton and the Geophysical Fluid Dynamics Laboratory (GFDL) NOAA.List of files is described in the readme