Saturation of the Inverse Cascade in Surface Gravity-Wave Turbulence

Numerical Validation of the Inverse Cascade of Surface Gravity Wave Action

We report numerical simulations of surface gravity waves forced at small scale and the subsequent inverse cascade of wave action. We combine the spectral approach to simulating weakly nonlinear waves with the capabilities of modern graphics processing units to reach unprecedented scale separation between the forcing and domain scales. The resulting broad inertial range allows for an unambiguous confirmation of the theoretical prediction for the spectrum in the inverse cascade regime, both in terms of spectral index and dependence of the spectral level on the action flux.

Inverse Cascade Spectrum of Gravity Waves in the Presence of a Condensate: A Direct Numerical Simulation

During the set of direct numerical simulations of the forced isotropic turbulence of surface gravity waves in the framework of primordial dynamical equations, the universal inverse cascade spectrum was observed. The slope of the spectrum is the same (in the margin of error) for different levels of pumping and nonlinearity as well as dissipation present in the system. In all simulation runs formation of the inverse cascade spectrum was accompanied by the appearance of a strong long wave background (condensate). The observed slope of the spectrum ∼k^{-3.07} is different from the constant wave action flux solution predicted by the wave turbulence theory ∼k^{-23/6}.

Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence

We investigate experimentally three-dimensional (3D) hydrodynamic turbulence at scales larger than the forcing scale. We manage to perform a scale separation between the forcing scale and the container size by injecting energy into the fluid using centimetric magnetic particles. We measure the statistics of the fluid velocity field at scales larger than the forcing scale (energy spectra, velocity distributions, and energy flux spectrum). In particular, we show that the large-scale dynamics are in statistical equilibrium and can be described with an effective temperature, although not isolated from the turbulent Kolmogorov cascade. In the large-scale domain, the energy flux is zero on average but exhibits intense temporal fluctuations. Our Letter paves the way to use equilibrium statistical mechanics to describe the large-scale properties of 3D turbulent flows.

Low-frequency spectra of bending wave turbulence

We study experimentally the dynamics of long waves among turbulent bending waves in a thin elastic plate set into vibration by a monochromatic forcing at a frequency f_{o}. This frequency is chosen large compared with the characteristic frequencies of bending waves. As a consequence, a range of conservative scales without energy flux on average exists for frequencies f<f_{o}. Within this range, we report a flat power density spectrum for the orthogonal velocity, corresponding to energy equipartition between modes. Thus, the average energy per mode β^{-1}-analogous to a temperature-fully characterizes the large-scale turbulent wave field. We present an expression for β as a function of the forcing frequency, amplitude, and of the plate characteristics.