Related papers: Testing the consistency of the resonant wave inter…
Ocean wind waves are a fundamental manifestation of complex dynamics in geophysical fluid systems, characterized by a rich interplay between dispersion and nonlinearity. While linear wave theory provides a first-order description of wave…
We report evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is {\em not}, in fact, slow. Instead nonlinear transfers lead to evolution time scales that are smaller than one wave…
Nonlinear triadic interactions are at the heart of our understanding of turbulence. In flows where waves are present modes must not only be in a triad to interact, but their frequencies must also satisfy an extra condition: the interactions…
High-frequency wave propagation in near-inertial wave shear has been considered fundamental in setting the spectral character of the oceanic internal wave continuum and for transporting energy to wave-breaking. We compare idealized ray…
To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the…
Across the stable density stratification of the abyssal ocean, deep dense water is slowly propelled upward by sustained, though irregular, turbulent mixing. The resulting mean upwelling determines large-scale oceanic circulation properties…
In this paper, using multiple scale analysis we derive a generalized mathematical model for amplitude evolution, and for calculating the energy exchange in resonant and near-resonant global triads consisting of weakly nonlinear internal…
It is generally accepted that the evolution of deep-water surface gravity wave spectrum is governed by quartet resonant and quasi-resonant interactions. However, it has also been reported in both experimental and computational studies that…
Weakly nonlinear internal wave-wave interaction is a key mechanism that cascades energy from large to small scales, leading to ocean turbulence and mixing. Oceans typically have a non-uniform density stratification profile; moreover,…
We study the spectral energy transfer due to wave-triad interactions in the Garrett-Munk spectrum of internal gravity waves (IGWs) based on a numerical evaluation of the collision integral in the wave kinetic equation. Our numerical…
Through basin-scale circulations, the ocean regulates global distributions of heat, nutrients, and greenhouse gases. To properly predict the future of the ocean under climate change, we need to develop a thorough understanding of the…
Modeling ocean surface waves under complex ocean current conditions is of crucial importance to many naval applications. For example, traveling ships and underwater vehicles generate spatially heterogeneous currents behind them through…
We analyze analytically and numerically the scale invariant stationary solution to the internal wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading order contributions are given (i) by triads with…
The high-frequency limit of the Garrett and Munk spectrum of internal waves in the ocean and the observed deviations from it are shown to form a pattern consistent with the predictions of wave turbulence theory. In particular, the high…
Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The simulation…
Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay…
Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic…
The multi-wave exact resonance condition is a fundamental principle for understanding energy transfer in condensed matter systems, yet the dynamical evolution of waves satisfying this condition remains unexplored. Here, we reveal that the…
Internal waves in the ocean interact in triads. Early work emphasized the importance of extreme-scale separated interactions in which two large wavenumber waves interact with one small wavenumber wave. More recent efforts have called this…
Consistency relations of internal gravity waves (IGWs) describe ratios of cross-spectral quantities as functions of frequency. It has been a common practice to evaluate the measured or simulated signals (e.g., time series of velocity,…