研究目的
To check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to the situations described by the Phillips spectrum.
研究成果
The study concludes that, even in the case of relatively high average steepness when the Phillips spectrum is present in the system, the spectral lines are still very narrow, at least in the region of the direct cascade spectrum. This justifies the construction of an appropriately adjusted dissipation term that can be used thereafter in wave forecasting.
研究不足
The study is limited by the weakly nonlinear approximation under which the model equations were derived. The description of wave breaking in all details would require a fully nonlinear simulation, which is challenging even in the case of 2-D hydrodynamics.
1：Experimental Design and Method Selection:
The study involves numerical simulations of primordial dynamical equations at different levels of nonlinearity, corresponding to weakly turbulent Kolmogorov–Zakharov spectra ω?4, Phillips spectra ω?5, and intermediate cases. The methodology is based on the framework of weakly nonlinear expansion of the Hamiltonian up to the fourth-order terms in steepness.
2：Sample Selection and Data Sources:
The simulations are performed in a 2π × 2π periodic box with 1024 × 1024 modes, using initial conditions of low-amplitude noise in all harmonics.
3：List of Experimental Equipment and Materials:
The study utilizes a pseudo-spectral code for solving weakly nonlinear Euler equations for dynamics of incompressible deep fluids with free surfaces in the presence of gravity.
4：Experimental Procedures and Operational Workflow:
The equations are solved numerically with a specific time step, and the dissipation function is chosen to mimic energy dissipation due to whitecapping through the regularization of the equations by relatively close dissipation regions.
5：Data Analysis Methods:
The analysis involves evaluating the spectral line width of the spectrum from the simulations, focusing on the shape of the line, i.e., the frequency spectra of certain spatial Fourier harmonics.
独家科研数据包，助您复现前沿成果，加速创新突破
获取完整内容
