Spectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulations
Spectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulations
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DOI：
10.1017/jfm.2018.185
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发表时间：
2016-04
影响因子：
3.7
通讯作者：
S. Annenkov;V. Shrira
中科院分区：
文献类型：
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作者：
S. Annenkov;V. Shrira
动力学方程广泛应用于许多学科领域，用来描述随机海浪谱的演化。为了检验这些方程的有效性，我们数值研究了长期演变的水波谱无风输入使用三种不同的模式。第一个模型是经典的动力学（Hasselmann）方程（KE）。第二种模型是广义动力学方程（gKE），采用相同的统计封闭KE，但没有假设的准平稳性。第三个模型，我们称之为DNS-ZE，是一个直接的数值模拟算法的基础上的Zakharov积分微分方程，它扮演的原始方程的弱非线性波场的作用。它不使用任何统计假设。我们进行了比较的谱演化相同的初始分布没有强迫，有/没有统计封闭和有/没有准平稳性假设。对于初始条件，我们选择了两个具有相同频率分布和不同方向性的窄带谱。这两个光谱的短期演变（$O（10^{2}）$波周期）以前已经彻底研究了实验和数值模拟使用各种方法。我们的DNS-ZE结果验证与现有的短期DNS通过其他方法和可用的实验室观测高阶矩（峰度）的演变。所有这三种模型表现出非常接近的光谱的积分特性的演变，随着时间的推移接近理论上的自相似阶段的演变。两个动力学方程给出几乎相同的光谱演化，除非光谱最初的角度太窄。然而，DNS-ZE和gKE/KE预测之间存在重大差异。首先，对于gKE和KE，初始窄角分布的角加宽速率比DNS-ZE大得多，尽管角宽度在大部分时间确实看起来倾向于相同的普适值。其次，频谱的形状有很大的不同（即使当非线性降低时），DNS-ZE谱比KE/gKE谱宽，并且具有低得多的谱峰。第三，与DNS-ZE规模的非线性，这对应于动态的时间尺度的演变，而不是典型的动力学时间尺度的KE所表现出的非线性的第六次幂的第四次幂得到的光谱的最大变化率。gKE的预测介于两者之间。虽然长期DNS显示出良好的协议与KE预测的积分特性的不断变化的波谱，一些特定的光谱特性的显着的系统差异要求修订的基本面的波动力学描述。
Kinetic equations are widely used in many branches of science to describe the evolution of random wave spectra. To examine the validity of these equations, we study numerically the long-term evolution of water wave spectra without wind input using three different models. The first model is the classical kinetic (Hasselmann) equation (KE). The second model is the generalised kinetic equation (gKE), derived employing the same statistical closure as the KE but without the assumption of quasistationarity. The third model, which we refer to as the DNS-ZE, is a direct numerical simulation algorithm based on the Zakharov integrodifferential equation, which plays the role of the primitive equation for a weakly nonlinear wave field. It does not employ any statistical assumptions. We perform a comparison of the spectral evolution of the same initial distributions without forcing, with/without a statistical closure and with/without the quasistationarity assumption. For the initial conditions, we choose two narrow-banded spectra with the same frequency distribution and different degrees of directionality. The short-term evolution ( $O(10^{2})$ wave periods) of both spectra has been previously thoroughly studied experimentally and numerically using a variety of approaches. Our DNS-ZE results are validated both with existing short-term DNS by other methods and with available laboratory observations of higher-order moment (kurtosis) evolution. All three models demonstrate very close evolution of integral characteristics of the spectra, approaching with time the theoretical asymptotes of the self-similar stage of evolution. Both kinetic equations give almost identical spectral evolution, unless the spectrum is initially too narrow in angle. However, there are major differences between the DNS-ZE and gKE/KE predictions. First, the rate of angular broadening of initially narrow angular distributions is much larger for the gKE and KE than for the DNS-ZE, although the angular width does appear to tend to the same universal value at large times. Second, the shapes of the frequency spectra differ substantially (even when the nonlinearity is decreased), the DNS-ZE spectra being wider than the KE/gKE ones and having much lower spectral peaks. Third, the maximal rates of change of the spectra obtained with the DNS-ZE scale as the fourth power of nonlinearity, which corresponds to the dynamical time scale of evolution, rather than the sixth power of nonlinearity typical of the kinetic time scale exhibited by the KE. The gKE predictions fall in between. While the long-term DNS show excellent agreement with the KE predictions for integral characteristics of evolving wave spectra, the striking systematic discrepancies for a number of specific spectral characteristics call for revision of the fundamentals of the wave kinetic description.