论文标题
可整合湍流的增长
Growing of integrable turbulence
论文作者
论文摘要
我们使用一种新方法（“湍流的增长”，在聚焦一维非线性Schrodinger方程的框架中数字研究的湍流。我们添加到方程式较弱的受控泵送项，并从统计上均匀的高斯噪声开始湍流的绝热演变。达到一定水平的平均强度后，我们关闭抽水，并意识到“成年”的湍流在统计上是固定的。我们测量其傅立叶光谱，强度的概率密度函数（PDF）和强度的自相关。此外，我们表明，作为绝热，我们的方法还会在泵送的中间力矩中产生可整合的湍流状态。目前，我们仅考虑相对较小的非线性的湍流。但是，即使是这种“中等”的湍流，也以增强的流氓波的产生为特征。
We study numerically the integrable turbulence in the framework of the focusing one-dimensional nonlinear Schrodinger equation using a new method -- the "growing of turbulence". We add to the equation a weak controlled pumping term and start adiabatic evolution of turbulence from statistically homogeneous Gaussian noise. After reaching a certain level of average intensity, we switch off the pumping and realize that the "grown up" turbulence is statistically stationary. We measure its Fourier spectrum, the probability density function (PDF) of intensity and the autocorrelation of intensity. Additionally, we show that, being adiabatic, our method produces stationary states of the integrable turbulence for the intermediate moments of pumping as well. Presently, we consider only the turbulence of relatively small level of nonlinearity; however, even this "moderate" turbulence is characterized by enhanced generation of rogue waves.
