Simonis Ashleigh, Pan Yulin
Department of Naval Architecture and Marine Engineering, <a href="https://ror.org/00jmfr291">University of Michigan, Ann Arbor</a>, Michigan 48109, USA.
Phys Rev E. 2024 Aug;110(2-1):024202. doi: 10.1103/PhysRevE.110.024202.
It is well known that wave collapses can emerge from the focusing one-dimensional (1D) Majda-McLaughlin-Tabak (MMT) model as a result of modulational instability. However, how these wave collapses affect the spectral properties and statistics of the wave field has not been adequately studied. We undertake this task by simulating the forced-dissipated 1D MMT model over a range of forcing amplitudes. Our results show that when the forcing is weak, the spectrum agrees well with the prediction by wave turbulence theory with few collapses in the field. As the forcing strength increases, we see an increase in the occurrence of collapses, together with a transition from a power-law spectrum to an exponentially decaying spectrum. Through a spectral decomposition, we find that the exponential spectrum is dominated by the wave collapse component in the nonintegrable MMT model, which is in analogy to a soliton gas in integrable turbulence.
众所周知，由于调制不稳定性，波塌缩可以从聚焦的一维（1D）Majda-McLaughlin-Tabak（MMT）模型中出现。然而，这些波塌缩如何影响波场的频谱特性和统计特性尚未得到充分研究。我们通过在一系列强迫振幅范围内模拟强迫耗散的一维MMT模型来承担这项任务。我们的结果表明，当强迫较弱时，频谱与波湍流理论的预测吻合良好，场中几乎没有塌缩。随着强迫强度的增加，我们看到塌缩的发生率增加，同时从幂律频谱过渡到指数衰减频谱。通过频谱分解，我们发现在不可积的MMT模型中，指数频谱由波塌缩分量主导，这类似于可积湍流中的孤子气体。
