Cui Shaoyan, Yu M Y, Zhao Dian
School of Mathematics and Information, Ludong University, Yantai 264025, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):053104. doi: 10.1103/PhysRevE.87.053104. Epub 2013 May 13.
Turbulence governed by a generalized nonlinear Schrödinger equation (GNSE) including viscous heating and nonlinear damping is numerically investigated. It is found that a large localized pulse can suffer modulational instability and then collapse into the shortest-wavelength modes, as for the classical nonlinear Schrödinger equation. However, the total energy of the nonconservative GNSE can also become constant during the collapse via local balance of energy gain and loss in the phase space. After the collapse, instead of inverse cascading into a state of strong turbulence with broad spectrum, a single-step cascade, or condensation, into modes of one predominant wavelength can occur. In fact, after attaining total energy balance the turbulent system as a whole evolves like a closed adiabatic system.
对由包含粘性加热和非线性阻尼的广义非线性薛定谔方程（GNSE）所支配的湍流进行了数值研究。结果发现，如同经典非线性薛定谔方程的情况一样，一个大的局域脉冲会遭受调制不稳定性，然后坍缩为最短波长模式。然而，在坍缩过程中，非保守GNSE的总能量也可通过相空间中能量得失的局部平衡而变得恒定。坍缩之后，不会逆级联进入具有宽频谱的强湍流状态，而是可能发生单步级联或凝聚，进入一个主要波长的模式。实际上，在达到总能量平衡之后，整个湍流系统就像一个封闭的绝热系统一样演化。
