We consider turbulence of waves interacting weakly via four-wave scattering (sea waves, plasma waves, spin waves, etc.). In the first order in the interaction, a closed kinetic equation has stationary solutions describing turbulent cascades. We show that the higher-order terms generally diverge both at small (IR) and large (UV) wave numbers for direct cascades. The analysis up to the third order identifies the most UV-divergent terms. To gain qualitative analytic control, we sum a subset of the most UV divergent terms, to all orders, giving a perturbation theory free from UV divergence, showing that turbulence becomes independent of the dissipation scale when it goes to zero. On the contrary, the IR divergence (present in the majority of cases) makes the effective coupling parametrically larger than the naive estimate and growing with the pumping scale L (similar to anomalous scaling in fluid turbulence). In such cases, the kinetic equation does not describe wave turbulence even of arbitrarily small level at a given k if kL is large enough that is the cascade is sufficiently long. We show that the character of strong turbulence is determined by whether the effective four-wave interaction is enhanced or suppressed by collective effects. The enhancement possibly signals that strong turbulence is dominated by multiwave bound states (solitons, shocks, cusps), similar to confinement in quantum chromodynamics. Published by the American Physical Society 2024

中文翻译：

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湍流态的交互重整化和动力学方程的有效性


我们考虑波的湍流通过四波散射（海波、等离子波、自旋波等）进行微弱交互。在交互作用的一阶中，封闭动力学方程具有描述湍流级联的稳态解。我们表明，对于直接级联，高阶项通常在小 （IR） 和大 （UV） 波数处发散。直到三阶的分析确定了最大的 UV 发散项。为了获得定性解析控制，我们将最紫外发散项的子集相加，对所有阶数求和，得到一个没有紫外发散的扰动理论，表明当湍流趋于零时，湍流变得与耗散尺度无关。相反，IR 散度（在大多数情况下存在）使有效耦合在参数上大于朴素估计值，并随着泵送尺度 L 的增长而增长（类似于流体湍流中的异常缩放）。在这种情况下，如果 kL 足够大，即级联足够长，则动力学方程不会描述给定 k 处任意小水平的波湍流。我们表明，强湍流的特征取决于有效的四波相互作用是被集体效应增强还是被抑制。这种增强可能表明强湍流由多波束缚态（孤子、激波、尖点）主导，类似于量子色动力学中的限制。 美国物理学会 2024 年出版