论文标题
表面重力波是否具有冷冻的湍流状态？
Do surface gravity waves have a frozen turbulence state?
论文作者
论文摘要
我们研究了有限的周期性空间结构域中表面重力波的精确共振。基于一个运动模型，模拟有限离散的波数空间中的活动波模式的产生$ \ MATHCAL {S} _R $，我们研究了直接和反向能量级联的可能性。更具体地说，我们设置了一个最初激动的区域，该区域将能量通过精确共振将能量传播到$ \ Mathcal {s} _r $中的波模式。在每次迭代中，我们首先从刻度共振（以新长度生成模式）激活新模式，然后考虑到角度共振的两种边界情况（它们以相同的长度尺度传递能量）：下界不包含无角度共振，而所有模式都具有与任何活动模式相同的所有模式。这种策略对于启用大型域$ \ mathcal {s} _r $的计算至关重要，并具有最大vavenumber $ r \ sim 10^3 $。我们表明，对于直接级联和反向级联，当最初激发的区域足够大时，可以建立$ \ Mathcal {s} _r $边界的能量级联，否则会发生冷冻的湍流状态，并且在这两个方案之间尤其是直接级联方向上的急剧过渡。通过对谐振四重奏结构的研究，阐明了与尖锐转变和角能传递作用相关的机制。
We study the energy transfer by exact resonances for surface gravity waves in a finite periodic spatial domain. Based on a kinematic model simulating the generation of active wave modes in a finite discrete wavenumber space $\mathcal{S}_R$, we examine the possibility of direct and inverse energy cascades. More specifically, we set an initially excited region which iteratively spreads energy to wave modes in $\mathcal{S}_R$ through exact resonances. At each iteration, we first activate new modes from scale resonances (which generate modes with new lengths), then consider two bounding situations for angle resonances (which transfer energy at the same length scale): the lower bound where no angle resonance is included and the upper bound where all modes with the same length as any active mode are excited. Such a strategy is essential to enable the computation for a large domain $\mathcal{S}_R$ with the maximum wavenumber $R\sim 10^3$. We show that for both direct and inverse cascades, the energy cascade to the boundaries of $\mathcal{S}_R$ can be established when the initially excited region is sufficiently large, otherwise a frozen turbulence state occurs, with a sharp transition between the two regimes especially for the direct cascade. Through a study on the structure of resonant quartets, the mechanism associated with the sharp transition and the role of angular energy transfer in the cascades are elucidated.
