超流氦中的双Kelvin波级联
Double Kelvin Wave Cascade in Superfluid Helium
摘要：
本文研究了超流涡丝局部模型中能量和波作用的双重级联。该模型是从截断扩展的二维局部感应近似，它被证明支持六波相互作用。我们认为，由于涡核轮廓的不确定性，该模型具有相同的有效性地位，传统上使用的Biot-Savart模型与截止，但它具有更简单的优势。我们的极小模型导致一个波动力学方程，我们预测存在两个不同的幂律标度的频谱，对应于一个直接级联的能量和一个反向的波行动。直接数值模拟证实了弱湍流区的理论预测。
英文摘要：
We study the double cascade of energy and wave action in a local model of superfluid vortex filaments. The model is obtained from a truncated expansion of the 2D Local Induction Approximation and it is shown to support six-wave interactions. We argue that, because of the uncertainty in the vortex core profile, this model has the same status of validity as the traditionally used Biot-Savart model with cutoff, but it has advantage of being much simpler. Our minimal model leads to a wave kinetic equation for which we predict existence of two distinct power-law scaling in the spectrum, corresponding to a direct cascade of energy and an inverse one of wave action. Direct numerical simulations confirm the theoretical predictions in the weak turbulence regime.
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