相动力学在被动平流标量随机模式中的作用
The role of phase dynamics in a stochastic model of a passively advected scalar
摘要：
在一个标量随机被动对流扩散模型中引入了相位的集体同步运动。相位耦合动力学的模型遵循著名的仓本模型范式的极限环振荡器。仓本模型中的固有频率被假定为通过漂移波形$-β\frac{k}{1+k^2}$的色散关系服从给定的尺度依赖性，其中$β$是表示梯度的典型强度的常数。本文的目的是研究集体相动力学对涨落能量特征时间演化和相干结构形成的重要性。我们的研究结果表明，一个完全随机的湍流相态的假设是更相关的$β$的高值，我们发现，能量谱遵循$k^{-7/2}$标度。而对于较低的$β$，在非同步和同步相位状态之间存在显著差异，并且可以预期在后一种情况下形成相干调制。
英文摘要：
Collective synchronous motion of the phases is introduced in a model for the stochastic passive advection-diffusion of a scalar with external forcing. The model for the phase coupling dynamics follows the well known Kuramoto model paradigm of limit-cycle oscillators. The natural frequencies in the Kuramoto model are assumed to obey a given scale dependence through a dispersion relation of the drift-wave form $-β\frac{k}{1+k^2}$, where $β$ is a constant representing the typical strength of the gradient. The present aim is to study the importance of collective phase dynamics on the characteristic time evolution of the fluctuation energy and the formation of coherent structures. Our results show that the assumption of a fully stochastic phase state of turbulence is more relevant for high values of $β$, where we find that the energy spectrum follows a $k^{-7/2}$ scaling. Whereas for lower $β$ there is a significant difference between a-synchronised and synchronised phase states, and one could expect the formation of coherent modulations in the latter case.
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