作为一维湍流模型的SLE曲线动力学中的标度律与能量耗散
Scaling laws and energy dissipation in the dynamics of SLE curve as a 1D turbulence model
- Institute of Natural Sciences, College of Humanities and Sciences, Nihon University（日本大学人文科学系自然科学研究所）
- College of Art, Nihon University（日本大学艺术学部）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究将随机Loewner演化（SLE）作为一维湍流模型，推导了满足Kolmogorov 4/5定律的κ与Loewner熵条件，经数值模拟验证其标度关系，表明标准SLE可作为一维湍流的有益模型。
AI中文摘要：
本研究展示了随机Loewner演化（SLE）作为一维（1D）湍流模型的特性。首先，我们证明通过SLE中的时间坐标变换得到的扩散过程x(t)成为满足Richardson定律的时变扩散过程。接着，我们推导了扩散率参数κ需满足的条件，使得扩散过程x(t)满足Kolmogorov的4/5定律，该定律确定了湍流粒子中平均能量耗散与速度之间的关系。进一步的数学分析表明，该条件可视为对Loewner熵S_Loew的约束，其中包含本模型Loewner驱动函数中的高斯白噪声项W_s。此外，我们进行了数值模拟以验证该一维湍流模型的标度关系。这些结果表明，通过引入合适的时间坐标变换并对κ和S_Loew施加条件，标准SLE可成为一维湍流的有益模型。
英文摘要：
In this study, we demonstrate the characteristics of the stochastic Loewner evolution (SLE) as a one-dimensional (1D) turbulence model. First, we show that the diffusion process $x(t)$ obtained by the time coordinate change in the SLE becomes the time dependent diffusion process that satisfies Richardson's law of turbulence.Subsequently, we derive the condition on the diffusivity parameter $κ$ such that the diffusion process $x(t)$ satisfies Kolmogorov's 4/5th law, which determines the relation between the mean energy dissipation and velocity in the particles of turbulence. Further mathematical analysis showed that this condition is seen as the condition on Loewner entropy $S_{\mathrm{Loew}}$, which includes the white Gaussian noise term $W_{s}$ in the Loewner driving function of the present model. In addition, the numerical simulations were performed to verify the scaling relations of this 1D turbulence model. These results suggest that the standard SLE becomes a beneficial model of 1D turbulence by introducing an appropriate time coordinate change and imposing the conditions on $κ$ and $S_{\mathrm{Loew}}$.
