标题： 量子湍流中有效粘度的定量估计 显示英文标题

标题： Quantitative estimation of effective viscosity in quantum turbulence

摘要： 我们通过在泰勒-格林几何中对格罗斯-皮塔耶夫斯基方程（GPE）进行高分辨率数值模拟，研究自由衰减的量子湍流。 我们使用的分辨率为从$1024^3$到$4096^3$的网格点。 能量谱确认了在大于涡旋间尺度$\ell$的尺度上存在科莫戈罗夫标度范围，并且在小于$\ell$的尺度上存在第二个惯性范围。 涡旋线可视化显示了由大量小尺度纽结涡旋形成的子结构。 接下来，我们通过使用随机金兹堡-朗道方程生成热态，然后利用GPE将这些热态与泰勒-格林初始条件相结合进行演化，来研究温度有限效应在量子湍流衰减中的影响。 我们通过测量从时空谱中获得的博戈留波夫色散关系中的光谱展宽，提取平均自由程，并将其用于量化有效粘度作为温度的函数。 最后，为了比较高温量子湍流和经典流动的衰减，并进一步校准GPE模拟中通过平均自由程估计的粘度，我们进行了低雷诺数的纳维-斯托克斯方程模拟。 显示英文摘要

摘要： We study freely decaying quantum turbulence by performing high resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from $1024^3$ to $4096^3$ grid points. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the intervortex scale $\ell$, and a second inertial range for scales smaller than $\ell$. Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. Next, we study finite temperature effects in the decay of quantum turbulence by using the stochastic Ginzburg-Landau equation to generate thermal states, and then by evolving a combination of these thermal states with the Taylor-Green initial conditions using the GPE. We extract the mean free path out of these simulations by measuring the spectral broadening in the Bogoliubov dispersion relation obtained from spatio-temporal spectra, and use it to quantify the effective viscosity as a function of the temperature. Finally, in order to compare the decay of high temperature quantum and that of classical flows, and to further calibrate the estimations of viscosity from the mean free path in the GPE simulations, we perform low Reynolds number simulations of the Navier-Stokes equations.