论文标题
超出通用极限的二维涡流凝结物的轮廓
Profile of a Two-Dimensional Vortex Condensate Beyond the Universal Limit
论文作者
论文摘要
众所周知，在有限的（$2π\ times2π$）中的二维周期域中的反向湍流级联导致系统大小的相干涡旋偶极子的出现。我们报告了其中一个涡流中空间涡度曲线的数值高视化研究。激动人心的力量很快就会随着时间的流逝而随机，并且具有相关长度$ l_f =2π/k_f $，$ k_f $从$ 100 $到$ 12.5 $。 Previously, it was found that in the asymptotic limit of small-scale forcing, the vorticity exhibits the power-law behavior $Ω(r) = (3 ε/α)^{1/2} r^{-1}$, where $r$ is the distance to the vortex center, $α$ is the bottom friction coefficient, and $ε$ is the inverse energy flux.现在，我们表明，对于有限的$ k_f $的空间均匀强迫，涡度轮廓变得更陡峭，随着泵量表的差异增加，但随着强迫量表的雷诺数而减小。从定性上讲，这种行为与与中心距离的有效泵送有效泵送有关。为了支持该语句，我们对空间本地化的强迫进行了额外的模拟，相反，相干涡流的有效泵浦随着$ r $的增加而增加，并首次显示在这种情况下，涡度轮廓可以比渐近限制更平坦。
It is well known that an inverse turbulent cascade in a finite ($2 π\times 2 π$) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random in space, and had a correlation length $l_f = 2π/k_f$ with $k_f$ ranging from $100$ to $12.5$. Previously, it was found that in the asymptotic limit of small-scale forcing, the vorticity exhibits the power-law behavior $Ω(r) = (3 ε/α)^{1/2} r^{-1}$, where $r$ is the distance to the vortex center, $α$ is the bottom friction coefficient, and $ε$ is the inverse energy flux. Now we show that for a spatially homogeneous forcing with finite $k_f$ the vorticity profile becomes steeper, with the difference increasing with the pumping scale but decreasing with the Reynolds number at the forcing scale. Qualitatively, this behaviour is related to a decrease in the effective pumping of the coherent vortex with distance from its center. To support this statement, we perform an additional simulation with spatially localized forcing, in which the effective pumping of the coherent vortex, on the contrary, increases with $r$ and show for the first time that in this case the vorticity profile can be flatter than the asymptotic limit.
