The evolution of thin frontal jets in large-scale shallow water quasigeostrophic flow is studied, with a focus on jet curvature and arclength. The flow is large-scale in the sense that mixed regions of potential vorticity (PV) are much larger than the deformation length . However the presence of sharp PV fronts with widths drives the ongoing growth of the flow's length scale; in particular the PV fronts and collocated jets support long undulations that facilitate jet interactions and the merger of mixed regions. The flow develops large dynamically active multilevel vortices containing two main mixed levels of PV, as well as small dynamically inactive vortices that persist for long times; these regions and their frontal jets display markedly different scaling properties. The frontal jets bounding the large dynamically active mixed regions follow power laws consistent with the scaling symmetries of the modified Korteweg-de Vries (mKdV) equation, which governs the motion of the jet axis in the thin-jet limit. These jets have population total arc length decaying approximately as , average arc length growing like , rms curvature as and typical curvature fluctuation as .

中文翻译：

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大规模浅水准地转流中的细射流结垢

研究了大尺度浅水准地转流中细锋射流的演化，重点是射流曲率和弧长。在势涡 (PV) 的混合区域远大于变形长度的意义上，流动是大规模的。然而，具有宽度的尖锐 PV 锋面的存在推动了流动长度尺度的持续增长；特别是 PV 锋面和并列射流支持长波状起伏，促进射流相互作用和混合区域的合并。流动发展出包含两个主要 PV 混合水平的大型动态活跃多级涡流，以及持续很长时间的小型动态非活跃涡流；这些区域及其锋面喷流显示出明显不同的缩放特性。界定大型动态活动混合区域的锋面射流遵循幂律，与修正的 Korteweg-de Vries (mKdV) 方程的标度对称性一致，该方程控制着细射流极限中射流轴的运动。这些射流的总体总弧长大约衰减为 ，平均弧长增加为 ，均方根曲率为 ，典型的曲率波动为 。