Thin-jet scaling in large-scale shallow water quasigeostrophic flow

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 L_D. However the presence of sharp PV fronts with O(L_D) 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 L_tot ∝ t^−1/3, average arc length growing like t^1/3, rms curvature as κ_rms∼t^−1/3 and typical curvature fluctuation as κ_fl∼t^−1/3.