Abstract. We improve the Lieb-Robinson bound for a wide class of quantum many-body systems with long-range interactions decaying by power law. As an application, we show that the group velocity of information propagation grows by power law in time for such systems, whereas systems with short-range interactions exhibit a finite group velocity as shown by Lieb and Robinson.

Recent studies suggest that the eddy kinetic energy is localized in the lee of significant topographic features in the Antarctic Circumpolar Current (ACC). Here we explore the importance of the local dynamics quantitatively using the outputs from the realistic ocean general circulation model hindcast with an aid of the modified Lorentz energy cycle. Results confirm the importance of energy transfer among reservoirs in the downstream region of standing meanders, showing that the major five standing meanders are responsible for more than 70% of the kinetic energy transfer to eddies and dissipation over the Antarctic Circumpolar Current region. The eddy kinetic energy is generated in the upper 3000 m depth downstream of the standing meanders and transported due to the vertical energy redistribution governed by the vertical pressure flux towards the deeper layer where the eddy energy is dissipated. Moreover, we also calculate the work done by the Ekman transport to confirm that the wind energy input works as the dominant energy source for the baroclinic energy pathway. The advantage of this quantity against the vertical mean density flux is that it is independent of the reference states defined arbitrarily. It is shown that the westerlies can supply sufficient energy locally to initiate baroclinic instability in the Indian and Pacific sectors of the ACC, whereas the non-local process is important in the Atlantic sector. Our results suggest that the five narrow regions associated with significant topography play key roles in the energy balance of the ACC region.

The non-locality of eddy-mean flow interactions, which appears explicitly in the modified Lorentz diagram as a form of the interaction energy, and its link to other estimation methods are revisited, and a new formulation for the potential enstrophy is proposed. The application of these methods to the Kuroshio extension region suggests that the combined use of energy analysis with other methods, including the potential enstrophy diagram, provides more comprehensive understandings for the eddy-mean flow interactions in the limited region. It is shown that the interaction energy is transported from the nearshore and upstream regions to the downstream region in the form of the interaction energy flux, causing acceleration of the Kuroshio extension jet in the downstream region. The potential enstrophy diagram indicates that the eddy field decelerates (accelerates) the jet in the nearshore (downstream) region, which is a consistent result with the energy analysis. It turns out that the interaction potential enstrophy flux is radiated from a region of the eddy kinetic energy maximum towards the upstream region, which is the opposite direction from the interaction energy flux. The interaction potential enstrophy flux originated from this eddy kinetic energy maximum region also convergences near the center of the northern recirculation gyre of the Kuroshio extension region and tends to stabilize the structures of the recirculation gyre. Together with the energy analysis that indicates the eddy field accelerates the northeastern part of the recirculation gyre through the local interactions, the present analyses support the arguments on the eddy-driven northern recirculation gyre.

Previous studies have suggested that the quasi-stationary jets, sometimes called the “Isoguchi jets” in the western North Pacific Ocean, regulate the warm and salty conditions in the transition domain between the Subarctic Boundary and the Subarctic Front. Here, we show that mesoscale eddies and interannual/decadal modulations are responsible for the Kuroshio water intrusion into the transition domain. A case study using the Lagrangian coherent structure suggests that the northward shift of the Kuroshio Extension forms a favorable velocity field for the Kuroshio water intrusion around the Subarctic Boundary, while the geometric structure inside the Isoguchi jet is quasi-permanent.

Recent studies suggest that local eddy-mean flow interactions associated with standing meanders play key roles in the dynamics of the Antarctic Circumpolar Current. Here we explore the importance of the local dynamics quantitatively with a viewpoint of energy transfer using the Lorentz diagram concept. Results confirm the importance of the eddy-mean flow interactions in the standing meander, showing that 55% of the wind energy input is converted to the eddy energy through the baroclinic instability in the standing meander region. It is also found that most of the eddy kinetic energy is dissipated local in the deeper layer due to the vertical energy redistribution governed by the vertical pressure flux. Contrary, the eddy effects are negligible outside the standing meander region.