Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with asymptotically periodic potentials

We consider one-dimensional Fokker-Planck and Schr\"odinger equations with a potential which approaches a periodic function at spatial infinity. We extend the low-energy expansion method, which was introduced in previous papers, to be applicable to such asymptotically periodic cases. Using this method, we study the low-energy behavior of the Green function.Comment: author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretica

Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials

We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials. We derive a formula for the power series expansion of reflection coefficients in terms of the wave number, and apply it to the low-energy expansion of the Green function

Structure and dynamics of the sudden acceleration of Kuroshio off Cape Shionomisaki

A sudden acceleration of the Kuroshio jet appears off Cape Shionomisaki in the high-resolution (horizontal resolution of 1/36°) JCOPE 2 ocean reanalysis data. Using this dataset, we investigated the structure of the Kuroshio acceleration. The increase in the velocity of the current is accompanied by a downstream flow separation from the coast and an outcrop of cold temperature inshore. The acceleration of Kuroshio appears when it takes a near-shore path. Cape Shionomisaki amplifies the responses to the Kuroshio flow by creating the zonal velocity acceleration toward the downstream region when the Kuroshio flows closer to the coast. The Kuroshio acceleration coincided with the topographic ridge on the continental shelf near Cape Shionomisaki. This relation suggests that the dynamics of the acceleration is linked to the topographic feature. We proposed an explanation of the Kuroshio acceleration using a hydraulic control theory. An analytical solution was applied to the coastal topography around the Kii Peninsula. The solution captured some aspects of the Kuroshio acceleration

Short-term fluctuations south of Japan and their relationship with the Kuroshio path: 8- to 36-day fluctuations

To detect short-term fluctuations south of Japan, we applied wavelet analysis to ocean-reanalysis data of the Japan Coastal Ocean Predictability Experiment 2 (JCOPE2) with a horizontal resolution of 1/36°. It was found that fluctuations of the 8- to 36-day period band appear as frontal waves in the Kuroshio Current. The amplitude of the fluctuations increases toward the downstream of Cape Shionomisaki. The fluctuations have a wavelength of about 300 km, and the signals propagate eastward. The fluctuations of the 8- to 36-day period band are stronger during the period of the nearshore non-large-meander Kuroshio path than during the period of the offshore non-large-meander Kuroshio path. We suggest that the 8- to 36-day fluctuation is a result of the instability of the accelerated velocity of the Kuroshio Current downstream of Cape Shionomisaki