Because the vertical homogeneous Bottom Water (BW) with N ~0 (N is the buoyancy frequency) is formed in the Japan Sea, the abyssal water always has a depth of N ~f (f is the inertial frequency) above the BW. In the present study, we propose the theoretical existence of buoyancy/inertial oscillation under the weak stratification with N ~f in the non-hydrostatic dynamics and term it "fN-Oscillation". Based on the dispersion relation of internal inertial waves in the limit of N→f, it is concluded that fN-Oscillation with lateral maximum group velocity fulfills the requirement of a finite spatial scale for a ratio of horizontal/vertical wavenumber k/m=1/√ 3. In the idealized stratification of N=f, in particular, this oscillation is confined to the generation area because it contains zero group velocity. Testing of numerical model experiments, including a localized front under the stratification with N~f, suggests that some of the fN-Oscillation energy trapped in this front escapes as internal waves. We observed that the benthic front existed stably between the Yamato Basin BW (YBBW) and the Japan Basin BW (JBBW) and was the plausible origin of energetic upward-propagating internal waves. The benthic front has a notably sharp structure with a horizontal scale of several hundreds meters. In the vicinity of this front, the periodic variations of temperature and dissolved oxygen were confirmed according to the internal waves, with the wavenumber satisfying approximately k/m~1/√3. Such disturbances represent indirect evidence for the trapping fN-Oscillation.