Lagrangian H/U³ values computed around fronts using a fine-resolution numerical model and ferryboat-monitored SST dataset

Front locations are identified as the local maximum of the sea surface temperature gradient revealed in the continuously ferryboat-monitored data in the Seto Inland Sea, Japan. In addition, Simpson and Hunter's H/ U³ values, where H is the water depth and U is the tidal-current amplitude, are computed at each cell using a fine-resolution, finite-volume ocean model to find the values at the fronts (i.e., Eulerian critical H/U³ values). Moreover, Lagrangian critical H/U³ values are computed using the same model in conjunction with particle-tracking experiments in which the particle's H/U³ values saved along their trajectories are all averaged at each cell. In comparison with the Eulerian H/U³ values, it is revealed that the standard deviation of the Lagrangian critical values considerably reduces, especially for the fronts near straits. This accurate estimate of the critical H/U³ values shows that critical values depend on the tidal-current amplitude at the front locations. The dependency of critical H/U³ values on the tidal-current amplitude is likely due to dependency of the efficiency factor for vertical mixing in the original Simpson and Hunter formula on the amplitude. It is suggested that the efficiency factor for vertical mixing must be small (large) at locations with the large (small) tidal-current amplitude.