Fig. 5: Forward energy cascade associated with submesoscale frontogenesis.
Depth profiles of (a) \({\Pi }_{\omega }^{2d}\), the coarse-grained horizontal kinetic energy flux from time scales > 2 days to shorter periods, (b) \(-{\bar{\delta }}^{2d}/f\), the normalized horizontal convergence smoothed at a 2 day scale, (c) \(K{E}^{{\prime} 2d}\), the kinetic energy of time scales < 2 days, and (e) w2d, the root-mean-square of vertical velocity smoothed at a 2 day scale, demonstrate the enhanced forward cascade and vertical motion at frontal regions, where the horizontal convergence is stronger. d Profiles of \({\Pi }_{\omega }^{2d}\) versus \(-{\bar{\delta }}^{2d}K{E}^{{\prime} 2d}\) (the quantities of (b) and (c)) at frontal regions demonstrate the agreement with the theoretical predictions of Srinivasan et al. (2023)20. Shaded areas in (a–e) denote the 95% confidence level. Here fronts are defined by the region hosting \(-{\bar{\delta }}^{2d} > \) 0.3.
