Figure  1.  Structures of the submesoscale cold filament, the background submesoscale currents diagnosed by the turbulent thermal wind balance, the surface cooling, and the Coriolis parameter. The black arrow indicates the direction of the submesoscale currents and the blue arrow indicates the direction of sea surface heat flux and the Coriolis parameter (f) is indicated by the red arrow.

Figure  2.  Time variation of the normalized average peak vertical velocity $ {\left\langle{w}\right\rangle}_{{\mathrm{p}}} $ in the middle of the upper mixed layer (z ≈ –30 m). The negative and positive $ {\left\langle{w}\right\rangle}_{{\mathrm{p}}} $ represent the frontogenesis and frontolysis.

Figure  3.  Cross-filament profiles for the normalized cross-filament velocity $ \left\langle{u}\right\rangle $ at t = 3.27 h in a near-surface layer of the depth (0 m > z > –5 m) (a), the normalized vertical velocity $ \left\langle{w}\right\rangle $ at t = 3.27 h in a middle-layer of the depth (–28 m > z > –32 m) (b), the normalized cross-filament velocity $ \left\langle{u}\right\rangle $ at t = 7.51 h in a near-surface layer of the depth (0 m > z > –5 m) (c), and the vertical velocity $ \left\langle{w}\right\rangle $ at t = 7.51 h in a middle-layer of the depth (–28 m > z > –32 m) (d).

Figure  4.  Average submesoscale flow fields of the normalized temperature $\left\langle{{T}_{\mathrm{s}0}-{T}_{0}}\right\rangle$ (a), the normalized cross-filament velocity $ \left\langle{u}\right\rangle $ (b), the normalized down-filament velocity $ \left\langle{v}\right\rangle $ (c), and the normalized velocity velocity $ \left\langle{w}\right\rangle $ (d) at t = 3.27 h corresponding to the frontogenesis arrest.

Figure  5.  Average submesoscale flow fields of the normalized temperature $\left\langle{{T}_{\mathrm{s}0}-{T}_{0}}\right\rangle\left(\mathrm{a}\right)$, the normalized cross-filament velocity $ \left\langle{u}\right\rangle\left(\mathrm{b}\right) $, the normalized down-filament velocity $ \left\langle{v}\right\rangle $ (c), and the normalized velocity $ \left\langle{w}\right\rangle $ (d) at t = 7.51 h corresponding to the frontolysis arrest.

Figure  6.  The time variation of the submesoscale flow fields in the cross-filament (x) direction for the normalized temperature field $\left\langle{{T}_{\mathrm{s}0}-{T}_{0}}\right\rangle$ in a near-surface layer (0 m > z > –5 m) (a), the normalized cross-filament current $ \left\langle{u}\right\rangle $ in a near-surface layer (0 m > z > –5 m) (b), the normalized down-filament current $ \left\langle{v}\right\rangle $ in a near-surface layer (0 m > z > –5 m) (c), and the normalized vertical current $ \left\langle{w}\right\rangle $(d) in the middle of the upper mixed layer (–28 m > z > –32 m).

Figure  7.  The time variation of the submesoscale flow fields in the vertical (z) direction for the normalized temperature field $\left\langle{{T}_{\mathrm{s}0}-{T}_{0}}\right\rangle$ at x = 0 that is averaged over –5 m < x < 5 m (a), the normalized cross-filament current $ \left\langle{u}\right\rangle $ at x = –1 000 m that is averaged over –995 m > x > –1 005 m (b), the normalized vertical current $ \left\langle{w}\right\rangle $ in a at x = 0 m that is averaged over 5 m > x > –5 m (c), and the normalized cross-filament current $ \left\langle{u}\right\rangle $ at x = 1 000 m that is averaged over 1005 m > x > 995 m (d).