Fig. 1

Regional eddy variability and eddy kinetic energy along cruises (a) Surface eddy kinetic energy distribution in the subtropical Northwest Atlantic based on the daily AVISO geostrophic current velocity anomaly data from 2005 to 2018. (b) Vertical structure of ADCP-derived eddy kinetic energy along the Oleander Project's repeating cruises. Here, eddy kinetic energy (contours) is evaluated by removing the time-mean ADCP-derived velocities from individual cruises. Note that white contours in (b) that denote the horizontal velocity data (unit: m·s-1) and is measured by the ship-board ADCP from 2005 to 2018 show the mean along-track flows. Black dotted line in (b) is the boundary between the strong current region and the weak current region of the Gulf Stream (the strong current region on the northwest and the weak current region on the southeast)"

Fig. 2

Velocity Spectra at 40 m in strong current region (a~c) and weak current region (d~f) Velocity spectra of along-track, cross-track, rotational and divergent are shown by $S^u,S^v,K^\psi\text{and}K^\phi$. Along-track versus cross-track balanced geostrophic velocity spectra are shown by $(S^{u}+S^{v}),(S_{V}^{u}+S_{V}^{v})\mathrm{~and~}(S_{W}^{u}+S_{W}^{v})$ indicate the total velocity spectra with its decomposition into balanced geostrophic motions and unbalanced motions. The vertical black solid line segment indicates the transition scale. Dashed gray lines in background denote the k-2 and k-3 reference curves and the 95% denote the 95% confidence intervals"

Fig. 3

Velocity spectra at 40 m depth in summer versus winter in the strong current (a, b) and weak current (c, d) regions Veloctiy spectra of total, geostrophic balanced motions and unbalanced motions are shown by $(S^{u}+S^{v}),(S_{V}^{u}+S_{V}^{v})\mathrm{and} \ (S_{W}^{u}+S_{W}^{v})$ Red dashed lines denote the summer transition scales and blue dashed lines denote the winter. Dashed gray lines in background denote the k-2 and k-3 reference curves and the 95% denote the 95% confidence intervals"

Fig. 4

The influence of hurricanes on transition scale at 40 m depth Monthly histograms of the integrated values of the velocity spectra of geostrophic balanced motions and unbalanced wave motions in the wavelength between 10 km and 30 km with transition scales in strong current and weak current region are shown by (a) and (b). The ratio of storm cruises for each month is shown by (c). The variation of each component in the strong and weak current region from July to September, when the frequency of hurricanes in the Gulf Stream is high, is circled by the magenta rectangle"

Fig. 5

Variation of geostrophic balanced and unbalanced kinetic energy with depth in strong current (a, b) and weak current (c, d) regions ( S V u + S V v ) and ( S W u + S W v ) show the kinetic energy of geostrophic balanced motions and unbalanced motions, respectively"

Fig. 6

The ratio of geostrophic balanced kinetic energy to unbalanced kinetic energy (solid line) and the transition scale (dashed line) change with depth. (a) and (b) are strong current region and weak current region, respectively"