Inverse energy cascade in ocean macroscopic turbulence: Kolmogorov self-similarity in surface drifter observations and Richardson-Obhukov constant

We combine two point velocity and position data from surface drifter observations in the Benguela upwelling region off the coast of Namibia. The compensated third order longitudinal velocity structure function $\left\langle{\Delta u_{\ell}^{\rm 3}}\right\rangle/s$ shows a positive plateau for inertial separations $s$ roughly between $9~\rm{km}$ and $120~\rm{km}$ revealing an inverse energy cascade with energy transfer rate $\varepsilon\simeq 1.2 \pm 0.1 \cdot 10^{-7} m^3/s^2$. Deviations from Gaussianity of the corresponding probability distribution $P(\Delta u_{\ell} |s)$ of two-point velocity increments $\Delta u_{\ell}$ for given pair separation $s$ show up in the n$^{th}$ antisymetric structure functions $S_{-}^{(n)}(r)=\int u^n(P(u)-P(-u)d u$, which scale in agreement with Kolmogorov's prediction, $S_{-}^{(n)}(r)\sim r^{(n/3)}$, for $n=2,4,6$. The combination of $\varepsilon$ with Richardson dispersion $\left\langle s^2(t)\right\rangle=g\varepsilon t^3$, where $\left\langle s^2(t)\right\rangle$ is mean squared pair separation at time $t$, reveals a Richardson-Obhukov constant of $g\simeq 0.11\pm 0.03$.Comment: 6 pages, 5 figure

Characterization of physical properties of a coastal upwelling filament with evidence of enhanced submesoscale activity and transition from balanced to unbalanced motions in the Benguela upwelling region

We combine high-resolution in situ data (acoustic Doppler current profiler (ADCP), Scanfish, and surface drifters) and remote sensing to investigate the physical characteristics of a major filament observed in the Benguela upwelling region. The 30–50 km wide and about 400 km long filament persisted for at least 40 d. Mixed-layer depths were less than 40 m in the filament and over 60 m outside of it. Observations of the Rossby number Ro from the various platforms provide the spatial distribution of Ro for different resolutions. Remote sensing focuses on geostrophic motions of the region related to the mesoscale eddies that drive the filament formation and thereby reveals |Ro|&lt;0.1. Ship-based measurements in the surface mixed layer reveal 0.5&lt;|Ro|&lt;1, indicating the presence of unbalanced, ageostrophic motions. Time series of Ro from triplets of surface drifters trapped within the filament confirm these relatively large Ro values and show a high variability along the filament. A scale-dependent analysis of Ro, which relies on the second-order velocity structure function, was applied to the latter drifter group and to another drifter group released in the upwelling zone. The two releases explored the area nearly distinctly and simultaneously and reveal that at small scales (&lt;15 km) Ro values are twice as large in the filament in comparison to its environment with Ro&gt;1 for scales smaller than ∼500 m. This suggests that filaments are hotspots of ageostrophic dynamics, pointing to the presence of a forward energy cascade. The different dynamics indicated by our Ro analysis are confirmed by horizontal kinetic energy wavenumber spectra, which exhibit a power law k−α with α∼5/3 for wavelengths 2π/k smaller than a transition scale of 15 km, supporting significant submesoscale energy at scales smaller than the first baroclinic Rossby radius (Ro1∼30 km). The detected transition scale is smaller than those found in regions with less mesoscale eddy energy, consistent with previous studies. We found evidence for the processes which drive the energy transfer to turbulent scales. Positive Rossby numbers (1) associated with cyclonic motion inhibit the occurrence of positive Ertel potential vorticity (EPV) and stabilize the water column. However, where the baroclinic component of EPV dominates, submesoscale instability analysis suggests that mostly gravitational instabilities occur and that symmetric instabilities may be important at the filament edges.</p