Inverse energy cascade in ocean macroscopic turbulence: Energy transfer rate ε and Richardson-Obhukov constant g from an surface drifter experiment in the Benguela upwelling system

<p>We derive the energy transfer rate ε from the 3<sup>rd</sup> order relative (longitudinal)  velocity structure function <Δu<sub>l</sub><sup>3</sup>>=(3/2)εs from ocean surface drifter trajectories in the turbulent mixed layer of the Benguela upwelling region off the coast of Namibia.  Combination with the  mean squared pair separation<s<sup>2</sup>(t)> =gεt<sup>3 </sup>reveals the Richardson-Obhukov constant g≅0.5, which is remarkably close to the one measured in  controlled two-dimensional turbulent flows in laboratory. We verify the  two coupled  cascades of energy (upscale/inverse) and enstrophy (downwscale) by  the  theoretically predicted  slope 1  for <Δu<sub>l</sub><sup>3</sup>> for inertial scales (above the injection scale) and slope 2 for  the 2<sup>nd</sup> order structure function <Δu<sub>l</sub><sup>2</sup>> for non-local scales (below the injection scale) respectively. We detect  additional 'ballistic contributions' in the central regime of the corresponding probability distribution P(st) of relative separations s for fixed time t, leading to an additional  power law factor s<sup>-α</sup> with  α ≅ 5/3. The algebraic decay with 1<α <2 revives  to the relevance of Levy distributions in the stochastic description of the turbulent transport process in contrast to former claims. Our findings  of a positively skewed   probability distribution P(Δu<sub>l</sub>s) of relative longitudinal velocity Δu<sub>l</sub>  for inertial scales s renews the question of intermittency in the  inverse energy cascade.</p>