Global observations of nonlinear mesoscale eddies

Abstract Sixteen years of sea-surface height (SSH) fields constructed by merging the measurements from two simultaneously operating altimeters are analyzed to investigate mesoscale variability in the global ocean. The prevalence of coherent mesoscale features (referred to here as “eddies”) with radius scales of O(100 km) is readily apparent in these high-resolution SSH fields. An automated procedure for identifying and tracking mesoscale features based on their SSH signatures yields 35,891 eddies with lifetimes ⩾16 weeks. These long-lived eddies, comprising approximately 1.15 million individual eddy observations, have an average lifetime of 32 weeks and an average propagation distance of 550 km. Their mean amplitude and a speed-based radius scale as defined by the automated procedure are 8 cm and 90 km, respectively. The tracked eddies are found to originate nearly everywhere in the World Ocean, consistent with previous conclusions that virtually all of the World Ocean is baroclinically unstable. Overall, there is a slight preference for cyclonic eddies. However, there is a preference for the eddies with long lifetimes and large propagation distances to be anticyclonic. In the southern hemisphere, the distributions of the amplitudes and rotational speeds of eddies are more skewed toward large values for cyclonic eddies than for anticyclonic eddies. As a result, eddies with amplitudes >10 cm and rotational speeds >20 cm s −1 are preferentially cyclonic in the southern hemisphere. By contrast, there is a slight preference for anticyclonic eddies for nearly all amplitudes and rotational speeds in the northern hemisphere. On average, there is no evidence of anisotropy of these eddies. Their average shape is well represented as Gaussian within the central 2/3 of the eddy, but the implied radius of maximum rotational speed is 64% smaller than the observed radius of maximum speed. In part because of this mismatch between the radii of maximum axial speed in the observations and the Gaussian approximation, a case is made that a quadratic function that is a very close approximation of the mode profile of the eddy (i.e., the most frequently occurring value at each radius) is a better representation of the composite shape of the eddies. This would imply that the relative vorticity is nearly constant within the interiors of most eddies, i.e., the fluid motion consists approximately of solid-body rotation. Perhaps the most significant conclusion of this study is that essentially all of the observed mesoscale features outside of the tropical band 20°S–20°N are nonlinear by the metric U / c , where U is the maximum circum-average geostrophic speed within the eddy interior and c is the translation speed of the eddy. A value of U / c > 1 implies that there is trapped fluid within the eddy interior. Many of the extratropical eddies are highly nonlinear, with 48% having U / c > 5 and 21% having U / c > 10. Even in the tropics, approximately 90% of the observed mesoscale features are nonlinear by this measure. Two other nondimensional parameters also indicate strong degrees of nonlinearity in the tracked eddies. The distributions of all three measures of nonlinearity are more skewed toward large values for cyclonic eddies than for anticyclonic eddies in the southern hemisphere extratropics but the opposite is found in the northern hemisphere extratropics. There is thus a preference for highly nonlinear extratropical eddies to be cyclonic in the southern hemisphere but anticyclonic in the northern hemisphere. Further evidence in support of the interpretation of the observed features as nonlinear eddies is the fact that they propagate nearly due west with small opposing meridional deflections of cyclones and anticyclones (poleward and equatorward, respectively) and with propagation speeds that are nearly equal to the long baroclinic Rossby wave phase speed. These characteristics are consistent with theoretical expectations for large, nonlinear eddies. While there is no apparent dependence of propagation speed on eddy polarity, the eddy speeds relative to the local long Rossby wave phase speeds are found to be about 20% faster in the southern hemisphere than in the northern hemisphere. The distributions of the propagation directions of cyclones and anticyclones are essentially the same, except mirrored about a central azimuth angle of about 1.5° equatorward. This small, but we believe statistically significant, equatorward rotation of the central azimuth may be evidence of the effects of ambient currents (meridional advection or the effects of vertical shear on the potential vorticity gradient vector) on the propagation directions of the eddies. While the results presented here are persuasive evidence that most of the observed westward-propagating SSH variability consists of isolated nonlinear mesoscale eddies, it is shown that the eddy propagation speeds are about 25% slower than the westward propagation speeds of features in the SSH field that have scales larger than those of the tracked eddies. This scale dependence of the propagation speed may be evidence for the existence of dispersion and the presence of features that obey linear Rossby wave dynamics and have larger scales and faster propagation speeds than the nonlinear eddies. The amplitudes of these larger-scale signals are evidently smaller than those of the mesoscale eddy field since they are not easily isolated from the energetic nonlinear eddies.