We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators O I ∼ trφ (i φ j) in N = 4 SYM 4 at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all powersingular terms in the 4-point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the R-symmetry current and the stress tensor. Operators dual to string modes decouple at strong coupling. We compute the anomalous dimensions and the leading 1/N 2 corrections to the normalization constants of the 2-and 3-point functions of scalar and vector double-trace operators with approximate dimensions 4 and 5 respectively. We also find that the conformal dimensions of certain towers of double-trace operators in the 105, 84 and 175 irreps are non-renormalized. We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the 20 irrep, its anomalous dimension vanishes. As by-products of our investigation, we derive explicit expressions for the conformal block of the stress tensor, and for the conformal partial wave amplitudes of a conserved current and of a stress tensor in d dimensions.1
Spatiotemporal evolution of a small localized meander on a Gulf Stream-type baroclinically unstable jet over a topographic slope is investigated numerically using a three-dimensional, primitive equation model. An unperturbed jet is prescribed by a potential vorticity front in the upper thermocline overlaying intermediate layers with weak isentropic potential vorticity gradients and a quiscent bottom layer over a positive (same sense as isopycnal tilt) cross-stream continental slope. A series of numerical experiments with the same initial conditions over a slope and flat bottom on the  plane and on the f plane has been carried out.An initially localized meander evolves into a wave packet and generates deep eddies that provide a positive feedback for the meander growth. Meanders found growing over a flat bottom are able to pinch off resembling warm and cold core rings, while in the presence of a weak bottom slope such as 0.002, the maximum amplitudes of meanders and associated deep eddies saturate with no eddy shedding. In the flat bottom case, the growth rate is only 10% larger than in the weak slope case. Nevertheless, the bottom slope efficiently controls nonlinear saturation of meander growth via constraining the development of deep eddies. The topographic slope modifies the evolution of deep eddies and causes the phase displacement of deep eddies in the direction of the upper layer troughs/crests, thus limiting growth of the meanders. Behind the wave packet peak deep eddies form a nearly zonal circulation that stabilizes the jet in an equilibrated state. The main equilibration mechanism is a homogenization of the lower-layer potential vorticity by deep eddies. The width of the homogenized zone is narrower for a larger slope and/or on the  plane.These results have the following implications to the Gulf Stream dynamics: 1) maximum of the meander amplitudes increase as the topographic slope relaxes in qualitative agreement with observed behavior of the Gulf Stream, 2) the phase locking of the meanders with deep eddies underneath at the nonlinear stage agrees qualitatively with the observed structure of large amplitude cyclonic troughs at the central array, and 3) the increase of the barotropic transport on the warm side of the jet and the generation of the recirculation on the cold side of the jet is consistent with observations in the Gulf Stream system downstream of Cape Hatteras.
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