A physical–statistical recipe for representation of small-scale oceanic turbulent mixing in climate models

It is well established that small-scale cross-density (diapycnal) turbulent mixing induced by breaking of overturns in the interior of the ocean plays a significant role in sustaining the deep ocean circulation and in regulating tracer budgets such as those of heat, carbon and nutrients. There has been significant progress in the fluid mechanical understanding of the physics of breaking internal waves. Connection of the microphysics of such turbulence to the larger scale dynamics, however, is significantly underdeveloped. We offer a hybrid theoretical–statistical approach, informed by observations, to make such a link. By doing so, we define a bulk flux coefficient, ΓB , which represents the partitioning of energy available to an ‘ocean box’ (such as a grid cell of a coarse resolution climate model), from winds, tides, and other sources, into mixing and dissipation. Here, ΓB depends on both the statistical distribution of turbulent patches and the flux coefficient associated with individual patches, Γi . We rely on recent parametrizations of Γi and the seeming universal characteristics of statistics of turbulent patches to infer ΓB , which is the essential quantity for representation of turbulent diffusivity in climate models. By applying our approach to climatology and global tidal estimates, we show that, on a basin scale, energetic mixing zones exhibit moderately efficient mixing that induces significant vertical density fluxes, while quiet zones (with small background turbulence levels), although highly efficient in mixing, exhibit minimal vertical fluxes. The transition between the less energetic to more energetic zones marks regions of intense upwelling and downwelling of deep waters. We suggest that such upwelling and downwelling may be stronger than previously estimated, which in turn has direct implications for the closure of the deep branch of the ocean meridional overturning circulation as well as for the associated tracer budgets

Kinks in the Hartree approximation

The topological defects of the lambda phi^4 theory, kink and antikink, are studied in the Hartree approximation. This allows us to discuss quantum effects on the defects in both stationary and dynamical systems. The kink mass is calculated for a number of parameters, and compared to classical, one loop and Monte Carlo results known from the literature. We discuss the thermalization of the system after a kink antikink collision. A classical result, the existence of a critical speed, is rederived and shown for the first time in the quantum theory. We also use kink antikink collisions as a very simple toy model for heavy ion collisions and discuss the differences and similarities, for example in the pressure. Finally, using the Hartree Ensemble Approximation allows us to study kink antikink nucleation starting from a thermal (Bose Einstein) distribution. In general our results indicate that on a qualitative level there are few differences with the classical results, but on a quantitative level there are some import ones.Comment: 20 pages REVTeX 4, 17 Figures. Uses amsmath.sty and subfigure.sty. Final version, fixed typo in published versio

Phase structures of strong coupling lattice QCD with finite baryon and isospin density

Quantum chromodynamics (QCD) at finite temperature (T), baryon chemical potential (\muB) and isospin chemical potential (\muI) is studied in the strong coupling limit on a lattice with staggered fermions. With the use of large dimensional expansion and the mean field approximation, we derive an effective action written in terms of the chiral condensate and pion condensate as a function of T, \muB and \muI. The phase structure in the space of T and \muB is elucidated, and simple analytical formulas for the critical line of the chiral phase transition and the tricritical point are derived. The effects of a finite quark mass (m) and finite \muI on the phase diagram are discussed. We also investigate the phase structure in the space of T, \muI and m, and clarify the correspondence between color SU(3) QCD with finite isospin density and color SU(2) QCD with finite baryon density. Comparisons of our results with those from recent Monte Carlo lattice simulations on finite density QCD are given.Comment: 18 pages, 6 figures, revtex4; some discussions are clarified, version to appear in Phys. Rev.