Mixed Layer Sub-Mesoscale Parameterization - Part 1: Derivation and Assessment

Several studies have shown that sub-mesoscales (SM 1km horizontal scale) play an important role in mixed layer dynamics. In particular, high resolution simulations have shown that in the case of strong down-front wind, the re-stratification induced by the SM is of the same order of the de-stratification induced by small scale turbulence, as well as of that induced by the Ekman velocity. These studies have further concluded that it has become necessary to include SM in ocean global circulation models (OGCMs), especially those used in climate studies. The goal of our work is to derive and assess an analytic parameterization of the vertical tracer flux under baroclinic instabilities and wind of arbitrary directions and strength. To achieve this goal, we have divided the problem into two parts: first, in this work we derive and assess a parameterization of the SM vertical flux of an arbitrary tracer for ocean codes that resolve mesoscales, M, but not sub-mesoscales, SM. In Part 2, presented elsewhere, we have used the results of this work to derive a parameterization of SM fluxes for ocean codes that do not resolve either M or SM. To carry out the first part of our work, we solve the SM dynamic equations including the non-linear terms for which we employ a closure developed and assessed in previous work. We present a detailed analysis for down-front and up-front winds with the following results: (a) down-front wind (blowing in the direction of the surface geostrophic velocity) is the most favorable condition for generating vigorous SM eddies; the de-stratifying effect of the mean flow and re-stratifying effect of SM almost cancel each other out

Comparison of Four Mixed Layer Mesoscale Parameterizations and the Equation for an Arbitrary Tracer

In this paper we discuss two issues, the inter-comparison of four mixed layer mesoscale parameterizations and the search for the eddy induced velocity for an arbitrary tracer. It must be stressed that our analysis is limited to mixed layer mesoscales since we do not treat sub-mesoscales and small turbulent mixing. As for the first item, since three of the four parameterizations are expressed in terms of a stream function and a residual flux of the RMT formalism (residual mean theory), while the fourth is expressed in terms of vertical and horizontal fluxes, we needed a formalism to connect the two formulations. The standard RMT representation developed for the deep ocean cannot be extended to the mixed layer since its stream function does not vanish at the ocean's surface. We develop a new RMT representation that satisfies the surface boundary condition. As for the general form of the eddy induced velocity for an arbitrary tracer, thus far, it has been assumed that there is only the one that originates from the curl of the stream function. This is because it was assumed that the tracer residual flux is purely diffusive. On the other hand, we show that in the case of an arbitrary tracer, the residual flux has also a skew component that gives rise to an additional bolus velocity. Therefore, instead of only one bolus velocity, there are now two, one coming from the curl of the stream function and other from the skew part of the residual flux. In the buoyancy case, only one bolus velocity contributes to the mean buoyancy equation since the residual flux is indeed only diffusive

Three-Dimensional, Space-Dependent Mesoscale Diffusivity: Derivation and Implications

Recently, we presented a parameterization of an arbitrary tracer 3D mesoscale flux that describes both diabatic and adiabatic regimes without using arbitrary tapering functions. However, we did not parameterize the mesoscale diffusivity, which is the subject of this work. A key difference between the present and previous diffusivity parameterizations is that in the latter, the two main ingredients, mesoscale drift velocity and eddy kinetic energy, were not parameterized but determined using present data, which deprives the models of predictive power. Since winds, stratification, etc., are predicted to change in the future, use of these parameterizations to study future climate scenarios becomes questionable. In this work, we parameterize drift velocity and eddy kinetic energy (verticalhorizontal components), which we first assess with data [WOCE, TOPEX/Poseidon (T/P), and North Atlantic Tracer Release Experiment (NATRE)] and then use in a coarse-resolution stand-alone ocean code under Coordinated Ocean-Ice Reference Experiment I (CORE-I) forcing. We present results for the global ocean temperature and salinity, Atlantic overturning circulation, meridional heat transport, and Drake Passage transport, which we compare with several previous studies. The temperature drift is less than that of five of seven previous OGCMs, and the salinity drift is among the smallest in those studies. The predicted winter Antarctic Circumpolar Current mixed layer depths (MLDs) are in good agreement with the data. Predicting the correct MLD is important in climate studies since models that predict very deep mixed layers transfer more of the radiative perturbation to the deep ocean, reducing surface warming (and vice versa)

Implications of the ALEPH tau-Lepton Decay Data for Perturbative and Non-Perturbative QCD

We use ALEPH data on hadronic $\tau$ decays in order to calculate Euclidean coordinate space correlation functions in the vector and axial-vector channels. The linear combination $V-A$ receives no perturbative contribution and is quantitatively reproduced by the instanton liquid model. In the case of $V+A$ the instanton calculation is in good agreement with the data once perturbative corrections are included. These corrections clearly show the evolution of $\alpha_s$. We also analyze the range of validity of the Operator Product Expansion (OPE). In the $V-A$ channel we find a dimension $d=6$ contribution which is comparable to the original SVZ estimate, but the instanton model provides a different non-singular term of the same magnitude. In the $V+A$ case both the OPE and the instanton model predict the same $d=4$ power correction induced by the gluon condensate, but it is masked by much larger perturbative contributions. We conclude that the range of validity of the OPE is limited to x\lsim0.3 fm, whereas the instanton model describes the data over the entire range.Comment: 4 pages, 6 figure

Renormalons as dilatation modes in the functional space

There are two sources of the factorial large-order behavior of a typical perturbative series. First, the number of the different Feynman diagrams may be large; second, there are abnormally large diagrams known as renormalons. It is well known that the large combinatorial number of diagrams is described by instanton-type solutions of the classical equations. We demonstrate that from the functional-integral viewpoint the renormalons do not correspond to a particular configuration but manifest themselves as dilatation modes in the functional space.Comment: 19 pages, latex, 5 eps figure

New Glueball-Meson Mass Relations

Using the ``glueball dominance'' picture of the mixing between q\bar{q} mesons of different hidden flavors, we establish new glueball-meson mass relations which serve as a basis for glueball spectral systematics. For the tensor glueball mass 2.3\pm 0.1 GeV used as an input parameter, these relations predict the following glueball masses: M(0^{++})\simeq 1.65\pm 0.05 GeV, M(1^{--})\simeq 3.2\pm 0.2 GeV, M(2^{-+})\simeq 2.95\pm 0.15 GeV, M(3^{--})\simeq 2.8\pm 0.15 GeV. We briefly discuss the failure of such relations for the pseudoscalar sector. Our results are consistent with (quasi)-linear Regge trajectories for glueballs with slope \simeq 0.3\pm 0.1 GeV^{-2}.Comment: Extensive revision including response to comments received, value of glueball Regge slope, and a consideration of radial excitations. 14 pages, LaTe

Drell-Yan diffraction: breakdown of QCD factorisation

We consider the diffractive Drell-Yan process in proton-(anti)proton collisions at high energies in the color dipole approach. The calculations are performed at forward rapidities of the leptonic pair. Effect of eikonalization of the universal "bare"dipole-target elastic amplitude in the saturation regime takes into account the principal part of the gap survival probability. We present predictions for the total and differential cross sections of the single diffractive lepton pair production at RHIC and LHC energies. We analyze implications of the QCD factorisation breakdown in the diffractive Drell-Yan process, which is caused by a specific interplay of the soft and hard interactions, and resulting in rather unusual properties of the corresponding observables.Comment: 19 pages, 7 figure

The spin dependence of high energy proton scattering

Motivated by the need for an absolute polarimeter to determine the beam polarization for the forthcoming RHIC spin program, we study the spin dependence of the proton-proton elastic scattering amplitudes at high energy and small momentum transfer.We examine experimental evidence for the existence of an asymptotic part of the helicity-flip amplitude phi_5 which is not negligible relative to the largely imaginary average non-flip amplitude phi_+. We discuss theoretical estimates of r_5, essentially the ratio of phi_5 to phi_+, based upon extrapolation of low and medium energy Regge phenomenological results to high energies, models based on a hybrid of perturbative QCD and non-relativistic quark models, and models based on eikonalization techniques. We also apply the model-independent methods of analyticity and unitarity.The preponderence of evidence at available energy indicates that r_5 is small, probably less than 10%. The best available experimental limit comes from Fermilab E704:those data indicate that |r_5|<15%. These bounds are important because rigorous methods allow much larger values. In contradiction to a widely-held prejudice that r_5 decreases with energy, general principles allow it to grow as fast as ln(s) asymptotically, and some models show an even faster growth in the RHIC range. One needs a more precise measurement of r_5 or to bound it to be smaller than 5% in order to use the classical Coulomb-nuclear interference technique for RHIC polarimetry. As part of this study, we demonstrate the surprising result that proton-proton elastic scattering is self-analysing, in the sense that all the helicity amplitudes can, in principle, be determined experimentally at small momentum transfer without a knowledge of the magnitude of the beam and target polarization