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

The photon-photon interaction at low xx in the theory of reggeized gluons with a running coupling and Nc→∞N_{c}\to\infty

The forward elastic amplitude for scattering of real and weakly virtual photons is studied in the framework of the theory of reggeized gluons, with large $N_{c}$ and a running coupling constant introduced in the manner which preserves the bootstrap condition. Transition from a single to multiple pomeron exchanges is observed as $x$ gets smaller. For very low $x$ the amplitude aquires an eikonal form. The photon structure function reveals a strong violation of scaling: it grows as $Q^{2}$. As a function of $x$ it behaves as $(\ln(1/x)\ln\ln(1/x))^{2}$. Correspondingly the cross-section for physical photons grows with energy as $(\ln s\ln\ln s)^{2}$. Hadronic structure functions and cross-sections are also briefly discussed.Comment: 12 pages, LATE

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)

Instanton-induced contributions to structure functions of deep inelastic scattering

We identify and calculate the instanton-induced contributions to deep inelastic scattering which correspond to nonperturbative exponential corrections to the coefficient functions in front of parton distributions of the leading twist.Comment: MPI-Ph/92-89 , LATEX, 15 pages, 3 figures incl. as uu-encoded fil

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

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

Direct Instantons in QCD Nucleon Sum Rules

We study the role of direct (i.e. small-scale) instantons in QCD correlation functions for the nucleon. They generate sizeable, nonperturbative corrections to the conventional operator product expansion, which improve the quality of both QCD nucleon sum rules and cure the long-standing stability problem, in particular, of the chirally odd sum-rule.Comment: 10 pages, UMD PP#93-17