D. C. Lewellen

A Relation Between Tree Amplitudes of Closed and Open Strings

We derive a formula which expresses any closed string tree amplitude in terms of a sum of the products of appropriate open string tree amplitudes. This formula is applicable to the heterotic string as well as to the closed bosonic string and type II superstrings. In particular, we demonstrate its use by showing how to write down, without any direct calculation, all four-point heterotic string tree amplitudes with massless external particles.

Construction of Fermionic String Models in Four-Dimensions

The construction of four-dimensional closed fermionic string models is discussed. The approach is based on a fermionic formulation of all internal (i.e. toroidally compactified) coordinates. Modular invariance, world sheet supersymmetry, (super)conformal invariance and proper space-time spin-statistics impose stringent constraints on the model building. Using these constraints on the boundary conditions (spin structure) of the world sheet fermions, we obtain a simple set of rules for constructing ultraviolet-finite closed fermionic string models. For a large subclass of these models, this “spin structure” construction can be related to bosonic constructions via the fermionic charge lattice. These charge lattices are odd lorentzian self-dual lattices shifted by a fixed. vector and form a nontrivial generalization of the lorentzian self-dual even-integer lattices considered by Narain. In particular, four-dimensional models with N = 4, N = 2, and N = 1 supersymmetry as well as non-supersymmetric tachyon-free chiral models can easily be constructed. Some models may be interpreted as charge lattices moded by discrete symmetries – in particular Z 2 type orbifolds. String interactions and other related issues are also discussed.

Evaluation of Large-Eddy Simulations via Observations of Nocturnal Marine Stratocumulus

Data from the first research flight (RF01) of the second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field study are used to evaluate the fidelity with which large-eddy simulations (LESs) can represent the turbulent structure of stratocumulus-topped boundary layers. The initial data and forcings for this case placed it in an interesting part of parameter space, near the boundary where cloud-top mixing is thought to render the cloud layer unstable on the one hand, or tending toward a decoupled structure on the other hand. The basis of this evaluation consists of sixteen 4-h simulations from 10 modeling centers over grids whose vertical spacing wa s5ma t thecloud-top interface and whose horizontal spacing was 35 m. Extensive sensitivity studies of both the configuration of the case and the numerical setup also enhanced the analysis. Overall it was found that (i) if efforts are made to reduce spurious mixing at cloud top, either by refining the vertical grid or limiting the effects of the subgrid model in this region, then the observed turbulent and thermodynamic structure of the layer can be reproduced with some fidelity; (ii) the base, or native configuration of most simulations greatly overestimated mixing at cloud top, tending toward a decoupled layer in which cloud liquid water path and turbulent intensities were grossly underestimated; (iii) the sensitivity of the simulations to the representation of mixing at cloud top is, to a certain extent, amplified by particulars of this case. Overall the results suggest that the use of LESs to map out the behavior of the stratocumulus-topped boundary layer in this interesting region of parameter space requires a more compelling representation of processes at cloud top. In the absence of significant leaps in the understanding of subgrid-scale (SGS) physics, such a representation can only be achieved by a significant refinement in resolution—a refinement that, while conceivable given existing resources, is probably still beyond the reach of most centers.

Simulations of Trade Wind Cumuli under a Strong Inversion

The fifth intercomparison of the Global Water and Energy Experiment Cloud System Studies Working Group 1 is used as a vehicle for better understanding the dynamics of trade wind cumuli capped by a strong inversion. The basis of the intercomparison is 10 simulations by 7 groups. These simulations are supplemented by many further sensitivity studies, including some with very refined grid meshes. The simulations help illustrate the turbulent dynamics of trade cumuli in such a regime. In many respects the dynamics are similar to those found in many previous simulations of trade cumuli capped by weaker inversions. The principal differences are the extent to which the cloud layer is quasi-steady in the current simulations, evidence of weak countergradient momentum transport within the cloud layer, and the development and influence of an incipient stratiform cloud layer at the top of the cloud layer. Although many elements of the turbulent structure (including the wind profiles, the evolution of cloud-base height, the statistics of the subcloud layer, and the nature of mixing in the lower and middle parts of the cloud layer) are robustly predicted, the representation of the stratiform cloud amount by the different simulations is remarkably sensitive to a number of factors. Chief among these are differences between numerical algorithms. These sensitivities persist even among simulations on relatively refined grid meshes. Part of this sensitivity is attributed to a physically realistic positive radiative feedback, whereby a propensity toward higher cloud fractions in any given simulation is amplified by longwave radiative cooling. The simulations also provide new insight into the dynamics of the transition layer at cloud base. In accord with observations, the simulations predict that this layer is most identifiable in terms of moisture variances and gradients. The simulations help illustrate the highly variable (in both height and thickness) nature of the transition layer, and we speculate that this variability helps regulate convection. Lastly the simulations are used to help evaluate simple models of trade wind boundary layers. In accord with previous studies, mass-flux models well represent the dynamics of the cloud layer, while mixing-length models well represent the subcloud layer. The development of the stratiform cloud layer is not, however, captured by the mass-flux models. The simulations indicate that future theoretical research needs to focus on interface rules, whereby the cloud layer is coupled to the subcloud layer below and the free atmosphere above. Future observational studies of this regime would be of most benefit if they could provide robust cloud statistics as a function of mean environmental conditions.

Large‐eddy simulation of the diurnal cycle of shallow cumulus convection over land

SUMMARY Large-eddy simulations of the development of shallow cumulus convection over land are presented. Many characteristics of the cumulus layer previously found in simulations of quasi-steady convection over the sea are found to be reproduced in this more strongly forced, unsteady case. Furthermore, the results are shown to be encouragingly robust, with similar results obtained with eight independent models, and also across a range of numerical resolutions. The datasets produced are already being used in the development and evaluation of parametrizations used in numerical weather-prediction and climate models.

Bulk and boundary operators in conformal field theory

Abstract In conformal field theory on a manifold with a boundary, there is a short-distance expansion expressing local bulk operators in terms of boundary operators at an adjacent boundary. We show how the coefficients of such an expansion are given solely by data appearing in the bulk theory on the sphere and torus. In particular, the coefficients of the identity operator, which fix the one-point functions, are determined by the elements of the matrix S which implements modular transformations on the torus. The other coefficients are related, in addition, to the elements of the matrices implementing duality transformations on the conformal blocks of the four-point functions on the sphere. Some examples are given.

Controls on precipitation and cloudiness in simulations of trade-wind cumulus as observed during RICO

Twelve large-eddy simulations, with a wide range of microphysical representations, are compared to each other and to independent measurements. The measurements and the initial and forcing data for the simulations are taken from the undisturbed period of the Rain in Cumulus over the Ocean (RICO) field study. A regional downscaling of meteorological analyses is performed so as to provide forcing data consistent with the measurements. The ensemble average of the simulations plausibly reproduces many features of the observed clouds, including the vertical structure of cloud fraction, profiles of cloud and rain water, and to a lesser degree the population density of rain drops. The simulations do show considerable departures from one another in the representation of the cloud microphysical structure and the ensuant surface precipitation rates, increasingly so for the more simplified microphysical models. There is a robust tendency for simulations that develop rain to produce a shallower, somewhat more stable cloud layer. Relations between cloud cover and precipitation are ambiguous.

Sewing constraints for conformal field theories on surfaces with boundaries

Abstract In a conformal field theory, correlation functions on any Riemann surface are in principle unambiguously defined by sewing together three-point functions on the sphere, provided that the four-point functions on the sphere are crossing symmetric, and the one-point functions on the torus are modular covariant. In this work we extend Sonodas proof of this result to conformal field theories defined on surfaces with boundaries. Four additional sewing constraints arise; three on the half-plane and one on the cylinder. These relate the various OPE coefficients in the theory (bulk, boundary, and bulk-boundary) to one another. In rational theories these relations can be expressed in terms of data arising solely within the bulk theory: the matrix S which implements modular transformations on the characters, and the matrices implementing duality transformations on the four-point conformal-block functions. As an example we solve these relations for the boundary and bulk-boundary structure constants in the Ising model with all possible conformally invariant boundary conditions. The role of the basic sewing constraints in the construction of open string theories is discussed.

Large-Eddy Simulations of a Drizzling, Stratocumulus-Topped Marine Boundary Layer

Cloud water sedimentation and drizzle in a stratocumulus-topped boundary layer are the focus of an intercomparison of large-eddy simulations. The context is an idealized case study of nocturnal stratocumulus under a dry inversion, with embedded pockets of heavily drizzling open cellular convection. Results from 11 groups are used. Two models resolve the size distributions of cloud particles, and the others parameterize cloud water sedimentation and drizzle. For the ensemble of simulations with drizzle and cloud water sedimentation, the mean liquid water path (LWP) is remarkably steady and consistent with the measurements, the mean entrainment rate is at the low end of the measured range, and the ensemble-average maximum vertical wind variance is roughly half that measured. On average, precipitation at the surface and at cloud base is smaller, and the rate of precipitation evaporation greater, than measured. Including drizzle in the simulations reduces convective intensity, increases boundary layer stratification, and decreases LWP for nearly all models. Including cloud water sedimentation substantially decreases entrainment, decreases convective intensity, and increases LWP for most models. In nearly all cases, LWP responds more strongly to cloud water sedimentation than to drizzle. The omission of cloud water sedimentation in simulations is strongly discouraged, regardless of whether or not precipitation is present below cloud base.

Large-Eddy Simulation of a Tornado’s Interaction with the Surface

High-resolution, fully three-dimensional, unsteady simulations of the interaction of a tornado vortex with the surface were performed in an attempt to answer questions about the character of turbulent transport in this unique flow. The authors demonstrate that sufficient resolution was achieved for the particular physical conditions of their example that the time-averaged velocity and pressure distributions showed little sensitivity in the region of maximum velocities to either finer resolution or modified subgrid turbulent model. The time-averaged velocity distributions show the maximum velocity values occurring within 50 m of the surface. The instantaneous velocity distributions show the turbulence dominated by a relatively small number of strong secondary vortices spiralling around the main vortex with the maximum instantaneous velocities typically one-third larger than the maximum time-averaged velocity. These eddies are centered a little inside of the cone of maximum mean swirl velocity and spiral around the mean vortex at velocities less than the average maximum velocity. Statistical analysis of the velocity fluctuations induced by the secondary vortices shows that the turbulent transport of angular momentum is predominantly inward at low levels, allowing the inner recirculating flow to acquire values of angular momentum of up to 30% of that provided by the inflow boundary conditions, thus enhancing the surface intensification of the velocities.