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Formulas are given for determining a conserved property of a storm and its centroid from an scalar field that has a tendency equation. The velocity of the centroid is also given. These formulas depend only on fields that are external to the storm.
A new algorithm for identifying and characterizing vortices in complex flows is presented. The scheme uses both the vorticity and pressure fields. A skeleton line along the center of a vortex is produced by a two-step predictor-corrector scheme. The technique uses the vector field to move in the direction of the skeleton line and the scalar field to correct the location in the plane perpendicular to the skeleton line. A general vortex cross section can be concisely defined with five parameters at each point along the skeleton line. The details of the method and examples of its use are discussed.
Turbulent transport of heat is studied by examining the flow fields obtained from a direct simulation of a turbulent channel flow. The turbulence structures associated with the velocity and scalar fields are presented using air (Pr = 0.71) as the medium. A comparison is made between the wall-layer structures identified by the temperature field and the structures found in the velocity field. Consideration is also given to the role of the organized turbulence structures in scalar transport.
Pairs of coordinates and derivatives of the constant gluon modes are mapped to new gluon-pair fields and their derivatives. Applying this mapping to the Hamiltonian of constant gluon fields results for large coupling constants into an effective Hamiltonian which separates into one describing a scalar field and another one for a field with spin two. The ground state is dominated by pairs of gluons coupled to color and spin zero with slight admixtures of color zero and spin two pairs. As color group we used SU(2).
The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.
The primary goal is to understand the sources of the near-Earth ambient magnetic field as observed by recent spacecraft surveys and surface variational magnetic observations so as to determine the electrical properties of the crust and upper mantle. Also included is the structure and changes on a short time scale of the core field which must be separated and identified. The Magsat data collection interval provides an opportunity to compare the vector field projections of ionospheric currents computed from surface data above the ionosphere as does the POGO data for scalar projections. The limitation of Magsat is its sun-synchronous orbit, which only sampled low latitudes at dawn and dusk, whereas POGO, though only making observations of the scalar field, sampled all local times. Magsat operated at a lower altitude than POGO (down to 350 km) whereas the orbits of the three POGO spacecraft ranged up to 1500 km and were never lower than about 400 km.
We analyze results of a premixed constant density flame propagating in three-dimensional turbulence, where a flame model developed by Kerstein, et al. (1988) has been used. Simulations with constant and evolving velocity fields are used, where peculiar results were obtained from the constant velocity field runs. Data from the evolving flow runs with various flame speeds are used to determine two-point correlations of the fluctuating scalar field and implications for flamelet modeling are discussed.
The theory of axially symmetric self-focusing of whistler waves, based on the full system of Maxwell equations, is developed. The plasma is described by the magnetohydrodynamic equations including the ponderomotive force from RF field. The nonlinear Schrodinger equations (NSE) for arbitrary azimuthal modes of whistler waves are derived. It is shown that they differ from the NSE for a scalar field; this is connected with an intrinsic angular momentum due to the rotating polarization of whistlers. It is shown that the self-focusing, as described by the NSE, differs in its final stage from the results following the full set of Maxwell equations. The latter gives defocusing after sufficient narrowing of the initial wave beam, due to transformation of the trapped wave into a nontrapped branch which is not contained in the NSE description. The oscillatory character of the defocusing is demonstrated.
New definitions of entrainment and mixing based on the passive scalar field in the plane mixing layer are proposed. The definitions distinguish clearly between three fluid states: (1) unmixed fluid, (2) fluid engulfed in the mixing layer, trapped between two scalar contours, and (3) mixed fluid. The difference betwen (2) and (3) is the amount of fluid which has been engulfed during the pairing process, but has not yet mixed. Trends are identified from direct numerical simulations and extensions to high Reynolds number mixing layers are made in terms of the Broadwell-Breidenthal mixing model. In the limit of high Peclet number (Pe = ReSc) it is speculated that engulfed fluid rises in steps associated with pairings, introducing unmixed fluid into the large scale structures, where it is eventually mixed at the Kolmogorov scale. From this viewpoint, pairing is a prerequisite for mixing in the turbulent plane mixing layer.
In order to calculate the velocity and scalar fields, the three dimensional, time-dependent equations of motion and the diffusion equation were solved numerically. The following cases were treated: isotropic, homogeneous turbulence with decay of a passive scalar; and homogeneous turbulent shear flow with a passive scalar whose mean varies linearly in the spanwise direction. The solutions were obtained at relatively low Reynolds numbers so that all of the turbulent scales could be resolved without modeling. Turbulent statistics such as integral length scales, Taylor microscales, Kolmogorov length scale, one- and two-point correlations of velocity-velocity and velocity-scalar, turbulent Prandtl/Schmidt number, r.m.s. values of velocities, the scalar quantity and pressure, skewness, decay rates, and decay exponents were calculated. The results are compared with the available expermental results, and good agreement is obtained.
The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.
Effects of organized turbulent structures on the propagation of an optical beam in a homogeneous shear flow were studied. A passive-scalar field in a computed turbulent shear flow is used to represent index-of-refraction fluctuations, and phase errors induced in a coherent optical beam by turbulent fluctuations are computed. The organized vortical structures produce a scalar distribution with elongated regions of intense fluctuations which have an inclination with respect to the mean flow similar to that of the characteristic hairpin eddies. It is found that r.m.s. phase error is minimized by propagating approximately normal to the inclined vortical structures. Two-point correlations of vorticity and scalar fluctuation suggest that the regions of intense scalar fluctuation are produced primarily by the hairpin eddies.
Effects of organized turbulent structures on the propagation of an optical beam in a homogeneous shear flow have been studied. A passive-scalar field in a computed turbulent shear flow is used to represent index-of-refraction fluctuations, and phase errors induced in a coherent optical beam by turbulent fluctuations are computed. The organized vortical structures produce a scalar distribution with elongated regions of intense fluctuations which have an inclination with respect to the mean flow similar to that of the characteristic hairpin eddies. It is found that rms phase error is minimized by propagating approximately normal to the inclined vortical structures. Two-point correlations of vorticity and scalar fluctuation suggest that the regions of intense scalar fluctuation are produced primarily by the hairpin eddies.
Phase distortion in a coherent optical beam propagating through a turbulent shear flow is studied. The instantaneous distribution of the index refraction is represented by a passive-scalar field in a computed homogeneous shear flow. The flow contains organized vortical structures (hairpin eddies), which are characteristic of turbulent shear flows. The phase distortion induced by turbulent fluctuations is calculated from the optical path difference through the flow. A conceptual model is proposed for the distribution of scalar fluctuations produced by the hairpin vortices in the shear flow. It is shown that the phase distortion of an optical beam can be minimized by propagating the beam at an angle approximately normal to the organized vortical structures in a turbulent shear flow.
Light fields with spatially varying backgrounds can modulate cosmic preheating, and imprint the nonlinear effects of preheating dynamics at tiny scales on large scale fluctuations. This provides us a unique probe into the preheating era which we dub the “cosmic microscope”. We identify a distinctive effect of preheating on scalar perturbations that turns the Gaussian primordial fluctuations of a light scalar field into square waves, like a diode. The effect manifests itself as local non-Gaussianity. We present a model, “modulated partial preheating”, where this nonlinear effect is consistent with current observations and can be reached by near future cosmic probes.
A new sub-grid mixing model for use in large eddy simulations of turbulent combustion is presented and applied to a hydrogen-air diffusion flame. The sub-grid model is based on Kerstein's Linear Eddy Model (1988). The model is first used to predict the mixing of a conserved scalar in a turbulent shear flow. The model correctly predicts the behavior of the pdf of the scalar field and displays a nonmarching peak at the preferred mixture fraction as the shear layer is traversed. It is then illustrated how a reduced chemical mechanism can be implemented within the linear eddy subgrid model formulation. The model is used to predict NO formation in hydrogen-air diffusion flame using a reduced chemical mechanism involving nine reactive scalars.
Problems were encountered in deriving a proper reference field to be subtracted from the aeromagnetic data obtained from Project MAGNET. Field models tried thus far do not seem to eliminate properly the main field. The MAGSAT data in the North American continent for the period November 1 to December 22, 1979 are being compiled and compared with MAGNET data. Efforts are being made to eliminate the orbital bias errors. A computer program was developed and successfully tested which computes a topographic profile of the Curie depth isotherm which fits best to the observed vector or scalar field magnetic data.
A simple model is constructed for the electric fields in the collapsing wave packets found in 3D simulations of driven and damped isotropic strong Langmuir turbulence. This model, based on a spherical-harmonic decomposition of the electrostatic potential, accounts for the distribution of wave-packet shapes observed in the simulations, particularly the predominance of oblate wave packets. In contrast with predictions for undamped and undriven subsonic collapse of scalar fields, oblate vector-field wave packets do not flatten during collapse but, instead, remain approximately self-similar and rigid.