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At least 253 records · Page 14

A Spreadsheet for the Mixing of a Row of Jets with a Confined Crossflow

An interactive computer code, written with a readily available software program, Microsoft Excel (Microsoft Corporation, Redmond, WA) is presented which displays 3 D oblique plots of a conserved scalar distribution downstream of jets mixing with a confined crossflow, for a single row, double rows, or opposed rows of jets with or without flow area convergence and/or a non-uniform crossflow scalar distribution. This project used a previously developed empirical model of jets mixing in a confined crossflow to create an Microsoft Excel spreadsheet that can output the profiles of a conserved scalar for jets injected into a confined crossflow given several input variables. The program uses multiple spreadsheets in a single Microsoft Excel notebook to carry out the modeling. The first sheet contains the main program, controls for the type of problem to be solved, and convergence criteria. The first sheet also provides for input of the specific geometry and flow conditions. The second sheet presents the results calculated with this routine to show the effects on the mixing of varying flow and geometric parameters. Comparisons are also made between results from the version of the empirical correlations implemented in the spreadsheet and the versions originally written in Applesoft BASIC (Apple Computer, Cupertino, CA) in the 1980's.

J D Holderman↗

Vertical Diffusivities of Active and Passive Tracers

The climate models that include a carbon-cycle need the vertical diffusivity of a passive tracer. Since an expression for the latter is not available, it has been common practice to identify it with that of salt. The identification is questionable since T, S are active, not passive tracers. We present the first derivation of the diffusivity of a passive tracer in terms of Ri (Richardson number) and Rq (density ratio, ratio of salinity over temperature z-gradients). The following results have emerged: (a) The passive tracer diffusivity is an algebraic function of Ri, Rq. (b) In doubly stable regimes (DS, partial derivative of T with respect to z > 0, partial derivative of S with respect to z < 0), the passive scalar diffusivity is nearly the same as that of salt/heat for any values of Rq < 0 and Ri > 0. (c) In DC regimes (diffusive convection, partial derivative of T with respect to z < 0, partial derivative of S with respect to z < 0, Rq > 1), the passive scalar diffusivity is larger than that of salt. At Ri = O(1), it can be more than twice as large. (d) In SF regimes (salt fingers, partial derivative of T with respect to z > 0, partial derivative of S with respect to z > 0, Rq < 1), the passive scalar diffusivity is smaller than that of salt. At Ri = O(1), it can be less than half of it. (e) The passive tracer diffusivity predicted at the location of NATRE (North Atlantic Tracer Release Experiment) is discussed. (f) Perhaps the most relevant conclusion is that the common identification of the tracer diffusivity with that of salt is valid only in DS regimes. In the Southern Ocean, where there is the largest CO2 absorption, the dominant regime is diffusive convection discussed in (c) above.

Canuto, V. M.↗

Comparison of Climatological Planetary Boundary Layer Depth Estimates Using the GEOS-5 AGCM

Planetary boundary layer (PBL) processes, including those influencing the PBL depth, control many aspects of weather and climate and accurate models of these processes are important for forecasting changes in the future. However, evaluation of model estimates of PBL depth are difficult because no consensus on PBL depth definition currently exists and various methods for estimating this parameter can give results that differ by hundreds of meters or more. In order to facilitate comparisons between the Goddard Earth Observation System (GEOS-5) and other modeling and observational systems, seven PBL depth estimation methods are used to produce PBL depth climatologies and are evaluated and compared here. All seven methods evaluate the same atmosphere so all differences are related solely to the definition chosen. These methods depend on the scalar diffusivity, bulk and local Richardson numbers, and the diagnosed horizontal turbulent kinetic energy (TKE). Results are aggregated by climate class in order to allow broad generalizations. The various PBL depth estimations give similar midday results with some exceptions. One method based on horizontal turbulent kinetic energy produces deeper PBL depths in the winter associated with winter storms. In warm, moist conditions, the method based on a bulk Richardson number gives results that are shallower than those given by the methods based on the scalar diffusivity. The impact of turbulence driven by radiative cooling at cloud top is most significant during the evening transition and along several regions across the oceans and methods sensitive to this cooling produce deeper PBL depths where it is most active. Additionally, Richardson number-based methods collapse better at night than methods that depend on the scalar diffusivity. This feature potentially affects tracer transport.

Planetary Boundary Layer Depth↗

Satellite Radiation Products for Ocean Biology and Biogeochemistry: Needs, State-Of-The-Art, Gaps, Development Priorities, and Opportunities

Knowing the spatial and temporal distribution of the underwater light field, i.e., the spectral and angular structure of the radiant intensity at any point in the water column, is essential to understanding the biogeochemical processes that control the composition and evolution of aquatic ecosystems and their impact on climate and reaction to climate change. At present, only a few properties are reliably retrieved from space, either directly or via water-leaving radiance. Existing satellite products are limited to planar photosynthetically available radiation (PAR) and ultraviolet (UV) irradiance above the surface and diffuse attenuation coefficient. Examples of operational products are provided, and their advantages and drawbacks are examined. The usefulness and convenience of these products notwithstanding, there is a need, as expressed by the user community, for other products, i.e., sub-surface planar and scalar fluxes, average cosine, spectral fluxes (UV to visible), diurnal fluxes, absorbed fraction of PAR by live algae (APAR), surface albedo, vertical attenuation, and heating rate, and for associating uncertainties to any product on a pixel-by-pixel basis. Methodologies to obtain the new products are qualitatively discussed in view of most recent scientific knowledge and current and future satellite missions, and specific algorithms are presented for some new products, namely sub-surface fluxes and average cosine. A strategy and roadmap (short, medium, and long term) for usage and development priorities is provided, taking into account needs and readiness level. Combining observations from satellites overpassing at different times and geostationary satellites should be pursued to improve the quality of daily-integrated radiation fields, and products should be generated without gaps to provide boundary conditions for general circulation and biogeochemical models. Examples of new products, i.e., daily scalar PAR below the surface, daily average cosine for PAR, and sub-surface spectral scalar fluxes are presented. A procedure to estimate algorithm uncertainties in the total uncertainty budget for above-surface daily PAR, based on radiative simulations for expected situations, is described. In the future, space-borne lidars with ocean profiling capability offer the best hope for improving our knowledge of sub-surface fields. To maximize temporal coverage, space agencies should consider placing ocean-color instruments in L1 orbit, where the sunlit part of the Earth can be frequently observed.

Frouin, Robert↗

Modeling of Cavity Residence Time via Modeled Lagrangian Particle Tracking

One of the critical components in a scramjet is the cavity flame holder. In evaluating the sizing of this component, the residence time of the fuel in the cavity is a common parameter used. However, to obtain the residence time via CFD is an expensive undertaking. One method is to perform an LES simulation of the cavity and use Lagrangian particle tracking to obtain both the mean and probability density function of the time that the particles remain in the cavity. While this method affords a significant amount of information, it is very costly in CPU run time. A simpler method involves performing a time accurate RANS simulation of the cavity, and when converged, overlay a traceable scalar in the cavity region, and then record the decay of this scalar’s flux at a downstream location. The time scale of the decay rate can then be estimated and a residence time inferred. This method is less computationally expensive than the LES approach, but still requires a time-accurate solution while only providing a mean cavity residence time evaluation. In this paper a method of determining the mean cavity residence time as well as the Probability Density Function (PDF) of the residence time is proposed and demonstrated. This method is based on Lagrangian particle tracking modeled by the Generalized Langevin Equation and is implemented as a post-processing step for a steady RANS solution. Computational cost is on the order of minutes and the results are in agreement with values obtained by the LES and scalar decay methods.

Langevin↗

Euler potentials

Products of gradients of scalars in plasma physics structure representation, discussing cross products of gradients of scalars in plasma physics

Stern, D. P.↗

Exact solutions to Brans-Dicke cosmologies in flat Friedmann universes.

The Brans-Dicke cosmological equations for flat Friedmann-type expanding universes are solved parametrically for time, density, expansion parameter, and scalar field. These results reduce to a previously obtained exact solution to the radiation cosmology. Although the scalar field may be undetectable at the present epoch, it is felt that, if it exists, it must play an important role as one approaches the initial singularity of the cosmology.

Morganstern, R. E.↗

Design of optimal probing signals for vector parameter estimation.

In the design of optimal inputs or probing signals for parameter estimation, it is more natural to consider functions of the Fisher information matrix as the criterion of optimality instead of some function of the error covariance matrix. The input which maximizes the Fisher information measure for efficient estimation of a scalar parameter also provides the minimum error variance. The information is thus a logical choice for the optimality criterion in scalar problems. No such obvious choice is apparent for vector parameter estimation. A number of performance measures are examined and compared in the present study, and a useful criterion is selected. The design of an optimal probing signal using this criterion is shown to be equivalent to an optimal control problem in which certain equality constraints must be satisfied. This problem may be solved by conventional techniques of deterministic or stochastic optimal control.

Nahi, N. E.↗

Stability conditions derived from spectral theory - Discrete systems with periodic feedback.

By use of the spectral theory of linear operators, necessary and sufficient conditions are derived for the stability of a class of discrete time feedback systems with a periodically time-varying feedback gain. These conditions involve a Nyquist plot for an equivalent time-invariant system which may be determined from the frequency response function of the system under consideration. In the special case of a scalar-input scalar-output system, these conditions may be given in a particularly simple form.

Davis, J. H.↗

Theoretical frameworks for testing relativistic gravity. IV - A compendium of metric theories of gravity and their post-Newtonian limits.

Metric theories of gravity are compiled and classified according to the types of gravitational fields they contain, and the modes of interaction among those fields. The gravitation theories considered are classified as (1) general relativity, (2) scalar-tensor theories, (3) conformally flat theories, and (4) stratified theories with conformally flat space slices. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained by comparing it with Will's version of the formalism. Results obtained here, when combined with experimental data and with recent work by Nordtvedt and Will and by Ni, show that, of all theories thus far examined by our group, the only currently viable ones are general relativity, the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan), and a recent, new vector-tensor theory by Nordtvedt, Hellings, and Will.

Ni, W.-T.↗

A magnetospheric field model incorporating the OGO 3 and 5 magnetic field observations

A magnetospheric field model is presented in which the usually assumed toroidal ring current is replaced by a circular disk current of finite thickness that extends from the tail to geocentric distances less than 3 earth radii. The drastic departure of this model from the concept of the conventional ring current lies in the fact that the current is continuous from the tail to the inner magnetosphere. This conceptual change was required to account for the recent results of analysis of the OGO 3 and 5 magnetic field observations. In the present model the cross-tail current flows along circular arcs concentric with the earth and completes circuit via surface currents on the magnetopause. Apart from these return currents in the tail magnetopause, Mead's model is used for the field from the magnetopause current. The difference scalar field, delta B, defined as the difference between the scalar field calculated from the present model and the magnitude of the dipole field is found to be in gross agreement with the observed delta B. An updated version of the delta B contours from the OGO 3 and 5 observations, which is used for the comparison, is presented.

Sugiura, M.↗

Time-delay test of general relativity and Earth-Mars ephemeris improvement from analysis of Mariner 9 tracking data

Because of the large systematic errors that accompany the conversion of spacecraft ranging data to equivalent Earth-Mars time delays, the corresponding determination of gamma does not now allow the predictions of general relativity to be distinguished from those of the Brans-Dicke scalar-tensor theory with the fraction s of scalar field admixture being 0.06. The uncertainty in the determination of (1 plus gamma)/2 at the present stage of the Mariner 9 data analysis is at about the 10% level. The ephemeris of Mars suffers from the same problem: Only with the elimination of a major fraction of the systematic errors affecting the Mariner 9 pseudo observables will a truly substantial improvement be possible in the determination of the orbit.

Shapiro, I. I.↗

A graphical test for checking the stability of a linear time-invariant feedback system.

A continuous-time scalar linear time-invariant feedback system is considered for the purpose of checking Willems' (1969, 1970) graphical test for a scalar linear time-invariant feedback system with constant feedback. Heavy reliance is placed on the theory of almost periodic functions. Following definition of the problem and layout of notation, attention is given to solution of the problem, considering only the almost periodic part of the open-loop transfer function.

Callier, F. M.↗

The ring current.

The topology of delta-B (i.e., the observed scalar magnetic field intensity minus a scalar reference field intensity) in the magnetosphere has been established by the Rb magnetometer observations on OGO's 3 and 5. This delta-B topology provides a convenient framework, on the basis of which the complex features found by the earlier magnetic field observations made by Explorers 10, 12, 14, 26 and Electron 2 can be reinterpreted to fit a unified simple picture of the magnetospheric field distortions including the inflation of the equatorial magnetosphere by the ring current. It is proposed that the quiet-time ring current consists of two parts, the inner ring current imbedded deeply inside the plasmapause and the outer ring current flowing in the plasma sheet.

Sugiura, M.↗

A magnetospheric field model incorporating the OGO 3 and 5 magnetic field observations.

A magnetospheric field model is presented in which the usually assumed toroidal ring current is replaced by a circular disk current of finite thickness that extends from the tail to geocentric distances less than 3 earth radii. The drastic departure of this model from the concept of the conventional ring current lies in that the current is continuous from the tail to the inner magnetosphere. This conceptual change was required to account for the recent results of analysis of the OGO 3 and 5 magnetic field observations. In the present model the cross-tail current flows along circular arcs concentric with the earth and completes circuit via surface currents on the magnetopause. Apart from these return currents in the tail magnetopause, Mead's (1964) model is used for the field from the magnetopause current. The difference scalar field, Delta B, defined as the difference between the scalar field calculated from the present model and the magnitude of the dipole field, is found to be in gross agreement with the observed Delta B.

Sugiura, M.↗

A NASTRAN DMAP alter for determining a local stiffness modification to obtain a specified eigenvalue

A technique is described which has been programmed as a DMAP Alter to Rigid Format 3, for determining a stiffness matrix modification to obtain a specified eigenvalue for a structure. The stiffness matrix modifications allowable are those that can be described as the product of a single scalar variable and a matrix of constant coefficients input by the user. The program solves for the scalar variable multiplier which will yield a specified eigenvalue for the complete structure (provided it exists), makes the modification to the stiffness matrix, and proceeds in Rigid Format 3 to obtain the eigenvalues and eigenvectors of the modified structure.

Case, W. R., Jr.↗