Theory of passive scalar fluctuations and transport caused by wave turbulence
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waves turbulence ocean transport↗
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Mechanical cosmology: Simulating scalar fluctuations in expanding universes using synthetic mechanical lattices
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Brendan Rhyno↗
Results from the Wilkinson Microwave Anisotropy Probe
The Wilkinson Microwave Anisotropy Probe (WMAP) mapped the distribution of temperature and polarization over the entire sky in five microwave frequency bands. These full-sky maps were used to obtain measurements of temperature and polarization anisotropy of the cosmic microwave background with the unprecedented accuracy and precision. The analysis of two-point correlation functions of temperature and polarization data gives determinations of the fundamental cosmological parameters such as the age and composition of the universe, as well as the key parameters describing the physics of inflation, which is further constrained by three-point correlation functions. WMAP observations alone reduced the flat Λ cold dark matter (Lambda Cold Dark Matter) cosmological model (six) parameter volume by a factor of > 68, 000 compared with pre-WMAP measurements. The WMAP observations (sometimes in combination with other astrophysical probes) convincingly show the existence of non-baryonic dark matter, the cosmic neutrino background, flatness of spatial geometry of the universe, a deviation from a scale-invariant spectrum of initial scalar fluctuations, and that the current universe is undergoing an accelerated expansion. The WMAP observations provide the strongest ever support for inflation; namely, the structures we see in the universe originate from quantum fluctuations generated during inflation.
The Wilkinson Microwave Anisotropy Probe (WMAP)↗
Large eddy simulation and direct numerical simulation of high speed turbulent reacting flows
The objective of this research is to make use of Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first phase of this research conducted within the past three years have been directed in several issues pertaining to intricate physics of turbulent reacting flows. In our previous 5 semi-annual reports submitted to NASA LaRC, as well as several technical papers in archival journals, the results of our investigations have been fully described. In this progress report which is different in format as compared to our previous documents, we focus only on the issue of LES. The reason for doing so is that LES is the primary issue of interest to our Technical Monitor and that our other findings were needed to support the activities conducted under this prime issue. The outcomes of our related investigations, nevertheless, are included in the appendices accompanying this report. The relevance of the materials in these appendices are, therefore, discussed only briefly within the body of the report. Here, results are presented of a priori and a posterior analyses for validity assessments of assumed Probability Density Function (PDF) methods as potential subgrid scale (SGS) closures for LES of turbulent reacting flows. Simple non-premixed reacting systems involving an isothermal reaction of the type A + B yields Products under both chemical equilibrium and non-equilibrium conditions are considered. A priori analyses are conducted of a homogeneous box flow, and a spatially developing planar mixing layer to investigate the performance of the Pearson Family of PDF's as SGS models. A posteriori analyses are conducted of the mixing layer using a hybrid one-equation Smagorinsky/PDF SGS closure. The Smagorinsky closure augmented by the solution of the subgrid turbulent kinetic energy (TKE) equation is employed to account for hydrodynamic fluctuations, and the PDF is employed for modeling the effects of scalar fluctuations. The implementation of the model requires the knowledge of the local values of the first two SGS moments. These are provided by additional modeled transport equations. In both a priori and a posteriori analyses, the predicted results are appraised by comparison with subgrid averaged results generated by DNS. Based on these results, the paths to be followed in future investigations are identified.
Adumitroaie, V.↗
Second order closure modeling of turbulent buoyant wall plumes
Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.
Zhu, Gang↗
First Year Wilkinson Microwave Anisotropy Probe (WMAP)Observations: Preliminary Maps and Basic Results
We present full sky microwave maps in five frequency bands (23 to 94 GHz) from the WMAP first year sky survey. Calibration errors are less than 0.5% and the low systematic error level is well specified. The cosmic microwave background (CMB) is separated from the foregrounds using multifrequency data. The sky maps are consistent with the 7 in. full-width at half-maximum (FWHM) Cosmic Background Explorer (COBE) maps. We report more precise, but consistent, dipole and quadrupole values. The CMB anisotropy obeys Gaussian statistics with -58 less than f(sub NL) less than 134 (95% CL). The 2 less than or = l less than or = 900 anisotropy power spectrum is cosmic variance limited for l less than 354 with a signal-to-noise ratio greater than 1 per mode to l = 658. The temperature-polarization cross-power spectrum reveals both acoustic features and a large angle correlation from reionization. The optical depth of reionization is tau = 0.17 +/- 0.04, which implies a reionization epoch of t(sub r) = 180(sup +220, sub -80) Myr (95% CL) after the Big Bang at a redshift of z(sub r) = 20(sup +10, sub -9) (95% CL) for a range of ionization scenarios. This early reionization is incompatible with the presence of a significant warm dark matter density. A best-fit cosmological model to the CMB and other measures of large scale structure works remarkably well with only a few parameters. The age of the best-fit universe is t(sub 0) = 13.7 +/- 0.2 Gyr old. Decoupling was t(sub dec) = 379(sup +8, sub -7)kyr after the Big Bang at a redshift of z(sub dec) = 1089 +/- 1. The thickness of the decoupling surface was Delta(sub z(sub dec)) = 195 +/- 2. The matter density of the universe is Omega(sub m)h(sup 2) = 0.135(sup +0.008, sub -0.009) the baryon density is Omega(sub b)h(sup 2) = 0.0224 +/- 0.0009, and the total mass-energy of the universe is Omega(sub tot) = 1.02 +/- 0.02. There is progressively less fluctuation power on smaller scales, from WMAP to fine scale CMB measurements to galaxies and finally to the Ly-alpha forest. This is accounted for with a running spectral index, significant at the approx. 2(sigma) level. The spectral index of scalar fluctuations is fit as n(sub s) = 0.93 +/-0.03 at wavenumber k(sub o) = 0.05/Mpc ((sub eff) approx. = 700), with a slope of dn(sub s)/d I(sub nk) = -0.031(sup + 0.016, sub -0.018) in the best-fit model.
Bennett, C. L.↗
Analysis and modeling of subgrid scalar mixing using numerical data
Direct numerical simulations (DNS) of passive scalar mixing in isotropic turbulence is used to study, analyze and, subsequently, model the role of small (subgrid) scales in the mixing process. In particular, we attempt to model the dissipation of the large scale (supergrid) scalar fluctuations caused by the subgrid scales by decomposing it into two parts: (1) the effect due to the interaction among the subgrid scales; and (2) the effect due to interaction between the supergrid and the subgrid scales. Model comparisons with DNS data show good agreement. This model is expected to be useful in the large eddy simulations of scalar mixing and reaction.
Girimaji, Sharath S.↗
Turbulent transport of a passive-scalar field by using a renormalization-group method
A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.
Hossain, Murshed↗
Scalar mixing in the supersonic shear layer
Experiments were conducted in a two-stream planar mixing layer facility at convective Mach numbers of 0.28 and 0.62. Mie scattering from condensed alcohol droplets and planar laser-induced fluorescence (PLIF) of nitric oxide were used for flow visualization in both the side and plan views. The PLIF signals were approximately proportional to mixture fraction and were used to generate statistical quantities. Visualizations using both the Mie scattering and PLIF indicate the structure is essentially two-dimensional at Mc = 0.28 and three-dimensional at Mc = 0.62. Perspective renderings of side view images show the structures are streamwise ramped at Mc = 0.28 and cross-stream ramped at Mc = 0.62. This difference appears to be associated with decreasing streamwise structure spacings at the higher Mc condition. The statistical analysis suggests that with increasing compressibility, the scalar fluctuations are smaller, and the fraction of mixed fluid is higher.
Clemens, N. T.↗
Passive turbulent flamelet propagation
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.
Ashurst, William T.↗
Remarks on the construction of a second-order closure description of turbulent reacting flows
In this paper an attempt is made to illustrate how second-order closure techniques might be used to make detailed calculations of turbulent diffusion flames. Two of the problems of closure that are peculiar to turbulent chemically reacting flows are discussed in some detail. These are the problem of computing in a consistent way all the correlations of fluctuations in scalar quantities needed for closure and the problem of the generation of turbulence by chemical reactions. Tentative closure models are put forward for both of these problems. Although the closure model for fluctuations in scalar quantities can, to a certain extent, be checked against idealized numerical examples for which exact solutions are known, the validity of both the closure models proposed here must, in the end, be determined by detailed comparison of computed results with experimental data.
DONALDSON C. DUP.↗
Turbulent density fluctuations in a subsonic and transonic free jet using crossed-beam schlieren techniques
Scalar density fluctuations were measured nonintrusively in the shear layer of a 5.08-cm (2-in.) cold air jet using a crossed-beam schlieren method. Two statistics, covariance and three-dimensional spectrum function, were estimated for an exit Mach number range of 0.3 to 0.97. The density fluctuation intensity, integral scale, and eddy convection speed were calculated and compared to available data where possible. Spectra were found to change significantly in shape becoming less peaked between 3 and 9 jet diameters downstream from the orifice, but they consistently exhibited a -5/3 power law decay at 3, 6, and 9 diameters for frequencies above the peak.
Martin, R. A.↗
Turbulent Fluctuation and Transport of Passive Scalars by Random Wave Fields
Turbulent transport of passive scalars by random wave fields is studied, with applications to statistics of chlorophyll concentration in the ocean.
Turbulent Fluctuation Passive Scalars Random Wave ↗
Ocean Wave Studies with Applications to Ocean Modeling and Improvement of Satellite Altimeter Measurements
Combining analysis of satellite data (altimeter, scatterometer, high-resolution visible and infrared images, etc.) with mathematical modeling of non-linear wave processes, we investigate various ocean wave fields (on scales from capillary to planetary), their role in ocean dynamics and turbulent transport (of heat and biogeochemical quantities), and their effects on satellite altimeter measuring accuracy. In 1998 my attention was focused on long internal gravity waves (10 to 1000 km), known also as baroclinic inertia-gravity (BIG) waves. We found these waves to be a major factor of altimeter measurements "noise," resulting in a greater uncertainty [up to 10 cm in terms of sea surface height (SSH) amplitude] in the measured SSH signal than that caused by the sea state bias variations (up to 5 cm or so). This effect still remains largely overlooked by the satellite altimeter community. Our studies of BIG waves address not only their influence on altimeter measurements but also their role in global ocean dynamics and in transport and turbulent diffusion of biogeochemical quantities. In particular, in collaboration with Prof Peter Weichman, Caltech, we developed a theory of turbulent diffusion caused by wave motions of most general nature. Applied to the problem of horizontal turbulent diffusion in the ocean, the theory yielded the effective diffusion coefficient as a function of BIG wave parameters obtainable from satellite altimeter data. This effort, begun in 1997, has been successfully completed in 1998. We also developed a theory that relates spatial fluctuations of scalar fields (such as sea surface temperature, chlorophyll concentration, drifting ice concentration, etc.) to statistical characteristics of BIG waves obtainable from altimeter measurements. A manuscript is in the final stages of preparation. In order to verify the theoretical predictions and apply them to observations, we are now analyzing Sea-viewing Wide Field of view Sensor (SeaWiFS) and Field of view Sensor (SeaWiFS) and Advanced Very High-Resolution Radiometer (AVHRR) data on sea surface temperature (SST) and chlorophyll concentration jointly with TOPEX/POSEIDON data on SSH variations.
Glazman, Roman E.↗
Turbulent Fluctuation and Transport of Passive Scalars by Random Wave Fields
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waves turbulent diffusion drift↗
Generation of fluctuations in cosmological models
The initial production of classical matter fluctuations in a scalar quantum field theory in curved spacetime is discussed. It is shown how quantum fluctuations generate classical matter inhomogeneities, and that the resulting spectrum is scale invariant. The relevant events that occur before the scale leaves the Hubble radius are studied.
Brandenberger, Robert H.↗
Optical propagation through a homogeneous turbulent shear flow
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.
Truman, C. Randall↗
Optical propagation through a homogeneous turbulent shear flow
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.
Truman, C. Randall↗