Lower-Dimensional Manifold (Algebraic) Representation of Reynolds Stress Closure Equations

For complex turbulent flows, Reynolds stress closure modeling (RSCM) is the lowest level at which models can be developed with some fidelity to the governing Navier–Stokes equations. Citing computational burden, researchers have long sought to reduce the seven-equation RSCM to the so-called algebraic Reynolds stress model which involves solving only two evolution equations for turbulent kinetic energy and dissipation. In the past, reduction has been accomplished successfully in the weak-equilibrium limit of turbulence. In non-equilibrium turbulence, attempts at reduction have lacked mathematical rigor and have been based on ad hoc hypotheses resulting in less than adequate models.?In this work we undertake a formal (numerical) examination of the dynamical system of equations that constitute the Reynolds stress closure model to investigate the following questions. (i) When does the RSCM equation system formally permit reduced representation? (ii) What is the dimensionality (number of independent variables) of the permitted reduced system? (iii) How can one derive the reduced system (algebraic Reynolds stress model) from the full RSCM equations? Our analysis reveals that a lower-dimensional representation of the RSCM equations is possible not only in the equilibrium limit, but also in the slow-manifold stage of non-equilibrium turbulence. The degree of reduction depends on the type of mean-flow deformation and state of turbulence. We further develop two novel methods for deriving algebraic Reynolds stress models from RSCM equations in non-equilibrium turbulence. The present work is expected to play an important role in bringing much of the sophistication of the RSCM into the realm of two-equation algebraic Reynolds stress models. Another objective of this work is to place the other algebraic stress modeling efforts in the lower-dimensional modeling context. Received 19 November 1999 and accepted 3 August 2000     

Magnetic Field Effects on Axis-Switching and Instabilities in Rectangular Plasma Jets

The effect of an external magnetic field on the evolution of rectangular plasma jets is examined. Specifically investigated is the influence of a primarily axial magnetic field on the uniquely characteristic axis-switching phenomenon of rectangular jets and flow instabilities. The results indicate that the magnetic field decelerates the jet (more rapid spreading), prevents axis-switching and inhibits instabilities. The key physical mechanisms underlying the changes are (1) the ability of the magnetic field to reverse the direction of vorticity and (2) transfer of energy from kinetic to magnetic forms. This study has important implications for magneto-hydro-dynamic flow control and propulsion applications.     

Flow-thermodynamics interactions in decaying anisotropic compressible turbulence with imposed temperature fluctuations

The fundamental nature of the non-linear flow-thermodynamics interactions in a compressible turbulent flow with imposed temperature fluctuations is investigated. Direct numerical simulations (DNS) of decaying anisotropic compressible turbulence (turbulent Mach number 0.06–0.6) with imposed temperature fluctuations are performed to examine: (i) interactions between solenoidal and dilatational kinetic energy; (ii) partition between dilatational kinetic energy and thermodynamic potential energy; and (iii) redistribution of solenoidal and dilatational kinetic energy among the various Reynolds stress components. It is found that solenoidal kinetic energy levels and return-to-isotropy are weakly dependent on Mach number but independent of imposed temperature fluctuations in the parameter range studied. The dilatational kinetic energy generated is proportional to the square of the pressure fluctuations associated with the initial solenoidal and temperature fluctuations and thus a strong function of Mach number and heat release intensity. The energy exchange between dilatational kinetic and potential energy is driven by a strong proclivity toward equipartition. Consequently, the dynamics of pressure-dilatation ( ${\overline{pd}}$ ), which is the mechanism of this energy exchange between dilatational and potential energies, is dictated entirely by the requirement to impose energy equipartition. Based on the results, we provide a physical picture of the solenoidal–dilatational–potential energy interactions and the action of pressure-dilatation. The identification of the fundamental precepts underlying the various interactions is of great utility for turbulence closure model development.     

Donor‐Induced Performance Tuning of Amorphous SrTiO3 Memristive Nanodevices: Multistate Resistive Switching and Mechanical Tunability

Metal–oxide valence‐change memristive devices are the key contenders for the development of multilevel nonvolatile analog memories and neuromorphic computing architectures. Reliable low energy performance and tunability of nonlinear resistive switching dynamics are essential to streamline the high‐density circuit level integration of these devices. Here, manipulation of room temperature‐synthesized defect chemistry is employed to enhance and tune the switching characteristics of high‐performance amorphous SrTiO₃ (a‐STO) memristors. Substitutional donor (Nb) doping with low concentrations in the a‐STO oxide structure allows extensive improvements in energy requirements, stability, and controllability of the memristive performance, as well as field‐dependent multistate resistive switching. Evidence is presented that room temperature donor doping results in a modified insulator oxide where dislocation sites act as charge carrier modulators for low energy and multilevel operation. Finally, the performance of donor‐doped a‐STO‐based memristive nanodevices is showcased, with the possibility of mechanical modulation of the nonlinear memristive characteristics of these devices demonstrated. These results highlight the potential of donor‐doped a‐STO nanodevices for high‐density integration as analog memories and multifunctional alternative logic elements.     

Influence of Temperature,Concentration, and Gas/Liquid Ratios on the Gas-Mobility Reduction of Foams in Porous Media

The gas-mobility reduction capability of sodium dodecylbenzene sulfonate foams was studied in sandpacks as a function of temperature at different surfactant concentrations and gas/liquid ratios. Increasing the temperature decreased the gas mobility at a given surfactant concentration and gas/liquid ratio. At any given temperature, the gas-mobility reduction was not increased beyond a certain limit with increasing surfactant concentration. While increasing the gas/liquid ratio improved the gas-mobility reduction at 20°C, at higher temperatures the reduction capability decreased after reaching a maximum at a gas/liquid ratio of 9. All the foams became weak at temperatures of 150°C and higher.