On the mixing models for stratified flows subjected to concomitant stable and unstable stratifications

The concurrence of stable and unstable stratification in stratified flows leads to dramatically different features of turbulent mixing. This unique flow is experimentally studied by introducing a horizontal jet of dense fluid into a pool of light fluid. The buoyancy flux from simultaneous velocity–density measurements is an indicator for competition between a stabilising mechanism and another destabilising mechanism. The difference of mixing efficiency, quantified by flux Richardson number Ri_f, between the (un)stable stratification is mainly contributed by the large-scale mixing. The behaviour of Ri_f can be modelled by the gradient Richardson number Ri_g linearly in the low-Ri case and nonlinearly in the high-Ri case (especially in a region where the counter-gradient flux emerges). The turbulent diapycnal diffusivity, quantifying the combined effect of reversible and irreversible mixing processes, increases as the buoyancy Reynolds number Re_b increases only when Re_b is large. The irreversible mixing diffusivity, which quantifies the sole irreversible mixing process, increases linearly as the turbulent Péclet number with the data points from the (un)stable stratification overlapped. The turbulent Prandtl number approaches 0.75 as Ri_g approaches zero, but does not show clear dependence on Ri_g in the examined regime.     

Large eddy simulation of turbulent horizontal buoyant jets

Large eddy simulations (LESs) of turbulent horizontal buoyant jets are carried out using a high-order numerical method and Sigma subgrid-scale (SGS) eddy-viscosity model, for a number of different Reynolds (Re) and Richardson (Ri) numbers. Simulations at previous experimental flow conditions (Re = 3200, 24, 000 and Ri = 0, 0.01) are carried out first, and the results are found to be qualitatively and quantitatively similar to the experimental results, thus validating the numerical methodology. The effect of varying Ri (values 2×10^?4, 0.001, 0.005, and 0.01) and Re (3200 and 24, 000) is studied next. The presence of stable stratification on one side and unstable stratification on the other side of the jet centreline leads to an asymmetric development of horizontal buoyant jets. It is found that this asymmetry, the total radial spread and the vertical deflection are significantly affected by Ri, while Re affects only the radial asymmetry. The need for developing improved integral models, accounting for this asymmetry, is pointed out. Turbulent production and dissipation rates are investigated, and are found to be symmetric in the horizontal plane, but asymmetric in the mid-vertical plane. A previously proposed model, for correlation between the vertical component of the fluctuating scalar flux vector and the vertical cross-correlation component of the Reynolds tensor, is modified based on the current LES results. Instantaneous scalar and velocity fields are analysed to reveal the structure of horizontal buoyant jets. Similar to the developed turbulent jet, the flow close to the nozzle too is found to be markedly different in the stable and unstable stratification regions. Persistent coherent vortex rings are found in the stable stratification region, while intermittent breakdown of vortex rings into small-scale structures is observed in the unstable stratification region. Similarities and differences between the flow structures in the horizontal buoyant jet configuration and those in the jet in crossflow configuration are discussed. Finally, a dynamic mode decomposition analysis is carried out, which indicates that the flow in the unstable stratification region is more energetic and prone to instabilities, as compared to the flow in the stable stratification region.     

Subgrid-scale dynamics and model test in a turbulent stratified jet with coexistence of stable and unstable stratification

The subgrid-scale dynamics of stratified flows is studied in a horizontally introduced turbulent jet with coexistence of stable and unstable stratification of a low Richardson number case and a high Richardson number case. The positive production of subgrid-scale kinetic energy and the production of scalar variance suggest the forward energy cascade. The subgrid-scale buoyant destruction plays a role as a sink of subgrid-scale kinetic energy in the stable stratification while holds a role of turbulent generation in the unstable stratification. The role-switch of buoyant destruction in the stable stratification of high-Ri case implies the occurrence of a destabilising process triggered by the coupled instability mechanisms. The energy balance assumption related to the production of and the dissipation of subgrid-scale kinetic energy as well as the subgrid-scale buoyant destruction may fail. The a-priori test suggests the scale-invariant dynamic and standard Smagorinsky models not to work properly here, while the scale-dependent dynamic model gives a decent performance but with restrictions of the ratio between two testing filter scales.     

On the relationship between the gradient and the bulk Richardson number for the atmospheric surface layer

Summary Semi-empirical formulations which have been proposed to describe the wind and potential temperature profiles are used to derive relationships between the gradient Richardson number, Ri, the finite-difference layer Richardson number, Ri_b, the surface layer Richardson number, Ri_s, and the bulk Richardson number,B, through the atmospheric surface layer. The theoretical analysis for stable conditions indicates that Ri (z ₃)=Ri_b, wherez ₃=(z ₂−z ₁)/ln(z ₂/z ₁), andz ₂;z ₁=upper and lower levels at which temperature and wind speed are specified. It is also found that, during stable conditions, the wind profile power law exponent,p, is computed at the heightz ₃, instead of the widely used geometric mean height,z _m, between top (z ₂) and bottom (z ₁) of the layer considered.     

Stability of magnetohydrodynamic stratified shear flows

Summary The linear stability of a stratified shear flow of a perfectly conducting bounded fluid in the presence of a magnetic field aligned with the flow and buoyancy forces has been studied under Boussinesq approximation. A new upper bound has been obtained for the range of real and imaginary parts of the complex wave velocity for growing perturbations. The upper bound depends on minimum Richardson number, wave number, Alfvén velocity and basic flow velocity. H?iland's necessary criterion for instability of hydrodynamic stratified homogeneous shear flow is modified and its analog for nonhomogeneous magnetohydrodynamic cases is derived. Finally the upper bound for the growth rate ofKC _i and its variants, whereK is the wave number andC _i the imaginary part of complex wave velocity, is derived as the necessary condition of instability. All estimates remain valid even when the minimum richardson numberJ ₁, for some practical problems, exceeds 1/4 for growing perturbations. The authors of this paper have agreed to not receive the proofs for correction.     

Temperatures in 3D optical lattices influenced by neighbouring transitions

A detailed experimental study of the steady-state temperature in a 3D optical lattice for cesium has been performed for a wide range of detunings. Specifically, we have investigated the situation with the cooling and trapping light detuned far red of a ( J _g↦J _e = J _g + 1)-transition, where the blue detuned interaction with a ( J _g↦J _e = J _g)-transition can not be neglected. We find that the temperature scales with the optical potential due to the interaction with just the ( J _g↦J _e = J _g + 1)-transition. This indicates that blue Sisyphus cooling has essentially no effect on the dynamics of the system, when there exists a neighbouring red detuned transition. Received 6 June 2000 and Received in final form 26 September 2000     

Numerical study of mixed convection flow in a lid-driven cavity with sinusoidal heating on sidewalls using nanofluid

Mixed convection flow of Cu–water nanofluid inside a lid-driven square cavity with adiabatic horizontal walls and sinusoidal heating on sidewalls has been investigated numerically. The effects of increase in shear force for a fixed buoyancy force and effects of increase in buoyancy force for a fixed shear force were investigated. Effects of variations of Richardson number, phase deviation of sinusoidal heating, and volume fraction of nanoparticles on flow and temperature field were studied. The obtained results showed that for a constant Grashof number at all Richardson numbers, a clockwise eddy was developed inside the cavity, also the rate of heat transfer increases with decrease in Richardson number and increase of volume fraction of nanoparticles. For a constant Reynolds number the clockwise eddy is observed up to Ri = 1. For Ri = 10 a multicellular flow pattern is formed inside the cavity. Moreover it was found that when the Reynolds number is kept constant, the rate of heat transfer increases with increase in Richardson number.     

On the theoretical relationship between the Monin-Obukhov stability parameter and the bulk Richardson number

Summary Nomograms were constructed to determine relations among different stability parameters in the surface layer. The variables interrelated were the Monin-Obukhov stability parameter, ξ=z/L, the bulk Richardson number, Ri_b, and the PasquillA-F stability classes. Also, the nomograms were used to estimate the Monin-Obukhov length variation, with respect to changes in surface roughness and atmospheric stability.     

隐埋“月牙”形InGaAsP/InP激光器动态特性研究

本文用计算机模拟方法分析了隐埋“月牙”形InGaAsP/InP激光器的动态特性,得到阈值电流,单模截止条件与有源区厚度(中心)d₀、沟宽W、条宽s、腔长L和材料的电阻率R_x等结构参数间的关系。在模拟分析的基础上,提供了阈值电流与结构参数间的近似表示式,从中能简捷地估算激光器的物理特性。文内还提出了注入载流子浓度高斯分布模型,应用这模型,可准确地计算电流扩展和增益分布,且导出了最大增益g_max,阈值电流密度J_th,模增益G_th,最佳有源区(中心)厚度d_0,min,最佳阈值电流密度J_th,min等一系列解析式。基于上述分析,该激光器最佳设计参数为d₀=0.15—0.2μm,W=2—4μm,s=10—15μm,L=200μm。 关键词：     

Two-color three-photon resonant excitation spectrum of strontium in the autoionization region

We report new studies of the odd parity autoionizing Rydberg series of strontium attached to the 4d( ² D _{3/2, 5/2}) ionic limits possessing J = 1-3 based on the two-color three photon resonant excitation technique in conjunction with an atomic beam apparatus. Using the 4d ²³ P ₀ intermediate levels, we have been able to record the autoionizing Rydberg series of J = 1 whereas, from the 4d ²³ P ₂ intermediate level the series of Rydberg levels possessing J = 1, 2 and 3 have been observed. The level assignments and the line shapes simulations of the autoionizing resonances have been made using the multichannel quantum defect theory. Received 21 November 2001 / Received in final form 2 May 2002 Published online 19 July 2002     

Structure of high spin states of76Kr and78Kr nuclei

Following a fully self-consistent cranked Hartree-Fock-Bogoliubov (CHFB) approach with a pairing+quadrupole+hexadecapole model interaction Hamiltonian the structure of the yrast states of^76,78Kr nuclei is studied up to angular momentumJ = 24. Evolution of the shape with spin, and rotation alignment of proton as well as neutron 0g_9/2 orbitals is investigated along with the inter and intra-nucleus variations of theg factors as a function ofJ. We find that the shape of⁷⁸Kr remains prolate all through up toJ = 24, whereas⁷⁶Kr becomes triaxial beyondJ = 12     

Theoretical studies on dielectronic recombination of neonlike gold and its effects on plasma ionization balance and radiation energy

The dielectronic recombination (DR) of neonlike gold ions is investigated employing the flexible atomic code based on the relativistic configuration interaction method, and its influence on the ionization balance and radiation energy in high-temperature plasma is also studied. The total resonance strength for LMM configuration complex is in a good agreement with the experimental measurement and other theoretical works. The DR rate coefficients are calculated and compared with the three-body recombination and radiative recombination rate coefficients. The DR process is the dominant recombination mechanism of Ne-like gold ions for plasma with temperature T_e≥6.5 keV and density n_e≤2×10²² cm^-3, which is close to the condition of X-ray conversion region in the inertial confinement fusion. Moreover, the DR satellite spectra of LMM, LMN and LMO resonances are simulated, and compared with the intensities of the corresponding resonance lines induced by the electron impact excitation. The intensity ratio of the satellite line 3D’ [(2p⁵_3/23d_3/23d_5/2)_J=5/2[(2p^{5}_{3/2}3d_{3/2}3d_{5/2})_{J=5/2}–(2p⁶3d_3/2) _J=3/2](2p^{6}3d_{3/2})_{ J=3/2}] and the resonance line 3D [(2p⁵_3/23d_5/2)_J=1[(2p^{5}_{3/2}3d_{5/2})_{J=1}–(2p⁶)_J=0](2p^{6})_{J=0}] is given, which can be applied for diagnostics of plasma temperature.     

Proton hyperfine interactions in the gas-phase E.P.R. spectra of SH (2Π3/2) in two lowest rotational levels

Gas-phase E.P.R. spectra of the SH radical (²Π_3/2) in the J = 5/2 and J = 3/2 rotational levels are described. Analysis of the hyperfine splittings gives the values of axial and non-axial components of the proton hyperfine interaction and the value of the constant d. The frequencies of the two strong lines in the zero-field spectrum are estimated by the use of the observed value of the hyperfine interaction constant d.     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998     

Sub-doppler laser cooling of thulium atoms in a magneto-optical trap

Sub-Doppler laser cooling in a magneto-optical trap for thulium atoms at a wavelength of 410.6 nm has been experimentally studied. Without any dedicated molasses period of sub-Doppler cooling, the cloud of 3 × 10⁶ atoms at a temperature of 25(5) μK was observed. The measured temperature is significantly lower than the Doppler limit of 240 μK for the cooling transition at 410.6 nm. The high efficiency of the sub-Doppler cooling process is due to a near-degeneracy of the Landé g-factors of the lower 4f ¹³6s ² (J = 7/2) and the upper 4f ¹²5d _3/26s ² (J = 9/2) cooling levels.     

Binary hard-sphere solute-solvent radial distribution function in the colloidal limit: exact calculation from an equation of state

An exact formula is derived relating the contact value of the solute-solvent radial distribution function for an additive binary hard-sphere (HS) mixture at infinite dilution, g ^∞ ₁₂(d ₁₂), to the mixture equation of state (EOS) (1 denotes the solvent and 2 denotes the solute). This result can also be considered to be a consistency condition involving approximations for g ^∞ ₁₂(d ₁₂) and for the mixture EOS. Employing three approximate HS mixture equations of state from the literature, we use our formula to derive corresponding analytical approximations for g ^∞ ₁₂(d ₁₂) In addition, new computer simulations were performed to obtain accurate results for g ^∞ ₁₂(d ₁₂) and for g ^∞ ₁₂(r ₁₂) at the solute-solvent diameter ratios {1, 3, 5, 7, 10, 20} and the reduced solvent density ρ? = 0.8. We compare our results for g ^∞ ₁₂(d ₁₂) with the simulation results and with the results of approximate analytical expressions for g ^∞ ₁₂(d ₁₂) proposed by several workers. The results obtained from our formula in conjunction with two of the EOS expressions considered are more accurate than all previously proposed approximations, with the exception of the approximation of Matyushov and Ladanyi [1997, J. chem. Phys., 107, 5815], which is of comparable accuracy.     

Centrality, Rapidity, and Transverse-Momentum Dependence of Gluon Shadowing and Antishadowing on J/ψ Production in dAu Collisions at {\sqrt{s} = 200} GeV

We have carried out a wide study of shadowing and antishadowing effects on J/ψ production in dAu collisions at ${\sqrt{s_{N N}} = 200}$ GeV. We have studied the effects of three different gluon nPDF sets, using the exact kinematics for a 2 → 2 process, namely g +?g → J/ψ?+?g as expected from LO pQCD. We have computed the rapidity dependence of R _CP and R _dAu for the different centrality classes of the PHENIX data. For mid rapidities, we have also computed the transverse-momentum dependence of the nuclear modification factor, which cannot be predicted with the usual 2 → 1 simplified kinematics. All these observables have been compared to the PHENIX data in dAu collisions.     

Experimentelle untersuchung der 5d6s6pz 2 F 5/2,7/2-Terme im Lanthan I-Spektrum unter Verwendung von Levelcrossing-Spektroskopie

The hyperfinestructure-interaction-constantsA/g _J andB/g _J of the 5d 6s6p z ² F _5/2,7/2 terms in the La I-spectrum were measured by levelcrossing technique. Using a La-atomic beam many levelcrossings between magnetic sublevels with ¦Δm¦=2 were detected in both terms by resonance scattering. Values for the lifetime of each state were deduced from the widths of Hanle-effect- and levelcrossing-signals.     

Molecular magnetism of a linear Fe(III)-Mn(II)-Fe(III) complex. Influence of long-range exchange interaction

The magnetic properties of [L-Fe(III)-dmg₃Mn(II)-Fe(III)-L] (ClO₄)₂ have been characterized by magnetic susceptibility, EPR, and Mössbauer studies. L represents 1,4,7-trimethyl-, 1,4,7-triazacyclononane and dmg represents dimethylglyoxime. X-ray diffraction measurements yield that the arrangement of the three metal centers is strictly linear with atomic distancesd _Fe-Mn=0.35 nm andd _Fe-Fe=0.7 nm. Magnetic susceptibility measurements (3–295 K) were analyzed in the framework of the spin-Hamiltonian formalism considering Heisenberg exchange and Zeeman interaction:=J _Fe-Mn(S _Fe1+S _Fe2)S _Mn +J _Fe-Fe(S _Fe1 S _Fe2) +g_B S _total B. The spinsS _Fe1=S _Fe2 =S _Mn=5/2 of the complex are antiferromagnetically coupled, yielding a total spin ofS _total=5/2 with exchange coupling constantsF _Fe-Mn=13.4 cm^–1 andJ _Fe-Fe= 4.5 cm^–1. Magnetically split Mössbauer spectra were recorded at 1.5 K under various applied fields (20 mT, 170 mT, 4T). The spin-Hamiltonian analysis of these spectra yields isotropic magnetic hyperfine coupling withA _total/(g _{N N})=–18.5 T. The corresponding local componentA _Fe is related toA _total via spin-projection:A _total=(6/7)A_Fe. The resultingA _Fe/(g _NN)=–21.6 T is in agreement with standard values of ferric high-spin complexes. Spin-Hamiltonian parameters as obtained from Mössbauer studies and exchange coupling constants as derived from susceptibility measurements are corroborated by temperature-dependent EPR studies.     

Effective interactions and superconductivity in the t-J model in the large-N limit

The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations of the point group C_4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature T_c is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. T_c increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. T_c is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of T_c is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively. Received: 16 June 1998 / Accepted: 14 July 1998