Deflection, drift and advective growth in variable-density, laminar mixing layers

Specific features of the variable-density mixing layers without gravity effects are studied using self-similar solutions to the laminar and time-evolving variant of this flow. Density variations come from either mass or temperature mixing, accounting for, in the latter case, the effect of the Mach number. The transverse profiles of the flow quantities, as well as the time evolutions of the global characteristic scales of the mixing layer, are given for a wide range of density ratio and Mach-number values. When compared to the constant-density case, it appears that most of the specificity of these flows comes from the emergence of a nonzero transverse component of the velocity. First, it produces a deflection of the flow that can be either confined in the core of the layer or global, the whole layer being tilted at an angle from the initial flow direction. In most cases, this deflection is such that some part of the higher-density fluid is "entrained" in the direction of the lower-density fluid, leaving no possibility to define a dividing streamline. Second, it leads to a shift between the density profile and the profiles of the other flow quantities. This shift scales on the time-increasing mixing-layer thickness and therefore appears as a time drift. When global deflection is present, the tilting of the layer can be shown to be equivalent to a global drift of the mixing/shear layer toward the light-fluid side of the flow. Third, transport by the transverse velocity component affects the spreading of the mixing layer, giving rise to an additional effect referred to as advective growth. Examination of the density-ratio and Mach-number effects leads to surprising results: While the momentum thickness is always observed to decrease when increasing these parameters, conventional thicknesses based on the profiles of the different variables can show opposite behaviors depending on the form of the diffusion model for the considered variable

The merger of two-dimensional radially stratified high-Froude-number vortices

We investigate the influence of density inhomogeneities on the merger of two corotating two-dimensional vortices at infinite Froude number. In this situation, buoyancy effects are negligible, yet density variations still affect the flow by pure inertial effects through the baroclinic torque. We first re-address the effects of a finite Reynolds number on the interaction between two identical Gaussian vortices. Then, by means of direct numerical simulations, we show that vortices transporting light fluid in a heavier counterpart merge from further distances than vortices in a uniform density medium. On the other hand, heavy vortices only merge from small separation distances. We measure the critical distance a/b0 of the vortex radii to their initial separation distance. It departs from the homogeneous threshold of 0.22 in response to increasing density contrasts between the vortices and their surroundings. An analysis of the contribution of the baroclinic vorticity to the dynamics of the flow is detailed and explains the observed behaviour. This analysis is completed by a simple model based on point vortices that mimics the flow. It is concluded that vortices carrying light fluid are more likely to generate large-scale structures than heavy ones in an inhomogeneous fluid

Direct numerical simulation of inertia-sensitive turbulence

Direct numerical simulations were performed of the turbulent mixing of a contrasted density field by a statistically homogeneous velocity field. The density ratio between the two initially unmixed fluids is 3, thus well beyond the passive-scalar situation. This low Mach number variable density turbulence is relevant to very large Froude-number turbulent mixing processes. In this paper the flow configuration is a forced homogeneous turbulence mixing an initially sharp density-gradient layer. Depending on the characteristic length scales of the velocity and density fields, the order of magnitude of the vortex-stretching and baroclinic enstrophy sources is compared. In the situation where turbulence is inertia affected and where strong baroclinic events are encountered, the deviations from the passive-scalar case are analysed both from the spectral and the statistical points of view

termodinamička jednakovaljanost Lennard-Jonesovog sustava i privlačnog Yukawinog sustava s tvrdom sredicom

Thermodynamic properties of the Lennard-Jones (LJ) fluid are investigated by studying a system of particles interacting with a potential of hard-core plus attractive Yukawa tail (HCY). Due to the similarity of the LJ and the HCY potentials in their overall form, it is worthwhile seeking to approximate the LJ potential in much the same way that the hard-sphere reference potential has been used. The study consists in describing the thermodynamics of the LJ fluid in terms of the equivalent HCY system, whose properties are known accurately, by means of mapping the thermodynamic quantities for the HCY potential parameters. The method is feasible owing to a convenient analytical expression for the Helmholtz free energy in the mean-spherical approximation expanded in powers of the inverse temperature. Two different procedures are used to determine the parameters of the HCY potential as a function of the thermodynamic states: one is based on the simultaneous fits of pressure and internal energy of the LJ system, and the other uses the concept of collision frequency. The reasonable homogeneity of the results in both procedures of mapping makes the HCY potential a very good reference system whose theoretical expressions can be used confidently to predict the thermodynamic properties of systems with more realistic potentialsIstražujemo termodinamička svojstva Lennard-Jonesove (LJ) tekućine proučavanjem sustava čestica koje međudjeluju potencijalom tvrda sredica i privlačan Yukawin rep (HCY). Zbog sličnosti LJ i HCY oblika potencijala, vrijedi tražiti približenje LJ potencijalu kao što se rabi referentni potencijal tvrdih kuglica. U ovom proučavanju opisujemo termodinamiku LJ tekućine pomoću jednakovaljanog HCY sustava čija su svojstva točno poznata računanjem termodinamičkih veličina za parametre HCY potencijala. Ta je metoda izvediva zbog pogodnog izraza za Helmholtzovu slobodnu energiju u prosječno-sfernom približenju, razvijenu po potencijama recipročne temperature. Rabe se dva postupka za određivanje parametara HCY potencijala kao funkcije termodinamičkog stanja: jedan se zasniva na istovremenoj prilagodbi tlaka i unutarnje energije LJ sustava, a drugi rabi zamisao sudarne frekvencije. Dobra jednolikost ishoda oba postupka snimanja čini HCY potencijal vrlo dobrim referentnim sustavom čiji se teorijski izrazi mogu s pouzdanošću rabiti za predviđanje termodinamičkih svojstava sustava sa stvarnim potencijalima

Resistivity in warm dense plasmas beyond the average-atom model

The exploration of atomic properties of strongly coupled partially degenerate plasmas, also referred to as warm dense matter, is important in astrophysics, since this thermodynamic regime is encountered for instance in Jovian planets' interior. One of the most important issues is the need for accurate equations of state and transport coefficients. The Ziman formula has been widely used for the computation of the static (DC) electrical resistivity. Usually, the calculations are based on the continuum wavefunctions computed in the temperature and density-dependent self-consistent potential of a fictive atom, representing the average ionization state of the plasma (average-atom model). We present calculations of the electrical resistivity of a plasma based on the superconfiguration (SC) formalism. In this modeling, the contributions of all the electronic configurations are taken into account. It is possible to obtain all the situations between the two limiting cases: detailed configurations (a super-orbital is a single orbital) and detailed ions (all orbitals are gathered in the same super-orbital). The ingredients necessary for the calculation are computed in a self-consistent manner for each SC, using a density-functional description of the electrons. Electron exchange-correlation is handled in the local-density approximation. The momentum transfer cross-sections are calculated by using the phase shifts of the continuum electron wavefunctions computed, in the potential of each SC, by the Schroedinger equation with relativistic corrections (Pauli approximation). Comparisons with experimental data are also presented.Comment: submitted to "Contributions to Plasma Physics

Baroclinic instabilities

1. Introduction - Illustrative examples from experiments and simulations 2. The baroclinic torque in high Froude number flows, its organization, scale and order of magnitude 3. Stability of the inhomogeneous mixing-layer 4. Transition of the inhomogeneous mixing-layer and the 2D secondary baroclinic instability 5. The strain field of 2D light jets 6. Transition to three-dimensionality in light jets and the question of side-jets 7. Baroclinic instability of heavy vortices and some elements on vortex interaction in inhomogeneous 2D turbulenc

Vortex dynamics in high Froude number variable-density flows

Outline of the presentation : 1.Introduction - Illustrative examples from experiments and simulations 2.The baroclinic torque in high Froude number flows, its organization, scale and order of magnitude 3.Transition of the inhomogeneous mixing--layer and the 2D secondary baroclinici instability 4.The strain field of 2D light jets and the question of side-jets 5.Mass segregation in 2D turbulence and the baroclinic instability of massive of vortice