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Register a new userSymmetry and Scaling of Turbulent Mixing
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The stationary condition (Hopf equation) for the ($n$+1) point correlation function of a passive scalar advected by turbulent flow is argued to have an approximate $SL(n, R)$ symmetry which provides a starting point for the perturbative treatment of less symmetric terms. The large scale anisotropy is found to be a relevant field, in contradiction with Kolmogorov phenomenology, but in agreement with the large scalar skewness observed in shear flows. Exponents are not universal, yet quantitative predictions for experiments to test the $SL(n, R)$ symmetry can be formulated in terms of the correlation functions.
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Radiative turbulent mixing layers should be ubiquitous in multi-phase gas with shear flow. They are a potentially attractive explanation for the high ions such as OVI seen in high velocity clouds and the circumgalactic medium (CGM) of galaxies. We perform 3D MHD simulations with non-equilibrium (NEI) and photoionization modeling, with an eye towards testing simple analytic models. Even purely hydrodynamic collisional ionization equilibrium (CIE) calculations have column densities much lower than observations. Characteristic inflow and turbulent velocities are much less than the shear velocity, and the layer width $h propto t_mathrm{cool}^{1/2}$ rather than $h propto t_mathrm{cool}$. Column densities are not independent of density or metallicity as analytic scalings predict, and show surprisingly weak dependence on shear velocity and density contrast. Radiative cooling, rather than Kelvin-Helmholtz instability, appears paramount in determining the saturated state. Low pressure due to fast cooling both seeds turbulence and sets the entrainment rate of hot gas, whose enthalpy flux, along with turbulent dissipation, energizes the layer. Regardless of initial geometry, magnetic fields are amplified and stabilize the mixing layer via magnetic tension, producing almost laminar flow and depressing column densities. NEI effects can boost column densities by factors of a few. Suppression of cooling by NEI or photoionization can in principle also increase OVI column densities, but in practice is unimportant for CGM conditions. To explain observations, sightlines must pierce hundreds or thousands of mixing layers, which may be plausible if the CGM exists as a `fog of tiny cloudlets.
We discuss our recently proposed S3(down)xS3(up) flavour-permutation-symmetric mixing observables, giving expressions for them in terms of (moduli-squared) of the mixing matrix elements. We outline their successful use in providing flavour-symmetric descriptions of (non-flavour-symmetric) lepton mixing schemes. We develop our partially unified flavour-symmetric description of both quark and lepton mixings, providing testable predictions for CP-violating phases in both B decays and neutrino oscillations.
Turbulent vertical transport driven by double-diffusive shear instabilities is identified as likely important in hot exoplanet atmospheres. In hot Jupiter atmospheres, the resulting vertical mixing appears sufficient to alleviate the nightside cold trap, thus facilitating the maintenance of nocturnal clouds on these planets. The strong level of vertical mixing expected near hot Jupiter thermal photospheres will impact their atmospheric chemistry and even their vertical structures where cloud radiative feedback proves important.
We present models of turbulent mixing at the boundaries between hot (T~10^{6-7} K) and warm material (T~10^4 K) in the interstellar medium, using a three-dimensional magnetohydrodynamical code, with radiative cooling. The source of turbulence in our simulations is a Kelvin-Helmholtz instability, produced by shear between the two media. We found, that because the growth rate of the large scale modes in the instability is rather slow, it takes a significant amount of time (~1 Myr) for turbulence to produce effective mixing. We find that the total column densities of the highly ionized species (C IV, N V, and O VI) per interface (assuming ionization equilibrium) are similar to previous steady-state non-equilibrium ionization models, but grow slowly from log N ~10^{11} to a few 10^{12} cm^{-2} as the interface evolves. However, the column density ratios can differ significantly from previous estimates, with an order of magnitude variation in N(C IV)/N(O VI) as the mixing develops.
We present a new physically-motivated parameterization, based on the ratio of Thorpe and Ozmidov scales, for the irreversible turbulent flux coefficient $Gamma_{mathcal M}= {mathcal M}/epsilon$, i.e. the ratio of the irreversible rate ${mathcal M}$ at which the background potential energy increases in a stratified flow due to macroscopic motions to the dissipation rate of turbulent kinetic energy. Our parameterization covers all three key phases (crucially, in time) of a shear-induced stratified turbulence life cycle: the initial, `hot growing phase, the intermediate energetically forced phase, and the final `cold fossilization decaying phase. Covering all three phases allows us to highlight the importance of the intermediate one, to which we refer as the `Goldilocks phase due to its apparently optimal (and so neither too hot nor too cold, but just right) balance, in which energy transfer from background shear to the turbulent mixing is most efficient. $Gamma_{mathcal M}$ is close to 1/3 during this phase, which we demonstrate appears to be related to an adjustment towards a critical or marginal Richardson number for sustained turbulence $sim 0.2-0.25$.
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