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Register a new userFluctuations and correlations of reactive scalars near chemical equilibrium in incompressible turbulence
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The statistical properties of species undergoing chemical reactions in a turbulent environment are studied. We focus on the case of reversible multi-component reactions of second and higher orders, in a condition close to chemical equilibrium sustained by random large-scale reactant sources, while the turbulent flow is highly developed. In such a state a competition exists between the chemical reaction that tends to dump reactant concentration fluctuations and enhance their correlation intensity and the turbulent mixing that on the contrary increases fluctuations and remove relative correlations. We show that a unique control parameter, the Damkh{o}ler number ($Da_theta$) that can be constructed from the scalar Taylor micro-scale, the reactant diffusivity and the reaction rate characterises the functional dependence of fluctuations and correlations in a variety of conditions, i.e., at changing the reaction order, the Reynolds and the Schmidt numbers. The larger is such a Damkh{o}ler number the more depleted are the scalar fluctuations as compared to the fluctuations of a passive scalar field in the same conditions, and vice-versa the more intense are the correlations. A saturation in this behaviour is observed beyond $Da_theta simeq mathcal{O}(10)$. We provide an analytical prediction for this phenomenon which is in excellent agreement with direct numerical simulation results.
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We use direct numerical simulations to compute turbulent transport coefficients for passive scalars in turbulent rotating flows. Effective diffusion coefficients in the directions parallel and perpendicular to the rotations axis are obtained by studying the diffusion of an imposed initial profile for the passive scalar, and calculated by measuring the scalar average concentration and average spatial flux as a function of time. The Rossby and Schmidt numbers are varied to quantify their effect on the effective diffusion. It is find that rotation reduces scalar diffusivity in the perpendicular direction. The perpendicular diffusion can be estimated from mixing length arguments using the characteristic velocities and lengths perpendicular to the rotation axis. Deviations are observed for small Schmidt numbers, for which turbulent transport decreases and molecular diffusion becomes more significant.
We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions and turbulent transport coefficients of passive scalars in turbulent rotating helical and non-helical flows. We show that helicity affects the inertial range scaling of the velocity and of the passive scalar when rotation is present, with a spectral law consistent with $sim k_{perp}^{-1.4}$ for the passive scalar variance spectrum. This scaling law is consistent with the phenomenological argument presented in cite{imazio2011} for rotating non-helical flows, wich states that if energy follows a $E(k)sim k^{-n}$ law, then the passive scalar variance follows a law $V(k) sim k^{-n_{theta}}$ with $n_{theta}=(5-n)/2$. With the second order scaling exponent obtained from this law, and using the Kraichnan model, we obtain anomalous scaling exponents for the passive scalar that are in good agreement with the numerical results. Intermittency of the passive scalar is found to be stronger than in the non-helical rotating case, a result that is also confirmed by stronger non-Gaussian tails in the probability density functions of field increments. Finally, Ficks law is used to compute the effective diffusion coefficients in the directions parallel and perpendicular to the rotation axis. Calculations indicate that horizontal diffusion decreases in the presence of helicity in rotating flows, while vertical diffusion increases. We use a mean field argument to explain this behavior in terms of the amplitude of velocity field fluctuations.
The character of turbulence depends on where it develops. Turbulence near boundaries, for instance, is different than in a free stream. To elucidate the differences between flows, it is instructive to vary the structure of turbulence systematically, but there are few ways of stirring turbulence that make this possible. In other words, an experiment typically examines either a boundary layer or a free stream, say, and the structure of the turbulence is fixed by the geometry of the experiment. We introduce a new active grid with many more degrees of freedom than previous active grids. The additional degrees of freedom make it possible to control various properties of the turbulence. We show how long-range correlations in the turbulent velocity fluctuations can be shaped by changing the way the active grid moves. Specifically, we show how not only the correlation length but also the detailed shape of the correlation function depends on the correlations imposed in the motions of the grid. Until now, large-scale structure had not been adjustable in experiments. This new capability makes possible new systematic investigations into turbulence dissipation and dispersion, for example, and perhaps in flows that mimic features of boundary layers, free streams, and flows of intermediate character.
We present an investigation of the root-mean-square (rms) temperature $sigma_T$ and the rms velocity $sigma_w$ in the bulk of Rayleigh-Benard turbulence, using new experimental data from the current study and experimental and numerical data from previous studies. We find that, once scaled by the convective temperature $theta_*$, the value of $sigma_T$ at the cell centre is a constant, i.e. $sigma_{T,c}/theta_* approx 0.85$, over a wide range of the Rayleigh number ($10^{8}leq Raleq 10^{15}$) and the Prandtl number ($0.7leq Pr leq 23.34$), and is independent of the surface topographies of the top and bottom plates of the convection cell. A constant close to unity suggests that $theta_*$ is a proper measure of the temperature fluctuation in the core region. On the other hand, $sigma_{w,c}/w_*$, the vertical rms velocity at the cell centre scaled by the convective velocity $w_*$, shows a weak $Ra$-dependence ($sim Ra^{0.07pm0.02}$) over $10^8leq Raleq 10^{10}$ at $Prsim4.3$ and is independent of plate topography. Similar to a previous finding by He & Xia ({it Phys. Rev. Lett.,} vol. 122, 2019, 014503), we find that the rms temperature profile $sigma_T(z)/theta_*$ in the region of the mixing zone with a mean horizontal shear exhibits a power-law dependence on the distance $z$ from the plate, but now the universal profile applies to both smooth and rough surface topographies and over a wider range of $Ra$. The vertical rms velocity profile $sigma_w(z)/w_*$ obey a logarithmic dependence on $z$. The study thus demonstrates that the typical scales for the temperature and the velocity are the convective temperature $theta_*$ and the the convective velocity $w_*$, respectively. Finally, we note that $theta_*$ may be utilised to study the flow regime transitions in the ultra-high-$Ra$-number turbulent convection.
For several flows of laboratory turbulence, we obtain long records of velocity data. These records are divided into numerous segments. In each segment, we calculate the mean rate of energy dissipation, the mean energy at each scale, and the mean total energy. Their values fluctuate significantly among the segments. The fluctuations are lognormal, if the segment length lies within the range of large scales where the velocity correlations are weak but not yet absent. Since the lognormality is observed regardless of the Reynolds number and the configuration for turbulence production, it is expected to be universal. The likely origin is some multiplicative stochastic process related to interactions among scales through the energy transfer.
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