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Register a new userEffective diffusivity of passive scalars in rotating turbulence
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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.
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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 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.
This article reviews recent studies of scale interactions in magnetohydrodynamic turbulence. The present day increase of computing power, which allows for the exploration of different configurations of turbulence in conducting flows, and the development of shell-to-shell transfer functions, has led to detailed studies of interactions between the velocity and the magnetic field and between scales. In particular, processes such as induction and dynamo action, the damping of velocity fluctuations by the Lorentz force, or the development of anisotropies, can be characterized at different scales. In this context we consider three different configurations often studied in the literature: mechanically forced turbulence, freely decaying turbulence, and turbulence in the presence of a uniform magnetic field. Each configuration is of interest for different geophysical and astrophysical applications. Local and non-local transfers are discussed for each case. While the transfer between scales of solely kinetic or solely magnetic energy is local, transfers between kinetic and magnetic fields are observed to be local or non-local depending on the configuration. Scale interactions in the cascade of magnetic helicity are also reviewed. Based on the results, the validity of several usual assumptions in hydrodynamic turbulence, such as isotropy of the small scales or universality, is discussed.
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