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Register a new userShear Effects in Non-Homogeneous Turbulence
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Motivated by recent experimental and numerical results, a simple unifying picture of intermittency in turbulent shear flows is suggested. Integral Structure Functions (ISF), taking into account explicitly the shear intensity, are introduced on phenomenological grounds. ISF can exhibit a universal scaling behavior, independent of the shear intensity. This picture is in satisfactory agreement with both experimental and numerical data. Possible extension to convective turbulence and implication on closure conditions for Large-Eddy Simulation of non-homogeneous flows are briefly discussed.
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In this paper we discuss the dynamical features of intermittent fluctuations in homogeneous shear flow turbulence. In this flow the energy cascade is strongly modified by the production of turbulent kinetic energy related to the presence of vortical structures induced by the shear. By using direct numerical simulations, we show that the refined Kolmogorov similarity is broken and a new form of similarity is observed, in agreement to previous results obtained in turbulent boundary layers. As a consequence, the intermittency of velocity fluctuations increases with respect to homogeneous and isotropic turbulence. We find here that the statistical properties of the energy dissipation are practically unchanged with respect to homogeneous isotropic conditions, while the increased intermittency is entirely captured in terms of the new similarity law.
Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The simulation results reveal that there is a clear inverse energy cascade to the large scales, as predicted by 2D Navier-Stokes equations for resonant interactions of slow modes. As the rotation rate increases, the vertically-averaged horizontal velocity field from 3D Navier-Stokes converges to the velocity field from 2D Navier-Stokes, as measured by the energy in their difference field. Likewise, the vertically-averaged vertical velocity from 3D Navier-Stokes converges to a solution of the 2D passive scalar equation. The energy flux directly into small wave numbers in the $k_z=0$ plane from non-resonant interactions decreases, while fast-mode energy concentrates closer to that plane. The simulations are consistent with an increasingly dominant role of resonant triads for more rapid rotation.
Recently, clustering of inertial particles in turbulence has been thoroughly analyzed for statistically homogeneous isotropic flows. Phenomenologically, spatial homogeneity of particles configurations is broken by the advection of a range of eddies determined by the Stokes relaxation time of the particles which results in a multi-scale distribution of local concentrations and voids. Much less is known concerning anisotropic flows. Here, by addressing direct numerical simulations (DNS) of a statistically steady particle-laden homogeneous shear flow, we provide evidence that the mean shear preferentially orients particle patterns. By imprinting anisotropy on large scales velocity fluctuations, the shear indirectly affects the geometry of the clusters. Quantitative evaluation is provided by a purposely designed tool, the angular distribution function of particle pairs (ADF), which allows to address the anisotropy content of particles aggregates on a scale by scale basis. The data provide evidence that, depending on the Stokes relaxation time of the particles, anisotropic clustering may occur even in the range of scales where the carrier phase velocity field is already recovering isotropy. The strength of the singularity in the anisotropic component of the ADF quantifies the level of fine scale anisotropy, which may even reach values of more than 30% direction-dependent variation in the probability to find two close-by particles at viscous scale separation.
Using different analytical methods (the quasi-linear approach, the path-integral technique and tau-relaxation approximation) we develop a comprehensive mean-field theory for a pumping effect of the mean magnetic field in homogeneous non-rotating helical turbulence with imposed large-scale shear. The effective pumping velocity is proportional to the product of alpha effect and large-scale vorticity associated with the shear, and causes a separation of the toroidal and poloidal components of the mean magnetic field along the direction of the mean vorticity. We also perform direct numerical simulations of sheared turbulence in different ranges of hydrodynamic and magnetic Reynolds numbers and use a kinematic test-field method to determine the effective pumping velocity. The results of the numerical simulations are in agreement with the theoretical predictions.
The turbulent energy cascade in dilute polymers solution is addressed here by considering a direct numerical simulation of homogeneous isotropic turbulence of a FENE-P fluid in a triply periodic box. On the basis of the DNS data, a scale by scale analysis is provided by using the proper extension to visco-elastic fluids of the Karman-Howarth equation for the velocity. For the microstructure, an equation, analogous to the Yaglom equation for scalars, is proposed for the free-energy density associated to the elastic behavior of the material. Two mechanisms of energy removal from the scale of the forcing are identified, namely the classical non-linear transfer term of the standard Navier-Stokes equations and the coupling between macroscopic velocity and microstructure. The latter, on average, drains kinetic energy to feed the dynamics of the microstructure. The cross-over scale between the two corresponding energy fluxes is identified, with the flux associated with the microstructure dominating at small separations to become sub-leading above the cross-over scale, which is the equivalent of the elastic limit scale defined by De Gennes-Tabor on the basis of phenomenological assumptions.
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