Multiscale three-point velocity increment correlation in turbulent flows

The three-point velocity increment correlation function is proposed to represent the multiscale correlations in turbulent flows. The inertial–inertial correlation and the inertial–dissipative correlation are discussed due to their endogenetic properties in turbulence and their roles in large-eddy simulation. The zero-correlation points are then emphasized as equilibrium points between them. The credibility of this theoretical result is numerically verified in both isotropic and anisotropic flows. Results imply the universality of this zero-correlation scaling in different turbulent flows. This work is expected to be a dependable theoretical base for creating multiscale subgrid models in large-eddy simulation.     

Origination and evolution of turbulent flows in a rotating spherical layer

The object of consideration is the turbulent flows of a viscous incompressible liquid that arises in a wide spherical layer with counter-rotating boundaries (the thickness of the layer equals the radius of the inner sphere). Regimes established when the outer sphere rotates with a constant velocity and the inner one rotates with an increasing velocity are studied in physical and numerical experiments. The averaged meridional circulation and the pulsation profiles of all velocity components are derived by direct calculation. It is found that both observed and simulated turbulent regimes are characterized by the continuous spectrum of velocity pulsation near their formation boundary. In going from the laminar to chaotic regime, the correlation dimension increases stepwise and then slightly varies with increasing Reynolds number in a nonlinear manner.     

Multiscale SOC in turbulent convection

Using data obtained in a laboratory thermal convection experiment at high Rayleigh numbers, it is shown that the multiscaling properties of the observed mean wind reversals are quantitatively consistent with analogous multiscaling properties of the Bak–Tang–Wiesenfeld prototype model of self-organized criticality in two dimensions.     

Generalized wall functions for turbulent flows with strong adverse pressure gradient

The generalized wall functions for turbulent flows with strong adverse pressure gradients are derived on the basis of the asymptotic theory of near-wall turbulence. The generalized wall functions have a correct asymptotic behavior in the limit of zero friction velocity and can be applied to computations of flows under a strong adverse pressure gradient and with separation or reattachment. Calculations of a turbulent boundary layer in a strong adverse pressure gradient with the aid of the developed modified k-ɛ model of turbulence and comparison with the experimental data validate the advantages of the generalized wall functions over traditional wall functions based on the logarithmic law of the wall.     

Development of the diffusion-inertia model of particle deposition in turbulent flows

There is presented a modification of the diffusion-inertia model that describes the distribution and deposition of low-inertia particles in turbulent near-wall flows. For the transport equation of the dispersed phase concentration, there is proposed a new wall function that takes into account the nonequilibrium effects and nonlocality of the turbulent transport of the dispersed phase in the near-wall zone caused by the particles’ inertia. This allowed widening the applicability limits of the diffusion-inertia model even for particles with a relaxation time with a magnitude of several hundred. The calculation results for the rate of the particles’ deposition from the turbulent flow to the walls in a round pipe are in good accord with the literature experimental data and the data of direct numerical simulation.     

Multiscale clustering in granular surface flows

We investigate steady granular surface flows in a rotating drum and demonstrate the existence of rigid clusters of grains embedded in the flowing layer. These clusters appear to be fractal and their size is power law distributed from the grain size scale up to the thickness of the flowing layer. The implications of the absence of a characteristic length scale on available theoretical models of dense granular flows are discussed. Finally, we suggest a possible explanation of the difference between velocity profiles observed in surface flows and in flows down a rough inclined plane.     

A Reynolds stress model for turbulent flows of viscoelastic fluids

A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic – Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.     

Multiscale laminar flows with turbulentlike properties

By applying fractal electromagnetic force fields on a thin layer of brine, we generate steady quasi-two-dimensional laminar flows with multiscale stagnation point topology. This topology is shown to control the evolution of pair separation (Delta) statistics by imposing a turbulentlike locality based on the sizes and strain rates of hyperbolic stagnation points when the flows are fast enough, in which case Delta(2) approximately t(gamma) is a good approximation with gamma close to 3. Spatially multiscale laminar flows with turbulentlike spectral and stirring properties are a new concept with potential applications in efficient and microfluidic mixing.     

Helicity generation in turbulent MHD flows

We study turbulent flow of a conducting liquid in a uniform external magnetic field. It is shown that intense helicity generation is possible in the presence of a mean shear flow. It is noted that even though the mean helicity of the initial flow can be zero, the presence of internal topological structure of the flow, for example the presence of helicity of different signs at different scales, is nevertheless necessary for helicity generation. Zh. éksp. Teor. Fiz. 114, 946–955 (September 1998)     

Evaporating droplets in turbulent reacting flows

Three-dimensional direct numerical simulations are carried out to determine the effects of turbulence on the preferential segregation of an evaporating spray and then to study the evolution of the resulting mixture fraction topology and propagating flame. First, the mixing between an initially randomly dispersed phase and the turbulent gaseous carrier phase is studied with non-evaporating particles. According to their inertia and the turbulence properties, the formation of clusters of particles is analyzed (formation delay, cluster characteristic size and density). Once the particles are in dynamical equilibrium with the surrounding turbulent flow, evaporation is considered through the analysis of the mixture fraction evolution. Finally, to mimic ignition, a kernel of burnt gases is generated at the center of the domain and the turbulent flame evolution is described.     

Effects of forcing in three-dimensional turbulent flows

We present the results of a numerical investigation of three-dimensional homogeneous and isotropic turbulence, stirred by a random forcing with a power-law spectrum, E(f)(k) approximately k(3-y). Numerical simulations are performed at different resolutions up to 512(3). We show that at varying the spectrum slope y, small-scale turbulent fluctuations change from a forcing independent to a forcing dominated statistics. We argue that the critical value separating the two behaviors, in three dimensions, is y(c)=4. When the statistics is forcing dominated, for yy(c), we find the same anomalous scaling measured in flows forced only at large scales. We connect these results with the issue of universality in turbulent flows.     

Development and application of a diffusion-inertia model for simulating gas-dispersed turbulent flows

The development and application of a diffusion-inertia model are shown for computing the propagation and deposition of aerosol particles in turbulent flows. Comparison with experimental and numerical results points to the fact that the developed model adequately describes all the typical peculiarities of the process of the sedimentation of aerosol particles in straight and curved pipes.     

Statistics of Lagrangian velocities in turbulent flows

We present a generalized Fokker-Planck equation for the joint position-velocity probability distribution of a single fluid particle in a turbulent flow. Based on a simple estimate, the diffusion term is related to the two-point two-time Eulerian acceleration-acceleration correlation. Dimensional analysis yields a velocity increment probability distribution with normal scaling v approximately t(1/2). However, the statistics need not be Gaussian.     

Micromixing models for turbulent flows

In transported probability density function and filtered density function methods, micromixing models are required to close the molecular mixing term. The accuracy and computational efficiency of improved versions of the parameterized scalar profile (PSP) model are assessed and compared with commonly used mixing models such as Curl, modified Curl, interaction by exchange with the mean and Euclidean minimum spanning tree. Different generalizations of the PSP mixing model for spatially inhomogeneous flow configurations are presented. The selected test cases focus on molecular mixing and avoid interference with other models. Simulation results for a three-stream problem, involving two inert scalars, and a multi-scalar test case with mean-scalar-gradients are presented.     

Completely integrable gradient flows

In this paper we exhibit the Toda lattice equations in a double bracket form which shows they are gradient flow equations (on their isospectral set) on an adjoint orbit of a compact Lie group. Representations for the flows are given and a convexity result associated with a momentum map is proved. Some general properties of the double bracket equations are demonstrated, including a discussion of their invariant subspaces, and their function as a Lie algebraic sorter.Supported in part by NSF Grant DMS-90-02136, NSF PYI Grant DMS-9157556, and a Seed Grant from Ohio State UniversitySupported in part by AFOSR grant AFOSR-96-0197, by U.S. Army Research Office grant DAAL03-86-K-0171 and by NSF grant CDR-85-00108Supported in part by NSF Grant DMS-8922699     

Long-wavelength modulation of turbulent shear flows

The reverse transition from turbulent to laminar flow is studied in very large aspect ratio plane Couette and Taylor–Couette experiments. We show that laminar-turbulence coexistence dynamics (turbulent spots, spiral turbulence, etc.) can be seen as the ultimate stage of a modulation of the turbulent flows present at higher Reynolds number leading to regular, long-wavelength, inclined stripes. This new type of instability, whose originality is to arise within a macroscopically fluctuating state, can be described in the framework of Ginzburg–Landau equations to which noise is heuristically added to take into account the intrinsic fluctuations of the basic state.