Small-scale-velocity-induced linear instability of large-scale turbulent flows

Analysis of a simplified equation derived previously for small-scale velocity components shows that any turbulent flow of an incompressible liquid becomes unstable against infinitesimal perturbations of small-scale velocity components if the strain rate tensor for the large-scale velocity is high. Such a statement comes into conflict with the classical stability theory, which specifically asserts that the Poiseuille flow in a circular tube is linearly stable against infinitesimal perturbations.     

Structure analysis of turbulent mixing patterns in inert and reactive turbulent liquid flows

The paper contains an extended summary of an invited plenary talk given at the Workshop on Active Chaos at the Los Alamos National Laboratory on 29-31 May 2001 by one of us (F.S.R.). (c) 2002 American Institute of Physics.     

Surface instability of a nuclear fermi liquid drop

A mechanical instability of an incompressible Fermi liquid drop with respect to surface distortions is considered. It is shown that the Fermi surface distortion (FSD) reduces the instability-growth rate for surface fluctuations due to its effects on both the viscosity and the increase in the stiffness coefficient. The dependence of the limiting temperature T_lim on the mass number and the multipolarity of the nuclear-surface distortion is calculated. It is shown that T_lim is not influenced by the FSD effect.     

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.     

Mechanism of turbulent pulsation in channels

The space-time pulsation field of hydrodynamic parameters for channel turbulent flow is derived from the wave model of turbulence. Conditions for pulsation field randomization are analyzed. Calculations of the longitudinal and transverse pulsations are compared with the Reichardt’s measurements.     

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.     

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.     

Heat transfer of non-Newtonian liquid flows in convergent-divergent channels with fourth-kind thermal boundary conditions

In the present paper, we consider the heat transfer of non-Newtonian liquid flows moving in convergent- divergent channels with common boundary. The case of flows moving in opposite directions was addressed. At the common boundary, continuity conditions for temperature and heat flow were adopted. A mathematical model, a calculation algorithm, and simulation data are reported. Plots of numerical data characterizing the channel flows are presented. A comparative analysis of heat transfer in smooth and convergent-divergent channels is given.     

Improved modeling of flows down inclined planes

New models of film flows down inclined planes have been derived by combining a gradient expansion at first or second order to weighted residual techniques with polynomials as test functions. The two-dimensional formulation has been extended to account for three-dimensional flows as well. The full second-order two-dimensional model can be expressed as a set of four coupled evolution equations for four slowly varying fields, the thickness h, the flow rate q and two other quantities measuring the departure from the flat-film semi-parabolic velocity profile. A simplified model has been obtained in terms of h and q only. Including viscous dispersion effects properly, it closely sticks to the asymptotic expansion in the appropriate limit. Our new models improve over previous ones in that they remain valid deep into the strongly nonlinear regime, as shown by the comparison of our results relative to travelling-wave and solitary-wave solutions with those of both direct numerical simulations and experiments. Received 14 September 1999 and Received in final form 6 January 2000     

Three-dimensional structure of the Lagrangian acceleration in turbulent flows

We report experimental results on the three-dimensional Lagrangian acceleration in highly turbulent flows. Tracer particles are tracked optically using four silicon strip detectors from high energy physics that provide high temporal and spatial resolution. The components of the acceleration are shown to be statistically dependent. The probability density function of the acceleration magnitude is comparable to a log-normal distribution. Assuming isotropy, a log-normal distribution of the magnitude can account for the observed dependency of the components. The time dynamics of the acceleration components is found to be typical of the dissipation scales, whereas the magnitude evolves over longer times, possibly close to the integral time scale.     

Onset of turbulence in open liquid flows as a nonequilibrium noise-induced secondorder phase transition

It is shown that there is a profound analogy between the transition to turbulence in open liquid flows and the noise-induced excitation of oscillations of a pendulum with a randomly oscillating pivot. It is significant that this analogy is based not on the similarity of the equations describing these processes, but on the generality of the laws of the theory of oscillations. The existence of this analogy makes it possible to understand and account for numerous phenomena observed in both numerical simulations and real experiments. Moreover, this analogy suggests several recommendations to experimenters for achieving a more thorough suppression of undesirable turbulent pulsations in subsonic jets. Zh. Tekh. Fiz. 68, 31–39 (January 1998)     

Blowout limits of inclined nonpremixed turbulent jet flames

The blowout behavior of inclined nonpremixed turbulent jet flames is investigated by varying the jet inclined angle in the range of -90° to 90° The critical jet velocity at blow-out limit is quantified experimentally for various nozzle diameters, different fuels and inclined angles. Numerical simulations are performed to emphasize the flow field difference for the positive and negative inclined angles. Physical modeling is conducted to incorporate the effect of the inclined angle on blow-out behavior. Major findings include: (1) The negatively inclined jet flames show more intense yellow luminosity with larger sooting zones than the positively inclined jet flames; (2) The blowout limit decreases appreciably with the jet inclined angle for the negatively inclined flames, while for the positively inclined jet flames, this decrease is relatively small; (3) Physical analysis of the flow development of inclined jets is conducted, indicating the centerline velocity along the jet trajectory decreases faster for the flame with smaller inclined angle. And the decrease rate is relatively larger for the negatively inclined jet flames; (4) Based on the analysis of the flow development as well as the characteristic velocity with the inclined angle variation, a model based on the Damköhler number (Da) accounting for the effect of jet inclined angle is developed to characterize the blowout limits of inclined jet flames. The proposed model successfully correlates the experimental data. The present findings provide new data and a basic scaling law for the blowout limit of nonpremixed inclined turbulent jet flames, revealing the effect of the relative angle between the jet momentum and buoyancy.     

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.     

On the baroclinic instability of nonplanar flows

Summary Different ocean models with one or two layers having constant static stability and supporting constant-shear flows, whose directions are allowed to change with depth, are examined in the frame-work of the linear nonzonal baroclinic stability theory and in the absence of the β-effect. The analysis is reduced to solving a simple Sturm-Liouville boundary value problem in one dimension. A fairly general dispersion relation is found which correctly reproduces several special cases analysed by other authors. This relation shows a fair variety of possible behaviours for stability curves of two-layer models. The results show that the presence of a nonplanar shear-flow may have profound consequences on the stability character of the stationary geostrophic flow. In fact, it appears that the stability properties are strongly dependent on the propagation angle of the disturbance so that wave numbers which appear stable in the usual zonal theory may result unstable on such a nonzonal flow andvice versa. Paper presented at the 1^o Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 19–22, 1984, Rome.