ALBERT

Description: Detailed facies analysis and morphotectonic investigations of the Malin River's alluvial fan in the western Ganga Plain, India, reveal that the morphology of the fan is largely tectonically controlled whereas the sedimentary processes are mainly climatically controlled. The sedimentation occurred in two distinct evolutionary cycles which are separated by a time gap. The older cycle deposited thick gravelly units up to the distal-fan area, whereas the sediment fill of the younger cycle is gavel-dominated in the proximal-fan area, gravel–sand dominated in the middle-fan area and sand–mud dominated in the distal-fan area. The gravels of the older cycle were emplaced by intense sediment gravity flows during periods of strengthened monsoon and steeper regional gradient. During the younger cycle, the proximal to distal parts of the fan were dominated by different sedimentary processes. This was a time of relatively weaker monsoon and gentler regional slopes, when gravels could travel only up to the middle-fan area. The gravels in the proximal-fan area have mainly been deposited by sediment gravity flows and channel processes; in the middle-fan area channel processes, sheetfloods and sediment gravity flows have been the main sedimentary processes; and in the distal-fan area fluvial processes of channel migration and overbank deposition have been the main sedimentary processes.

Description: The spectral mechanisms of the differential diffusion of pairs of passive scalars with different molecular diffusivities are studied in stationary isotropic turbulence, using direct numerical simulation data at Taylor-scale Reynolds number up to 160 on 1283 and 2563 grids. Of greatest interest are the roles of nonlinear triadic interactions between different scale ranges of the velocity and scalar fields in the evolution of spectral coherency between the scalars, and the effects of mean scalar gradients. Analysis of single-scalar spectral transfer (extending the results of a previous study) indicates a robust local forward cascade behaviour at high wavenumbers, which is strengthened by both high diffusivity and mean gradients. This cascade is driven primarily by moderately non-local interactions in which two small-scale scalar modes are coupled via a lower-wavenumber velocity mode near the peak of the energy dissipation spectrum. This forward cascade is coherent, tending to increase the coherency between different scalars at high wavenumbers but to decrease it at lower wavenumbers. However, at early times coherency evolution at high wavenumbers is dominated by de-correlating effects due to a different type of non-local triad consisting of two scalar modes with a moderate scale separation and a relatively high-wavenumber velocity mode. Consequently, although the small-scale motions play little role in spectral transfer, they are responsible for the rapid de-correlation observed at early times. At later times both types of competing triadic interactions become important over a wider wavenumber range, with increased relative strength of the coherent cascade, so that the coherency becomes slow-changing. When uniform mean scalar gradients are present, a stationary state develops in the coherency spectrum as a result of a balance between a coherent mean gradient contribution (felt within about 1 eddy-turnover time) and the net contribution from scale interactions. The latter is made less de-correlating because of a strengthened coherent forward cascade, which is in turn caused by uniform mean gradients acting as a primarily low-wavenumber source of scalar fluctuations with the same spectral content as the velocity field.

Description: It is well known that the drag in a turbulent flow of a polymer solution is significantly reduced compared to Newtonian flow. Here we consider this phenomenon by means of a direct numerical simulation of a turbulent channel flow. The polymers are modelled as elastic dumbbells using the FENE-P model. In the computations the polymer model is solved simultaneously with the flow equations, i.e. the polymers are deformed by the flow and in their turn influence the flow structures by exerting a polymer stress. We have studied the results of varying the polymer parameters, such as the maximum extension, the elasticity and the concentration. For the case of highly extensible polymers the results of our simulations are very close to the maximum drag reduction or Virk (1975) asymptote. Our simulation results show that at approximately maximum drag reduction the slope of the mean velocity profile is increased compared to the standard logarithmic profile in turbulent wall flows. For the r.m.s. of the streamwise velocity fluctuations we find initially an increase in magnitude which near maximum drag reduction changes to a decrease. For the velocity fluctuations in the spanwise and wall-normal directions we find a continuous decrease as a function of drag reduction. The Reynolds shear stress is strongly reduced, especially near the wall, and this is compensated by a polymer stress, which at maximum drag reduction amounts to about 40% of the total stress. These results have been compared with LDV experiments of Ptasinski et al. (2001) and the agreement, both qualitatively and quantitatively, is in most cases very good. In addition we have performed an analysis of the turbulent kinetic energy budgets. The main result is a reduction of energy transfer from the streamwise direction, where the production of turbulent kinetic energy takes place, to the other directions. A substantial part of the energy production by the mean flow is transferred directly into elastic energy of the polymers. The turbulent velocity fluctuations also contribute energy to the polymers. The elastic energy of the polymers is subsequently dissipated by polymer relaxation. We have also computed the various contributions to the pressure fluctuations and identified how these change as a function of drag reduction. Finally, we discuss some cross-correlations and various length scales. These simulation results are explained here by two mechanisms. First, as suggested by Lumley (1969) the polymers damp the cross-stream or wall-normal velocity fluctuations and suppress the bursting in the buffer layer. Secondly, the 'shear sheltering' mechanism acts to amplify the streamwise fluctuations in the thickened buffer layer, while reducing and decoupling the motions within and above this layer. The expression for the substantial reduction in the wall drag derived by considering the long time scales of the nonlinear fluctuations of this damped shear layer, is shown to be consistent with the experimental data of Virk et al. (1967) and Virk (1975).

Description: The hypothesis of the small scales being passively swept along by the large-scale motions in turbulent flow is extended to passive scalars in isotropic turbulence. A theory based on strong mutual cancellation between local and advective derivatives and other assumptions is shown to capture the Reynolds and Schmidt number dependence of time scales characterizing Eulerian and Lagrangian rates of change. Agreement with direct numerical simulation data improves systematically with increasing Reynolds number. In accordance with the physics of random sweeping, the Eulerian frequency spectrum is very similar in shape to the wavenumber spectrum, but is broadened at higher frequencies compared to its Lagrangian counterpart. Overall the hypothesis appears to be even more valid for transported scalars than for the velocity field, which gives support to the use of Lagrangian approaches in the study of turbulent mixing.

Description: A new model for Lagrangian particle-pair separation in turbulent flows is developed and compared with data from direct numerical simulations (DNS) of isotropic turbulence. The model formulation emphasizes (i) non-Gaussian behaviour in Eulerian and Lagrangian statistics, (ii) the occurrence of large separation velocities, (iii) the role of straining and streaming flow structure as recognized in kinematic simulations of turbulence, and (iv) the role of conditionally averaged accelerations in stochastic modelling of turbulent relative dispersion. Previous stochastic models of relative dispersion have produced unrealistic behaviour, particularly in the dissipation subrange where viscous effects are important, which have led to questions on the adequacy of stochastic modelling. However, this failure can now be recognized as inadequate detail in formulation, which is explained and rectified in this paper. The model is quasi-one-dimensional in nature, and is focused on the statistics of particle-pair separation distance and its rate of change, referred to as the separation speed. Detailed comparisons are presented at several Reynolds numbers using the DNS database reported in a companion paper (Part 1). Up to fourth-order moments for these quantities are examined, as well as the separation-distance probability density function, which is discussed in the context of recent claims of Richardson scaling in the literature. The model is able to account for the spatial representation of straining regions as well as incompressibility of the flow, and is shown to reproduce strong non-Gaussianity and intermittency in the Lagrangian separation statistics observed in DNS. Comparisons with recent physical experiments are also remarkably consistent. This work demonstrates that stochastic models when properly formulated are effective and efficient representations of the dispersion process and this general class of models therefore possess great utility for calculations of both one-particle and two-particle dispersion. The techniques developed in this paper will facilitate such general model development. © 2004 Cambridge University Press.

Description: We examine available data from experiment and recent numerical simulations to explore the supposition that the scalar dissipation rate in turbulence becomes independent of the fluid viscosity when the viscosity is small and of scalar diffusivity when the diffusivity is small. The data are interpreted in the context of semi-empirical spectral theory of Obukhov and Corrsin when the Schmidt number, Sc, is below unity, and of Batchelor's theory when Sc is above unity. Practical limits in terms of the Taylor-microscale Reynolds number, Rλ, as well as Sc, are deduced for scalar dissipation to become sensibly independent of molecular properties. In particular, we show that such an asymptotic state is reached if RλSc1/2 ≫ 1 for Sc 〈 1, and if ln(Sc)/Rλ ≫ 1 for Sc 〈 1. © 2005 Cambridge University Press.

Description: We explore very fine scales of scalar dissipation in turbulent mixing, below Kolmogorov and around Batchelor scales, by performing direct numerical simulations at much finer grid resolution than was usually adopted in the past. We consider the resolution in terms of a local fluctuating Batchelor scale and study the effects on the tails of the probability density function and multifractal properties of the scalar dissipation. The origin and importance of these very fine-scale fluctuations are discussed. One conclusion is that they are unlikely to be related to the most intense dissipation events. © 2005 Cambridge University Press.

Description: This paper is concerned with the jet of liquid, open to the atmosphere, that emerges from a two-dimensional channel in which there is Poiseuille flow far upstream, the flow being driven by an applied pressure gradient. The problem is discussed with the aid of the method of matched asymptotic expansions; the small parameter involved is the inverse Reynolds number. A boundary layer forms adjacent to the free surface, and a classical boundary-layer analysis is applied to find the flow there (for moderate distances downstream); the influence of this boundary layer on the flow in the core of the jet is then investigated. Higher-order boundary-layer effects, such as indeterminacy and eigensolutions, are also discussed. The first few terms are found of an asymptotic expansion for the equation of the free surface, and considerations of momentum balance are applied to find the asymptotic contraction ratio of the jet.

Description: The stability of fully developed pipe-Poiseuille flow to finite-amplitude axisymmetric and non-axisymmetric disturbances has been studied using the equilibrium-amplitude method of Reynolds & Potter (1967). In both the cases the least-stable centre-modes were investigated. Also, for the non-axisymmetric case the mode investigated was the one with azimuthal wavenumber equal to one. Many higher-order Landau coefficients were calculated, and the Stuart—Landau series was analysed by the Shanks (1955) method and by using Pade approximants to look for the existence of possible equilibrium states. The results show in both cases that, for each value of the Reynolds number R, there is a preferred band of spatial wavenumbers a in which equilibrium states are likely to exist. Moreover, in both cases it was found that the magnitude of the minimum threshold amplitude for a given R decreases with increasing R. The scales of the various quantities obtained agree very well with those deduced by Davey & Nguyen (1971). © 1985, Cambridge University Press. All rights reserved.