ALBERT

Description: The structure of initially isotropic homogeneous turbulence interacting with a columnar vortex (with circulation Γ and radius σ), idealized both as a solid cylinder and a hollow core model is analysed using the inhomogeneous form of linear rapid distortion theory (RDT), for flows where the r.m.s. turbulence velocity u0 is small compared with Γ / σ. The turbulent eddies with scale L are distorted by the mean velocity gradient and also, over a distance L from the surface of the vortex, by their direct impingement onto it, whether it is solid or hollow. The distortion of the azimuthal component of turbulent vorticity by the differential rotation in the mean flow around the columnar vortex causes the mean-square radial velocity away from the cylinder to increase as (Γ t / 2πr2)2(L(x) / r)u02, when (r - σ) 〉 L(x), but on the surface of the vortices ((r - σ) 〈 L(x)) where 〈u(r)2〉 is reduced, 〈u(z)2〉 increases to the same order, while the other components do not grow. Statistically, while the vorticity field remains asymmetric, the velocity field of small-scale eddies near the vortex core rapidly becomes axisymmetric, within a period of two or three revolutions of the columnar vortex. Calculation of the distortion of small-scale initially random velocity fields shows how the turbulent eddies, as they are wrapped around the columnar vortex, become like vortex rings, with similar properties to those computed by Melander and Hussain (1993) using a fully nonlinear direct numerical simulation. A mechanism is proposed for how interactions between the external turbulence and the columnar vortex can lead to non-axisymmetric vortex waves being excited on the vortex and damped fluctuations in its interior. If the columnar vortex is not significantly distorted by these linear effects, estimates are made of how nonlinear effects lead to the formation of axisymmetric turbulent vortices which move as result of their image vorticity (in addition to the self-induction velocity) at a velocity of order u0tΓ / σ2 parallel to the vortex. Even when the circulation (γ) of the turbulent vortices is a small fraction of Γ, they can excite self-destructive displacements through resonance on a time scale σ/u0.

Description: The flow field around pairs of small particles moving and rotating in a shear flow close to a wall at low but finite Reynolds number (Re) is computed as a function of time by means of the lattice-Boltzmann technique. The total force and torque acting on each particle is computed at each time step and the position of the particles is updated. By considering the lift force and the disturbances induced by the particles, the trajectories of the pair of particles are explained as a function of the distances from the wall and the Reynolds number. It is shown that when particles are positioned in a particular form, they collide forming strings. In particular, we are interested in particle-bridge formation in shear flows, and two collided particles (a string) can be considered as a nucleus of a particle bridge. © 2006 Cambridge University Press.

Description: The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. (1998) are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations on either side of a thin randomly moving interface. Comparisons are made with a wake that is ‘forced’ by amplifying initial velocity fluctuations. A temperature field T, with constant values of 1.0 and 0 above and below the wake, is transported across the wake as a passive scalar. The value of the Reynolds number based on the centreplane mean velocity defect and half-width b of the wake is Re ≈ 2000.The thickness of the continuous interface is about 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement yI(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of yI and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y−yI the conditional mean velocity 〈U〉 and temperature 〈T〉 profiles show sharp jumps at the interface adjacent to a thick zone where 〈U〉 and 〈T〉 vary much more slowly.Statistics for the conditional vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. While mean Reynolds stresses (in the fixed reference frame) decrease gradually in the intermittent zone, conditional stresses are roughly constant and then decrease sharply towards zero at the interface. Flow fields around the interface, analysed in terms of the local streamline pattern, confirm and explain previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion.Terms used in one-point turbulence models are evaluated both conventionally and conditionally in the interface region, and the current practice in statistical models of approximating entrainment by a diffusion process is assessed.

Description: The interaction between an initially laminar boundary layer developing spatially on a flat plate and wakes traversing the inlet periodically has been simulated numerically. The three-dimensional, time-dependent Navier-Stokes equations were solved with 5.24 ×107 grid points using a message passing interface on a scalable parallel computer. The flow bears a close resemblance to the transitional boundary layer on turbomachinery blades and was designed following, in outline, the experiments by Liu & Rodi (1991). The momentum thickness Reynolds number evolves from Reθ = 80 to 1120. Mean and second-order statistics downstream of Reθ = 800 are of canonical flat-plate turbulent boundary layers and are in good agreement with Spalart (1988). In many important aspects the mechanism leading to the inception of turbulence is in agreement with previous fundamental studies on boundary layer bypass transition, as summarized in Alfredsson & Matsubara (1996). Inlet wake disturbances inside the boundary layer evolve rapidly into longitudinal puffs during an initial receptivity phase. In the absence of strong forcing from free-stream vortices, these structures exhibit streamwise elongation with gradual decay in amplitude. Selective intensification of the puffs occurs when certain types of turbulent eddies from the free-stream wake interact with the boundary layer flow through a localized instability. Breakdown of the puffs into young turbulent spots is preceded by a wavy motion in the velocity field in the outer part of the boundary layer. Properties and streamwise evolution of the turbulent spots following breakdown, as well as the process of completion of transition to turbulence, are in agreement with previous engineering turbomachinery flow studies. The overall geometrical characteristics of the matured turbulent spot are in good agreement with those observed in the experiments of Zhong et al. (1998). When breakdown occurs in the outer layer, where local convection speed is large, as in the present case, the spots broaden downstream, having the vague appearance of an arrowhead pointing upstream. The flow has also been studied statistically. Phase-averaged velocity fields and skinfriction coefficients in the transitional region show similar features to previous cascade experiments. Selected results from additional thought experiments and simulations are also presented to illustrate the effects of streamwise pressure gradient and free-stream turbulence.

Description: In stably stratified flow over a three-dimensional hill, we can define a dividing streamline that separates those streamlines that pass around the hill from those that pass over the hill. The height Hs of this dividing streamline can be estimated by Sheppard's simple energy argument; fluid parcels originating far upstream of a hill at an elevation above Hs have sufficient kinetic energy to rise over the top, whereas those below Hs must pass around the sides. This prediction provides the basis for analysing an extensive range of laboratory observations and measurements of stably stratified flow over a variety of shapes and orientations of hills and with different upwind density and velocity profiles. For symmetric hills and small upwind shear, Sheppard's expression provides a good estimate for Hs. For highly asymmetric flow and/or in the presence of strong upwind shear, the expression provides a lower limit for Hs. As the hills become more nearly two-dimensional, these experiments become less well defined because steady-state conditions take progressively longer to be established. The results of new studies are presented here of the development of the unsteady flow upwind of two-dimensional hills in a finite-length towing tank. These measurements suggest that a very long tank would be required for steady-state conditions to be established upstream of long ridges with or without small gaps and cast doubt upon the validity of previous laboratory studies.