Fazle Hussain

On the identification of a vortex

Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor S 2 +Ω 2 ; here S and Ω are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ⊇u. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier-Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of ⊇u or the complex eigenvalues of ⊇u, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear

Coherent structure generation in near-wall turbulence

We present a new mechanism for generation of near-wall streamwise vortices { which dominate turbulence phenomena in boundary layers { using linear perturbation analysis and direct numerical simulations of turbulent channel flow. The base flow, consisting of the mean velocity prole and low-speed streaks (free from any initial vortices), is shown to be linearly unstable to sinuous normal modes only for relatively strong streaks, i.e. for wall inclination angles of streak vortex lines exceeding 50. Analysis of streaks extracted from fully developed near-wall turbulence indicates that about 20% of streak regions in the buer layer exceed the strength threshold for instability. More importantly, these unstable streaks exhibit only moderate (twofold) normalmode amplication, the growth being arrested by self-annihilation of streak-flank normal vorticity due to viscous cross-diusion. We present here an alternative, streak transient growth (STG) mechanism, capable of producing much larger (tenfold) linear amplication of x-dependent disturbances. Note the distinction of STG { responsible for perturbation growth on a streak velocity distribution U(y;z) { from prior transient growth analyses of the (streakless) mean velocity U(y). We reveal that streamwise vortices are generated from the more numerous normal-mode-stable streaks, via a new STG-based scenario: (i) transient growth of perturbations leading to formation of a sheet of streamwise vorticity !x (by a ‘shearing’ mechanism of vorticity generation), (ii) growth of sinuous streak waviness and hence @u=@x as STG reaches nonlinear amplitude, and (iii) the !x sheet’s collapse via stretching by @u=@x (rather than rollup) into streamwise vortices. Signicantly, the three-dimensional features of the (instantaneous) streamwise vortices of x-alternating sign generated by STG agree well with the (ensemble-averaged) coherent structures educed from fully turbulent flow. The STGinduced formation of internal shear layers, along with quadrant Reynolds stresses and other turbulence measures, also agree well with fully developed turbulence. Results indicate the prominent { possibly dominant { role of this new, transient-growth-based vortex generation scenario, and suggest interesting possibilities for robust control of drag and heat transfer.

Elliptic jets. I: Characteristics of unexcited and excited jets

This paper summarizes experimental studies of incompressible elliptic jets of different aspect ratios and initial conditions, and effects of excitations at selected frequencies and amplitudes. Elliptic jets are quite different from the extensively studied plane and circular jets - owing mainly to the fact that the azimuthal curvature variation of a vortical structure causes its non-uniform self-induction and hence complex three-dimensional deformation. Such deformation, combined with properly selected excitation can substantially alter entrainment and other turbulence phenomena, thus suggesting preference for the elliptic shape in many jet applications. The dominance of coherent structures in the jet far field is evident from the finding that switching over of the cross-section shape continues at least up to 100 equivalent diameters D e . The locations and the number of switchovers are strongly dependent on the initial condition, on the aspect ratio, and, when excited, on the Strouhal number and the excitation level. We studied jets with constant exit momentum thickness θ e , all around the perimeter, thus separating the effects of azimuthal variations of θ e , (typical of elliptic jets) and of the shear-layer curvature. Also investigated are the instability characteristics, and enhanced entrainment caused by bifurcation as well as pairing of vortical structures. We discuss shear-layer and jet- column domains, and find the latter to be characterized by two modes : the preferred mode and the stable pairing mode - similar to those found in circular jets -both modes scaling on the newly-defined lengthscale D e . The paper documents some time- average measurements and their comparison with those in circular and plane jets.

Propagation velocity of perturbations in turbulent channel flow

A database obtained from direct numerical simulation of a turbulent channel flow is analyzed to extract the streamwise component of the propagation velocity V of velocity, vorticity, and pressure fluctuations from their space‐time correlations. A surprising result is that V is approximately the same as the local mean velocity for most of the channel, except for the near‐wall region. For y+≤15, V is virtually constant, implying that perturbations of all flow variables propagate like waves near the wall. In this region, V is 55% of the centerline velocity Uc for velocity and vorticity perturbations and 75% of Uc for pressure perturbations. This is equal to U at y+=15 for velocity and vorticity perturbations, and equal to U at y+=20 for pressure perturbations, indicating that the dynamics of the near‐wall turbulence is controlled by turbulence structures present near y+≂15–20. Scale dependence of V is also examined by analyzing the bandpass‐filtered flow fields. This paper contains comprehensive documentatio...

Rapid tumoritropic accumulation of systemically injected plateloid particles and their biodistribution

Nanoparticles for cancer therapy and imaging are designed to accumulate in the diseased tissue by exploiting the Enhanced Permeability and Retention (EPR) effect. This limits their size to about 100nm. Here, using intravital microscopy and elemental analysis, we compare the in vivo localization of particles with different geometries and demonstrate that plateloid particles preferentially accumulate within the tumor vasculature at unprecedented levels, independent of the EPR effect. In melanoma-bearing mice, 1000×400nm plateloid particles adhered to the tumor vasculature at about 5% and 10% of the injected dose per gram organ (ID/g) for untargeted and RGD-targeted particles respectively, and exhibited the highest tumor-to-liver accumulation ratios (0.22 and 0.35). Smaller and larger plateloid particles, as well as cylindroid particles, were more extensively sequestered by the liver, spleen, and lungs. Plateloid particles appeared well-suited for taking advantage of hydrodynamic forces and interfacial interactions required for efficient tumoritropic accumulation, even without using specific targeting ligands.

In-line recording and off-axis viewing technique for holographic particle velocimetry

Prior approaches (e.g., off-axis holography) to overcoming the limitations of in-line holography for particle fields, namely, intrinsic speckle noise and depth resolution, involved an increased complexity of the optical system. The in-line recording and off-axis viewing (IROV) technique employs a single laser beam to record an in-line hologram, which is then viewed off axis during reconstruction. The signal-to-noise ratio and depth resolution of IROV are higher than conventional in-line holography by an order of magnitude and are comparable with off-axis holography. IROV is a much simpler approach than off-axis holography and is highly promising for holographic particle velocimetry. Measurements of the three dimensional flow velocity field of a vortex ring obtained by an IROV-based holographic particle velocimetry system are presented.

Three-dimensionality of organized structures in a plane turbulent wake

This paper describes a quantitative study of the three-dimensional nature of organized motions in a turbulent plane wake. Coherent structures are detected from the instantaneous, spatially phase-correlated vorticity field using certain criteria based on size, strength and geometry of vortical structures. With several combinations of X-wire rakes, vorticity distributions in the spanwise and transverse planes are measured in the intermediate region (10 d [les ] x [les ] 40 d ) of the plane turbulent wake of a circular cylinder at a Reynolds number of 13000 based on the cylinder diameter d . Spatial correlations of smoothed vorticity signals as well as phase-aligned ensemble-averaged vorticity maps over structure cross-sections yield a quantitative measure of the spatial coherence and geometry of organized structures in the fully turbulent field. The data demonstrate that the organized structures in the nominally two-dimensional wake exhibit significant three-dimensionality even in the near field. Using instantaneous velocity and vorticity maps as well as correlations of vorticity distributions in different planes, some topological features of the dominant coherent structures in a plane wake are inferred.

A large-scale control strategy for drag reduction in turbulent boundary layers

Using direct numerical simulations of turbulent channel flow, we present a new method for skin friction reduction, enabling large-scale flow forcing without requiring instantaneous flow information. As proof-of-principle, x-independent forcing, with a z wavelength of 400 wall units and an amplitude of only 6% of the centerline velocity, produces a significant sustained drag reduction: 20% for imposed counterrotating streamwise vortices and 50% for colliding, z-directed wall jets. The drag reduction results from weakened longitudinal vortices near the wall, due to forcing-induced suppression of an underlying streak instability mechanism. In particular, the forcing significantly weakens the wall-normal vorticity ωy flanking lifted low-speed streaks, thereby arresting the streaks’ sinuous instability which directly generates new streamwise vortices in uncontrolled flows. These results suggest promising new drag reduction techniques, e.g., passive vortex generators or colliding spanwise jets from x-aligned sl...

Blood flow and coherent vortices in the normal and aneurysmatic aortas: a fluid dynamical approach to intra-luminal thrombus formation

Abdominal aortic aneurysms (AAAs) are frequently characterized by the development of an intra-luminal thrombus (ILT), which is known to have multiple biochemical and biomechanical implications. Development of the ILT is not well understood, and shear–stress-triggered activation of platelets could be the first step in its evolution. Vortical structures (VSs) in the flow affect platelet dynamics, which motivated the present study of a possible correlation between VS and ILT formation in AAAs. VSs educed by the λ2-method using computational fluid dynamics simulations of the backward-facing step problem, normal aorta, fusiform AAA and saccular AAA were investigated. Patient-specific luminal geometries were reconstructed from computed tomography scans, and Newtonian and Carreau–Yasuda models were used to capture salient rheological features of blood flow. Particularly in complex flow domains, results depended on the constitutive model. VSs developed all along the normal aorta, showing that a clear correlation between VSs and high wall shear stress (WSS) existed, and that VSs started to break up during late systole. In contrast, in the fusiform AAA, large VSs developed at sites of tortuous geometry and high WSS, occupying the entire lumen, and lasting over the entire cardiac cycle. Downward motion of VSs in the AAA was in the range of a few centimetres per cardiac cycle, and with a VS burst at that location, the release (from VSs) of shear-stress-activated platelets and their deposition to the wall was within the lower part of the diseased artery, i.e. where the thickest ILT layer is typically observed. In the saccular AAA, only one VS was found near the healthy portion of the aorta, while in the aneurysmatic bulge, no VSs occurred. We present a fluid-dynamics-motivated mechanism for platelet activation, convection and deposition in AAAs that has the potential of improving our current understanding of the pathophysiology of fluid-driven ILT growth.

Cross‐linking of two antiparallel vortex tubes

The detailed mechanisms in vortex cross‐linking are unveiled by adequately resolved, direct numerical simulation of two viscous vortex tubes. There are three characteristic phases: (i) inviscid induction followed by core flattening and stretching; (ii) bridging of the two vortices by accumulation of annihilated and then cross‐linked vortex lines; and (iii) threading of the remnants of the initial vortex pair in between the two bridges as they pull apart. These phases and the role of threading—along with bridging—in the mixing and the enstrophy cascade are explained, and it is shown that the mechanism is insensitive to asymmetries.