The evolution of hairpin conditional eddies is being studied by direct numerical simulation. It is found that eddies of sufficient strength are capable of autogeneration creating replicas of themselves which can eventually form long packets of hairpins that fill the wall layer.

A pulsed laser instrument is being used to measure instan- taneous velocity fields in low and moderate Reynolds number turbulent flow in channels, pipes, and boundary layers. The structure in these flows is being studied as a function of Reynolds number, and the two-point spatial correlation is being measured. High-resolution techniques are being employed to examine the mechanisms that create the logarithmic layer and the outer wake region.

The structure of thermal convection is being studied by particle-image velocimetry techniques in which two-dimensional velocity vector fields in a planar ``slice'' of the flow are measured. Of particular interest are the structure at high Rayleigh number and measurement of two-point spatial correlations in convection between hot and cold horizontal plates, convection under a stably stratified layer, and convection over nonuniformly heated horizontal surfaces.

A pulsed Nd:YAG system has been developed to record holographically sequential images of fine particles in air for the purpose of measuring three-dimensional vector fields in a volume. The system is being applied to studies of the structure of turbulence in pipe flow and in internal combustion.

The particle-image velocimeter (PIV) technique makes simultaneous measurements of fluid velocity vectors at several thousand points in a fluid flow and provides instantaneous flow patterns. New methods of interrogation and image analysis are being investigated. Systems under development include a new interrogation approach that yields superresolution and a stereo method for 3-D vectors.

Nonequilibrium in a turbulent boundary layer is studied by suddenly imposing transverse shear. The change in shear occurs either at the wall, where the small scales are affected first, or at the outer region of the boundary layer, where the large scales are affected first. The response of the structure of the eddies to the change in surface conditions is being observed by particle-image velocimetry.

A new approach to fluid advection is presented which utilizes the Thurston-Nielsen classification theorem. The prototypical problem of stirring of fluid confined to a disk by a finite number of stirrers is considered. A key role is played by the representation of a given stirring action as a braid in a (2+1)-dimensional space-time made up of the flow plane and a time axis. An experiment using a viscous fluid stirred by three rods is performed to illustrate the practical applicability of the theoretical developments.

We are exploring various vortex systems in which the vorticity is concentrated in well-defined ``coherent structures'' as models of turbulent flow situations. These include forced shear layers and wakes, both in two and three dimensions. We are also exploring certain families of analytical solutions that may provide benchmarks for computer simulation codes. The hope is that these models will provide insight into turbulent flows not easily obtained by conventional Reynolds stress models.

The topology and three-dimensional structure of foams are being studied using both experiments and numerical simulations, with the aim of building realistic models of their behavior, e.g., how they react to bulk forces and how their coarsening proceeds in time. Thin-film soap foams are used for experimental examination of the internal structure of several layers of foam cells. Direct observation with video cameras can follow the coarsening and the associated change in topology. Computer simulations of three-dimensional foams present an algorithmically challenging and computationally taxing problem, since the constraints which govern the growth of 2-D foams cannot be used in 3-D.

Flow along a corner formed by the intersection of two solid surfaces, such as a wing-body junction, has been experimentally observed to be more unstable than the corresponding flow over a single flat surface. In this study, a self-similar mean flow in the corner region is obtained through the boundary-layer approximation. The stability of this mean flow is investigated through linear stability analysis for both inviscid and viscous modes. The resulting eigenvalue problems are very large, and efficient computational algorithms involving Arnoldi iteration and polynomial filtering are currently under investigation. Nonlinear evolution of these linearly unstable disturbances will be investigated through direct numerical simulations.

Here we focus on the instability mechanisms responsible for the complex nature of flow behind two-dimensional cylinders at moderate Reynolds numbers. Using linear and weakly nonlinear stability analysis, we investigate the Hopf bifurcation and onset of periodic shedding behind circular and elliptic cylinders. A Floquet stability analysis will be used to study the secondary instability and associated onset of three-dimensionality in the wake. Direct numerical simulations of the cylinder wake have provided a detailed picture of the self-sustained autogeneration of three-dimensional streamwise vortices. Subsequent spanwise subharmonic instability and associated period-doubling mechanisms are currently under investigation.

Here we consider two basic mechanisms for enhanced heat transfer in louvered fin geometries: periodic tripping of the viscous and thermal boundary layers at an interrupted fin surface and periodic unsteadiness in the flow due to separation by the fin geometry. The need to account for complex heat-exchanger geometry and at the same time resolve the range of length and time scales associated with unsteady flows poses computational challenges. Here we adopt a novel numerical methodology that will enable computation of unsteady flow in a complex geometry. Simultaneous experimental verification of numerical results is also underway.

There are many situations in which it is desirable to control turbulent flows. Two obvious examples are the reduction of drag and the enhancement of mixing of chemical reactants. One promising technique is to take advantage of the extreme sensitivity of chaotic systems, such as turbulence, to disturbances. In particular, one finds a desirable but unstable periodic behavior of the chaotic system and designs a control scheme to stabilize this be havior. Such techniques have been used successfully for simple dynamical systems. In this research they are being applied in a systematic way to fluid turbulence for the first time.

Large-eddy simulation (LES) is a promising technique for turbulence prediction in which the largest, most energetic turbulent eddies are simulated while the effects of smaller-scale turbulence is modeled. New techniques for performing such simulations are being developed based on the formalism of stochastic estimation and on concepts from chaotic dynamical systems. In this new approach, it is possible to optimize both the subgrid model and the filtering operation by which the large scales are defined. Further, one can determine how accurate it is possible for an LES to be. This new approach should allow LES to fulfill its great promise as an accurate and reliable engineering prediction tool.

Most fundamental work in the modeling of turbulence has been done for incompressible turbulence. In this research, we extend these incompressible models to the compressible case using low-Mach-number asymptotics. Such approximations can be valid even in quite large Mach-number flows because the turbulence in these flows is generally at much lower Mach numbers. Thus, by treating the mean flow as fully compressible and the turbulence as only weakly compressible, an approximation valid to very large Mach numbers can be obtained. This asymptotic analysis will be used to develop a rational technique for applying ideas from incompressible turbulence modeling to compressible flows.

Despite the importance of compressibility in engineering applications, compressible turbulence is not as well understood as its incompressible counterpart. In particular, there are uncertainties as to exactly what the effects of compressibility on turbulence are. Direct numerical simulation provides an opportunity to address these uncertainties because it allows us to use diagnostics that are not possible in experiments. The simulations performed here will be used to distinguish between compressibility and variable property (i.e., density and viscosity) effects, including fluctuating properties.

Models of axisymmetric cylindrical plumes are being developed for turbulent thermal convection using asymptotic and scaling analyses. These models are based on the restrictions of infinite Prandtl number and steady-state conditions. The models will be extended to arbitrary Prandtl number, unsteady cases, and to nonaxisymmetric flow conditions and will be compared with the available experimental observations.

Renormalization group theory and other modeling techniques are being developed for nonhomogeneous turbulence. The goal is to develop reliable and rational turbulence models that can be used for large-eddy simulations of complex nonhomogeneous turbulence problems.

Effects of roughness elements of arbitrary shape, placed on the boundary of a layer of fluid, on the flow structures and instabilities are studied by analytical and computational methods. Certain conditions are determined under which the preferred flow structure is controlled and the heat flux is enhanced by the surface corrugation effects.

This research concerns instabilities that exist in wall-bounded turbulent shear flows and their roles and origins in relation to streaks and large structures in such flows. Studies are based on both analytical and computational methods.

Effects of crystallization on nonlinear convection in a normal or high-gravity binary-alloy melt are investigated. Emphasis is given to examination of the mushy layer near the solidification front. Finite-amplitude effects are studied under certain controlling processes by analytical and computational techniques. The models include the basic physical conditions that are of interest in the field of materials processing.

This research involves studies of the fundamentals of the cross-flow instability mechanism and, in particular, the mechanism of flow instability in the leading-edge region of a swept wing. Nonlinear, higher instability, and wave-interaction regimes are studied by both computational and asymptotic techniques.

Formal concepts from probability theory are being used to readdress a now classical problem in averaging of Navier-Stokes turbulent fields. The resulting theory has a structure similar to those originating from renormalization-group approaches. The present approach, however, relies on a rational theory of conditional averaging. Work is starting on applications to heterogeneous media, such as randomized reactive beds, and to the use of new theoretical tools that we have developed for the turbulence problem.

An AASERT grant from AFOSR supports an effort to compute reacting compressible flow. Previous efforts have developed a new high-resolution code called AXS, which can simulate two-dimensional, time-dependent reacting compressible flow. We are engaged in setting up AXS to simulate detonation channel flows and flows past blunt bodies to compare with careful theoretical work in detonation stability.

An experimental apparatus is being devised to study the effects of buoyancy forces on the vortical structures in a stably stratified fluid. A stably stratified, three-layer water channel will be constructed and instrumented with video particle-image velocimetry. Laser-induced fluorescence will also be used to study the baroclinic generation of vorticity in two parallel shear layers. The inhibition of mixing will be quantified in relation to the stratification strength and shear rates. A uniformly stratified shear channel will also be constructed, based on a new design, employing a real-time mixing manifold.

A partially filled circular cylinder is rotated about its horizontal axis of symmetry. The fluid is pulled up the sides of the cylinder, as in the rotomolding manufacturing process. A complicated interplay between gravity, inertial, and viscous forces, characterized by the cylinder rotation rate, volume filling ratio, and viscosity of the fluid, leads to a number of different flow regimes, some exhibiting instabilities. Experiments performed over a wide range of parameter space are aimed at mapping out stable and unstable regimes to help with the design of manufacturing protocols leading to a uniform coating on the inside of the cylinder. Special attention is being paid to the hysteresis in the process.

Multipoint measurements in homogeneous turbulence generated in a wind tunnel are being used to study the statistical structure of turbulent quantities. The preferential location of the small-scale dissipative structures in the turbulent field are being sought by conditional averages of large-scale flow features, such as regions of large rotation or streamwise shear fronts. The aim of the research is to develop efficient models to simulate the intermittent nature of the extreme events observed in high-Reynolds-number turbulence.

The fluid dynamics of the rapid distortion of a fluid drop impacting either a solid wall or a thin layer of fluid is studied. High-speed flash photography demonstrates the formation of a thin jet of fluid being ejected from the drop along the surface. The speed of this jet and its breakup into a fingering pattern is being studied systematically. The inertia of the fluid, its viscosity, the surface tension, and the wettability of the surface all have important effects and make theoretical analysis very difficult. The theoretical approach is based on perturbation, similarity, asymptotic, and characteristic methods.

Voids are processing defects that significantly degrade the strength of polymer composites. Their control and elimination during processing is extremely important. How they nucleate and when they grow during processing are not well known. A transparent test cell that allows observation of void growth during processing is used to investigate the void growth behavior of expoxies during curing. A video record of the cure cycle is made, and an image analyzer is used to obtain void distributions and diameters. A refined void-growth model is correlated to the experimental data.