Annual Review of Fluid Mechanics - Volume 31, 1999

This article reviews the transport properties of coherent vortices in rotating barotropic flows. It is shown that vortices induce regular Lagrangian motion inside their cores and are highly impermeable to inward and outward particle fluxes. Passive tracers can be trapped inside vortex cores for long times and are transported by the vortex motion over large distances. Absolute dispersion in vortex-dominated flows is discussed by studying particle dynamics in 2D turbulence, point-vortex systems, and subsurface float trajectories in the ocean. Finally, it is shown that anticyclonic coherent vortices in cyclonically rotating reference frames can concentrate heavy impurities (e.g. dust grains) in their cores. This process may play an important role in the formation of planetesimals in the early solar nebula.

Nuclear magnetic resonance (NMR) measurements of flowing materials are reviewed with emphasis on applications to multiphase flows. After a brief presentation of NMR physics, experimental considerations related to flow measurements are discussed. Both imaging and non-imaging NMR as well as topics such as Earth's field NMR and rapid imaging are covered. Specific topics that follow are tagging and time-of-flight, phase measurement of velocity, diffusion, turbulence, and calibration and validations. Finally, recent applications are reviewed in the areas of sedimentation, suspension flows in Couette and pipe geometries, rheometers and viscometers, liquid-liquid multiphase flows, porous media flow, granular flows, and turbulence.

The current state of the art in computational aerodynamics for whole-body aircraft flowfield simulations is described. Recent advances in geometry modeling, surface and volume grid generation, and flow simulation algorithms have led to accurate flowfield predictions for increasingly complex and realistic configurations. As a result, computational aerodynamics has emerged as a crucial enabling technology for the design and development of flight vehicles. Examples illustrating the current capability for the prediction of transport and fighter aircraft flowfields are presented. Unfortunately, accurate modeling of turbulence remains a major difficulty in the analysis of viscosity-dominated flows. In the future, inverse design methods, multidisciplinary design optimization methods, artificial intelligence technology, and massively parallel computer technology will be incorporated into computational aerodynamics, opening up greater opportunities for improved product design at substantially reduced costs.

In this review, we describe the dynamics and thermodynamics of liquid and vapor flow through hot fractured rock. Such flows occur in geothermal reservoirs and have important implications for geothermal power generation; we describe both forced flows associated with liquid injection into such systems, and natural convective flows associated with the vertical heat transfer through such systems. First we focus on permeable media and describe the heat transfer of single-phase liquid or vapor flow through a medium of different temperature. Then we consider the dynamics and thermodynamics of a liquid front as it advances into a superheated region and boils. The morphological stability of such an interface is discussed, and we describe conditions under which the interface breaks down to form a two-phase zone between the liquid and vapor. We next examine the heat transfer and boiling in gravity-driven flows advancing through a superheated permeable rock, identifying that at large times such currents asymptote to a family of similarity solutions. In the second part of the review, we describe the analogous heat transfer and boiling processes associated with liquid flow along a fracture embedded in an impermeable rock. We describe some simple asymptotic solutions for the temperature distribution in the bounding rock, which reveal that in the fracture, a two-phase boiling region develops between the purely liquid and purely vapor zones. Model predictions are successfully tested with laboratory experiments. In the final section of the review, we briefly discuss natural convective flows, illustrating how single-phase and two-phase convective regions interact and in some cases produce instability.

Natural ventilation of buildings is the flow generated by temperature differences and by the wind. The governing feature of this flow is the exchange between an interior space and the external ambient. Although the wind may often appear to be the dominant driving mechanism, in many circumstances temperature variations play a controlling feature on the ventilation since the directional buoyancy force has a large influence on the flow patterns within the space and on the nature of the exchange with the outside. Two forms of ventilation are discussed: mixing ventilation, in which the interior is at an approximately uniform temperature, and displacement ventilation, where there is strong internal stratification. The dynamics of these buoyancy-driven flows are considered, and the effects of wind on them are examined. The aim behind this work is to give designers rules and intuition on how air moves within a building; the research reveals a fascinating branch of fluid mechanics.

Noncircular jets have been the topic of extensive research in the last fifteen years. These jets were identified as an efficient technique of passive flow control that allows significant improvements of performance in various practical systems at a relatively low cost because noncircular jets rely solely on changes in the geometry of the nozzle. The applications of noncircular jets discussed in this review include improved large- and small-scale mixing in low- and high-speed flows, and enhanced combustor performance, by improving combustion efficiency, reducing combustion instabilities and undesired emissions. Additional applications include noise suppression, heat transfer, and thrust vector control (TVC).

The flow patterns associated with noncircular jets involve mechanisms of vortex evolution and interaction, flow instabilities, and fine-scale turbulence augmentation. Stability theory identified the effects of initial momentum thickness distribution, aspect ratio, and radius of curvature on the initial flow evolution. Experiments revealed complex vortex evolution and interaction related to self-induction and interaction between azimuthal and axial vortices, which lead to axis switching in the mean flow field. Numerical simulations described the details and clarified mechanisms of vorticity dynamics and effects of heat release and reaction on noncircular jet behavior.

The research on noncircular jets has also led to technology transfer. A topic that started as an academic curiosity—an interesting flow phenomenon—subsequently has had various industrial applications. The investigations reviewed include experimental, theoretical, numerical, and technological aspects of the subject.

Magnetic fields can be used to melt, pump, stir, and stabilize liquid metals. This provides a nonintrusive means of controlling the flow of metal in commercial casting and refining operations. The quest for greater efficiency and more control in the production of steel, aluminum, and high-performance superalloys has led to a revolution in the application of magnetohydrodynamics (MHD) to process metallurgy. Three typical applications are described here, chosen partially on the basis of their general interest to fluid dynamicists, and partially because of their considerable industrial importance. We look first at magnetic stirring, where a rotating magnetic field is used to agitate and homogenize the liquid zone of a partially-solidified ingot. This is a study in Ekman pumping. Next, we consider magnetic damping, where an intense, static magnetic field is used to suppress fluid motion. In particular, we look at the damping of jets, vortices, and turbulence. We conclude with a discussion of the magnetic destabilization of liquid-liquid interfaces. This is of particular importance in aluminum production.

This review deals primarily with the bifurcation, stability, and evolution of gravity and capillary-gravity waves. Recent results on the bifurcation of various types of capillary-gravity waves, including two-dimensional solitary waves at the minimum of the dispersion curve, are reviewed. A survey of various mechanisms (including the most recent ones) to explain the frequency downshift phenomenon is provided. Recent significant results are given on “horseshoe” patterns, which are three-dimensional structures observable on the sea surface under the action of wind or in wave tank experiments. The so-called short-crested waves are then discussed. Finally, the importance of surface tension effects on steep waves is studied.

We discuss the thickness of the liquid layer entrained by a solid drawn out of a bath, focusing on the case where the solid is a fiber or a wire. Slow withdrawals out of a pure or a complex fluid are described as well as quick coatings. We specify the general laws of entrainment and stress the cases where the fiber curvature plays a role. We finally give an overview on the further evolution of the coated film.

An overview of preconditioning for the steady-state compressible inviscid fluid dynamic equations is presented. Extensions to the Navier-Stokes equations are also considered. These preconditioners are necessary for many algorithms in order to have the correct behavior at low speeds and to converge to the solution of the incompressible equations as the Mach number goes to zero. In addition, the preconditioning accelerates the convergence to a steady state for problems in which a significant portion of the flow is low speed. This low speed preconditioner can be combined with Jacobi and line preconditioners to damp high frequencies at all speeds. This is necessary for use with multigrid methods. Such combined methods are also better at accelerating problems with high aspect ratios. Details of the implementation are presented including several different variants for the preconditioning matrix.

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.

A review of planetary-entry gas dynamics is presented. Evolution of a blunt-body flowfield from a free molecular flow environment to a continuum environment is described. Simulations of near-wake flow phenomena, important for defining aerobrake payload environments, are also discussed. Some topics to be highlighted include aerodynamic coefficient predictions with emphasis on high-temperature gas effects; surface heating and temperature predictions for thermal protection system (TPS) design in a high-temperature, thermochemical nonequilibrium environment; and thermochemical models required for numerical flow simulation. Recent applications involving atmospheric entry into Jupiter (Galileo), Mars (Pathfinder and Global Surveyor), and a planned mission in which dust from the tail of a comet will be returned to Earth (Stardust) will provide context for this discussion.

We illustrate how cogent visiometrics can provide peak insights that lead to pathways for discovery through computer simulation. This process includes visualizing, quantifying, and tracking evolving coherent structure morphologies. We use the vortex paradigm (Hawley & Zabusky 1989) to guide, interpret, and model phenomena arising in numerical simulations of accelerated inhomogeneous flows, e.g. Richtmyer-Meshkov shock-interface and shock-bubble environments and Rayleigh-Taylor environments. Much of this work is available on the Internet at the sites of my collaborators, A Kotelnikov, J Ray, and R Samtaney, at our Vizlab URL, http://vizlab.rutgers.edu/vizlab.html.

The paper reviews striking features of swirling flows—collapse, swirl generation, vortex breakdown, hysteresis, and axisymmetry breaking—and the mechanisms involved with the help of conical similarity solutions of the Navier-Stokes equations. The strong accumulation of axial and angular momenta, observed in tornadoes and flows over delta wings, corresponds to collapse, i.e. the singularity development in these solutions. Bifurcation of swirl explains the threshold character of swirl development in capillary and electrovortex flows. Analytical solutions for fold catastrophes and hysteresis reveal why there are so few stable states and why the jump transitions between the states occur—features typical of tornadoes, of flows over delta wings, and in vortex devices. Finally, the divergent instability explains such effects as the splitting of a tornado and the development of spiral branches in tree and near-wall swirling flows.