Fluid Dynamicists Research Articles

Two-phase flow in crust and mantle

The fortieth William Smith meeting of the Geological Society was a one-day lecture meeting held at Burlington House on 30 April 1986, with the William Smith Lecture presented by Professor R. K. O'Nions. The meeting was convened by Dr K. Coe (University of Exeter) and Professor D. McKenzie (University of Cambridge). The meeting’s theme ‘Two-phase flow in crust and mantle’ relates to the interaction between, and relative movements of, the ‘solid’ and ‘fluid’ phases within the crust and mantle. The terms solid and fluid, while being convenient terms to distinguish two such phases in upper levels of the crust, become increasingly imprecise at greater depths. It then becomes better to refer to differences between two phases of sharply contrasting viscosities; a matrix of high viscosity and an ‘intergranular’ component of much lower viscosity. The behaviour of the two phases can be described in terms of fluid dynamics, and application of this technique has much potential for producing major advances across the spectrum of the geological sciences. There is also potential for the field and laboratory based geologist to integrate with the theoretical fluid dynamicist for the advancement of the science. This set of papers aims to demonstrate this link and there is much to be gained from this thematic set for both types of specialist. This theme is particularly topical in the geological sciences at the present time with active interest in the field of fluid processes and fluid-rock interaction. The seven papers presented at the meeting form this thematic

Quantized Vortices in Superfluid Helium-4

When liquid helium-4 is cooled to 2.17 K it changes from an ordinary fluid to a superfluid somewhat similar in nature to superfluid helium-3 and to the electron fluid in superconductors. Extensive investigation over the last five decades has given us a highly refined phenomenological description of how superfluid He4 behaves, even though the underlying quantum theory is only partially understood. Much of the current research on superfluid He4 is part of a continuing effort to work out the implications of this phenomenological description, in the same way as classical fluid dynamicists are still working out the implications of the Navier-Stokes equations.

Internal Kinematics of Salt Diapirs

The internal structure of intrusive and extrusive salt bodies elucidates their external shape and the mechanism and history of diapiric emplacement--information relevant to petroleum exploration. Trace amounts of brine can act like heat to weaken salt and promote geologic creep by solution-transfer mechanisms. We compare natural strain markers in salt with the artificial markers used by fluid dynamicists: stream lines are the smooth flow paths followed by fluid particles; stream surfaces separate flow laminae and contain the stream lines. Grain-shape fabrics in salt anneal readily and have strain memories so short that lineations map the stream lines and foliations map the stream surfaces of the last stages of deformation. By contrast, larger structures, like folded beddi g, have much longer strain memories. As a result, multiple generations of tonguelike, recumbent flow folds formed by unsteady flow in the mother source layer rotate to upright sheath folds or spines in the stems of diapirs. Here they are constricted and refolded into steep curtain folds to form crescentic and other interference patterns visible in the roofs of salt mines. Mature diapirs can form crestal bulbs, which may be balloon or mushroom shaped and which potentially form larger petroleum traps than previously supposed. Screens of country rock may be entrained between the stem and peripheral overhanging lobes caused by episodic sedimentation.

The intrusion of fluid mechanics into geology

During the last few years, a number of fluid dynamicists, often in collaboration with geologists, have been investigating problems suggested by geology and creating the new field of geological fluid mechanics. The research has uncovered many new fluid-mechanical phenomena and the studies’ have ranged widely over theoretical contributions, laboratory experiments and confirmatory field observations. This paper presents an overview of part of the field, with a strong emphasis on the novel fluid-mechanical concepts. The presentation includes discussion of some of the effects of cooling and crystallization and the resulting convective motions, the flow of gravity currents at both high and low Reynolds number, and the erosion of solid retaining walls by hot, turbulent flows.

Retrospective

Charting a course toward an uncertain future is always a risky business, especially among shoals of fiscal restraint or national tragedy, and the prudent navigator is well advised to remember where he's been as he looks ahead. The ocean and space sciences are poised for grand joint adventures, but shrinking budgets and the lingering Challenger numbness are restrictive lee shores that must be considered when laying plans. To sharpen the focus on future choices, it may be helpful to glance in the geophysical rearview mirror and remember some of the challenges and opportunities of a different era.A quarter century is a long time, but many images from 25 years ago can still be recalled in crisp detail, like photographs in a scrapbook. In 1961, results from the International Geophysical Year (IGY) filled the pages of the Transactions of the American Geophysical Union, and the U.S. program of space exploration finally was underway with conviction. The Indian Ocean Expedition, conceived during the IGY, ushered in a new era of international oceanography. The TIROS III satellite beamed to earth fuzzy pictures of tropical storms and revealed the intricate writhings of the Gulf Stream. Forecasters and fluid dynamicists suddenly saw new horizons, and geophysical turbulence became a major topic at the IUGG Symposium in Marseilles, France. Papers with prescient themes were presented at the AGU Ocean Section meeting: June Pattullo (then at Oregon State College, Corvallis) on heat storage in the Pacific; Ferris Webster (then at Woods Hole Oceanographic Institution, Woods Hole, Mass.) on Gulf Stream meanders. Polar oceanography was well represented in AGU journals: Kenneth Hunkins (at what was then called the Lamont Geological Observatory, Palisades, N.Y.) described the Alpha Rise, discovered from a drifting Arctic ice island, and Edward Thiel (then at the University of Minnesota, Minneapolis) and his co‐workers discussed open ocean tides, gravimetrically measured from Antarctic ice shelves.

Von Kármán: Fluid Dynamics and Other Things

It is a pleasure to write about Theodore von Kármán. I am somewhat concerned, however, as I consider the audience for this article, many of whom are also fluid dynamicists: I can imagine quite a few old friends who knew von Kármán—perhaps as well as I—saying, “Oh, that isn't the way it really was.” Well, I can only say that what I am going to write about is the way I remember it. (There must be some kind of “statute of limitations” that says that when you get to a certain age—and I suppose I have—you're entitled to tell it the way you remember it, and let the chips fall where they may.)

Eddies, Waves, Circulation, and Mixing: Statistical Geofluid Mechanics

The complexity of geophysical flows, from scales of planetary radius down to scales of molecular diffusion, has long posed a fascinating and frustrat­ ing challenge to fluid dynamicists. It is not only a tantalizing theo­ retical question but also one of practical importance. Despite determined study, understanding of the oceans and atmosphere and, especially, the pre­ diction of responses to our trespasses upon these environments remain dangerously suspect. Much of the dynamical difficulty arises from nonlinear coupling across many scales of motion. Occasionally one refers to the atmo­ sphere or the ocean. Just as often it is remarked that these systems are not altogether turbulent if that adjective is taken to connote a condition that is highly chaotic, dissipative, diffusive, or possessed of whatever other attributes that one may assign to turbulence. Examples of wavelike phenomena abound but often are partly obscured by nonlinear interactions. Persistent, coherent, finite-amplitude flow features also are observed. Moreover there is the disturbingly nontrivial problem of distinguishing mean and fluctuating fields. Geophysical flows often are characterized by spectra, both in frequency and in wave number, that are continuous and red in character. Then the definition of a mean field becomes more or less

Combustion Physics: Turbulent combustion modelling

Turbulent combustion modelling as a major distinctive topic has been with us now for more than ten years. Increasingly it has attracted the interest of fluid dynamicists and applied mathematicians, groups without established interests in chemically reacting flows.

An update on non-stationary oblique shock-wave reflections: actual isopycnics and numerical experiments

Nonstationary oblique shock-wave reflections over compressive wedges in air and argon were investigated using infinite-fringe interferometric techniques. These allowed direct, continuous and accurate observations of the isopycnics (lines of constant density) of the flow field. The initial pressures for these experiments were made as high as possible (15 to 250 torr) in order to increase the number of isopycnics and to enhance their details and distribution along the wedge surface over a shock-Mach-number range 2.0 < Ms [les ] 8.7. Included in the study were two cases of regular reflection (RR) and one of each single Mach reflection (SMR), complex Mach reflection (CMR) and double-Mach reflection (DMR) for air, and one RR, SMR, CMR and DMR for argon. These particular cases, which we investigated previously in N2 and Ar using a finite-fringe technique, have been used by computational fluid dynamicists to check their finite-difference results against our experimental data. It will be shown that the isopycnic structure previously reported by us differs in detail, in most cases, from that of the present study. The major difference arises from the fact that it was only possible previously to obtain discrete points on isopycnics and along the wedge surface. Consequently, the results obtained before were not as accurate. Comparisons were made of actual wall-density distributions with numerical simulations of the density contours of the various flows obtained by a number of authors. Each numerical method displays its advantages and disadvantages in describing the details of the flow fields. The present experimental results for air are new. They are of great interest from a practical viewpoint. The experiments in argon were redone to provide better data for a gas free from real-gas effects in the range of initial conditions considered, in order to simplify the computations in the numerical simulations. Although the recent numerical simulations are better than those reported previously, additional efforts are required to improve the predictions of the shape, location and values of the isopycnics and other flow isolines in the various regions and along the wall, and to render the predictions free of computer ‘noise’. It is worth noting that real-gas effects did not play any significant role in determining the various wave systems in RR, SMR, CMR and DMR; a different claim was made in our previous work. Relaxation of nitrogen in air can be seen however, at the highest shock Mach numbers (Ms = 7.19 and 8.70), with relaxation lengths in good agreement with accepted predictions.

Improving Spectral Models By Unfolding Their Singularities

Abstract Maximally truncated spectral models have been used recently by fluid and atmospheric dynamicists to study nonlinear behavior of the governing partial differential system. However, too few external control parameters may be available in the truncated model to describe adequately the steady states near singular parameter values at which two or more stationary solutions meet. These missing parameters correspond in many cases to small but significant physical effects whose inclusion may be critically important for the model results to be realistic. We apply to truncated spectral models a recently developed contact catastrophe method that allows determination of the crucial physical effects that govern the steady states of a fluid system. Spectral systems of three different fluid flow models of interest in atmospheric science are considered. Two parameters are necessary for modeling Rayleigh-Benard convection. One represents the magnitude of the horizontal component, the other the magnitude of the ver...

Fluid Mechanics Research in 1986

In 1965, a book was published with the title Research Frontiers in Fluid Dynamics, edited by Raymond Seeger and G. Temple. It was intended to give a panoramic view of some exciting vistas in fluid dynamics. It covered the following areas: (1) High-speed aerodynamics; (2) magnetophydrodynamics (MHD); (3) physics of fluids (low or high density, low or high temperature, etc); (4) constitutive properties of fluids (viscosity, viscoelasticity, etc.); (5) oceanography and meterology; (6) astrophysical and planetary fluid mechanics; and (7) mathematical aspects and numerical aspects. A few of these areas, such as MHD, have blossomed and faded away within a short decade. Some others, such as high-speed aerodynamics, have reached maturity and hope to keep their momentum. In the intervening years, we have witnessed that a number of fields in fluid mechanics have revived from their old times into a new life; still, some have emerged with brand new growth. For instance, the subject of long waves has had a colorful development, with the result of improving our understanding of at least seven different physical phenomena, though originally the solitary water wave was its home base. Low Reynolds number flows have again received new stimuli from many needed applications such as aerosol physics, two-phase flows, rheology, geophysics of the earth interior, as well as micro and molecular biology. Oil exploration has motivated various aspects of marine-related research and development, giving ever-increasing activities in ocean engineering. The energy program, a new glamorous field by its own importance, has brought forth investigations of fluid mechanical problems pertaining to nuclear, geothermal, solar, wind, ocean wave, and other forms of energy sources. Riding on the waves of these broad movements that have carried us thus far, we now hope to forecast the future of fluid mechanics research in 1986. We may like to put the focus at a slightly different depth and ask: What will be the most significant areas of fluid mechanics that by 1986 will enjoy the best prospects of vigorous development, most rewarding not only to the fluid dynamicist but also to mankind, and by then, still offer the expectation of longevity into the 1990's? The task is almost as hard as to make a prophecy on what the political world will be in 1986.

Double-diffusive convection

In this paper we present a rather personal view of the important developments in double-diffusive convection, a subject whose evolution has been the result of a close interaction between theoreticians, laboratory experimenters and sea-going oceano-graphers. More recently, applications in astrophysics, engineering and geology have become apparent. In the final section we attempt to draw some general conclusions and suggest that further progress will again depend on a close collaboration between fluid dynamicists and other scientists.

Waves in Fluids

James Lighthill 1979 Cambridge: Cambridge University Press xv + 504 pp price £7.95 (paperback) During the last decade or so, Professor Lighthill has pioneered the involvement in biology of serious fluid dynamicists – in blood flow and the locomotion of fish and fowl. In this authoritative textbook he returns to a broad topic to which he has made numerous contributions throughout his career, and gives us the lucid exposition we have come to take for granted.

Domains and boundaries of non-stationary oblique shock-wave reflexions. 2. Monatomic gas

Interferometric data were obtained in the 10 cm × 18 cm hypervelocity shock tube of oblique shock-wave reflexions in argon at initial temperatures and pressures of nearly 300 °K and 15 Torr. The shock Mach-number range covered was 2 [les ] Ms [les ] 8 over a series of wedge angles 2° [les ] θw [les ] 60°. Dual-wavelength laser interferograms were obtained by using a 23 cm diameter field of view Mach-Zehnder interferometer. In addition to our numerous results, the available data for argon and helium obtained over the last two decades were also utilized. It is shown analytically and experimentally that in non-stationary flows six domains exist in the (Ms, θw) plane where regular reflexion (RR), single-Mach reflexion (SMR), complex-Mach reflexion (CMR) and double-Mach reflexion (DMR) can occur. The transition boundaries between these regions were all established analytically. The experimental results from different sources substantiate the present analysis, and areas of disagreement which existed in the literature are now clarified and resolved. It is shown that real-gas effects have a significant influence on the size of the regions and their boundaries. In addition, isopycnics (constant density lines) are given for the four types of reflexion, as well as the density distribution along the wedge surface. This data should provide a solid base for computational fluid dynamicists in comparing numerical techniques with actual experimental results.

Differential Rotation in Stars with Convection Zones

The topic I was originally assigned for this colloquium was “Generation of Non Thermal, Non Oscillatory Motions”. Being basically a fluid dynamicist, at first I thought this meant I was supposed to talk about the origin of motions which are not thermally driven, i.e., I should not talk about convection. But then I realized all that was meant was that I was to talk about bulk fluid motions, rather than the molecular “thermal” motion of stellar gas that defines its temperature. Obviously the original question was posed by a stellar spectroscopist! Having surmounted that small semantic hurdle, I began to think about all the ways circulatory motions might be generated in a star. All manner of fluid dynamical instabilities come to mind--not only convective instability, but also barotropic or inertial, baroclinic, Kelvin-Helmholz, Rayleiqh-Taylor, Goldreich-Shubert, Solberg-Hoiland, etc. The list is large, overlapping, I am sure confusing to an observer (and to many a theoretician). Then there are Eddington-Sweet currents, and several additional motions arising from the presence of magnetic fields--fields which give rise to magnetic buoyancy of flux tubes, and large collection of magnetohydrodynamic instabilities.

Wakes in Stratified Fluids

In this article we review research activities concerning wakes generated by moving bodies in stratified fluids. A wake is defined to be the non­ propagating disturbance produced by a moving body, and thus research activities concerning internal waves generated by a moving body are not included. Wakes have been of interest to many fluid dynamicists and engineers because they are a basic flow phenomenon associated with fluid flowing over an obstacle or with the movement of a natural or man-made body. The wake flow depends strongly on the Reynolds number RD == VoDjv, which is defined as the ratio of the inertia force to the viscous force. Here U 0 is the body speed, D is the characteristic length, e.g. the diameter of a cylinder or a sphere, and v is the kinematic viscosity of the fluid. For small Reynolds numbers, the viscous force dominates the inertia force and the wake is laminar. As the Reynolds number increases, the wake becomes unstable and a regular flow pattern, such as Karman's vortex street in the wake of a cylinder, can be observed. At still higher Reynolds numbers, the flow pattern becomes irregular and a turbulent flow is formed. Books written by Townsend (1956), Hinze (1959), and Schlichting ( 1960) can be referred to for further information about wakes. When the fluid is stratified thermally or with foreign additives, such as salt, a gravitational force, in addition to inertia and viscous forces, is exerted on the flow. A stratified fluid occurs very commonly in the

Atmospheric environment — The next twenty years

In recent years the problems posed by air pollution have been tackled by people who previously had little in common… As research in air pollution proceeds, scientists become educated in related disciplines: the engineer and chemist learn some meteorology, the fluid dynamicist some medicine; all become aware of the associated economic and legislative problems… There has until recently been much emphasis given to propaganda designed to create a climate of opinion in which effective action can be taken to reduce pollution. But more scientific investigations are required to define precisely the mechanisms and effects of pollution, and to discover ways of preventing it, otherwise legislation may be misguided. At the same time, scientists have to realize that the pollution is produced as a result of very convenient ways of using fuel and of very profitable industrial processes and, in thinking of remedies, they must be conscious of economic considerations. The confidence that this journal can be valuable to its various readers arises from a consciousness of a community of interest and of a desire to learn from one another the importance and relevance of one's own studies in the broader field. The journal's justification in a world where scientists have difficulty, in keeping abreast of the literature is not only that it will be a point of convergence for publication and discussion of research, but that it can be a focus of thought on air pollution which is now growing into a branch of applied science in its own right.

Measurement of vorticity in the surface layer using an acoustic echo sounder array

The earth's atmospheric surface layer is usually defined as that region of the lower atmosphere (generally below about 10 m above the earth's surface) where surface friction causes vertical fluxes of heat, moisture and momentum to be constant with height. Within the surface layer, either in response to surface friction or to the atmosphere above, horizontal circular eddies often develop. These circular motions may provide the source of rotation for dust devils so often seen on hot and dry days particularly in desert regions. Also, at larger scales ( ∼ 1 km in diameter ) regions of warm and therefore buoyant upward moving air, called thermal plumes, may acquire rotation. These plumes may extend from the earth's surface to more than a kilometer in height on a warm afternoon. Fluid dynamicists quantify this horizontal rotation with a parameter known as the vertical component of vorticity. Vorticity is very difficult to measure in the earth's atmosphere at scales of close to a kilometer because the calculation involves wind-speed differences over horizontal distances of about 500 m. The winds must be measured quite accurately because the differences can be quite small and, therefore, the errors in these measurements are often quite large. This work describes a method of measuring vertical vorticity at scales down to 500 m using an array of three acoustic sounders about 2 m above the earth's surface which overcomes some of the accuracy problems mentioned above. We relate these vorticity measurements to other atmospheric parameters and compute temporal spectra of these quantities to help explain the relationship between vorticity, thermal plume activity, and the smaller-scale dust devils.

Colliding heavy ions: Nuclei as dynamical fluids

Heavy ion experiments are already enriching nuclear science with a tapestry of new phenomena which require explanation. In response, theoretical nuclear physics is rapidly expanding its insights to encompass these new observations, especially those concerned with the macroscopic aspects. Preliminary theoretical studies already suggest that the dynamical nuclear fluid must sometimes be considered viscous, compressible, and/or rotational, if its microscopic properties are to be encompassed. These and some threads already well placed in the picture will be discussed. Other reasons will be cited to support the expectation that theoretical nulear macroscopists may more and more come to be fluid dynamicists who specialize in those few thousand fluids called nuclei. Three such reasons are (a) the promised richness of their structure as dynamical fluids, (b) their unique prospect, among all the objects of modern physical science, of allowing a complete microscopic, as well as a phenomenological macroscopic, description, and (c) the possible overflow of such nuclear implications into classical fluid theory, from the viewpoint of which the nuclear heavy ion data are a significant novelty.

Fluid Mechanics of Combustion Symposium Issue

Perhaps one of the most significant of recent changes in the career of the fluid dynamicist is the expansion of his activity into diverse fields of application. In years past, his efforts were concentrated in such obvious areas as the design and conceptual development of turbomachiner y, vehicle aerodynamics, and fluid conveying systems. However, the change in this situation is obvious when one considers the recent contributions of bioengineers to the knowledge of the functioning of the cardio­ vascular circulatory system or the inroads made in the field of logic and control systems by fluidic devices. Most of the tech­ nology applied in developing these concepts was not new to the fluids engineer but rather was matured and applied because the necessary social and technical environment had evolved. Another such area of development is the field of combustion related fluid dynamics. Combustion has been traditionally a part of the science of thermochemistry, but, at the same time, an empirical art in design, involving cut and try methods and drawing heavily from prior experience and evolutionary knowhow. As a consequence, the combustion process was considered at one time to be well under control when these devices were adjusted to the conditions where so called clean burning was observed. Recent demands for the conservation of fuels and the association of atmospheric pollution with undesirable byproducts of combustion or the products of inefficient combustion has forced a reassessment of the state of the art and a search for means to improve the combustion process. When one examines the sequence of events occurring in any combustion process, be it in a furnace, a gas turbine combustor, a reciprocating engine, or any other device, it is apparent that fluid mechanics plays a critical part. The initial atomization and dispersion of fuel, stabilization and propagation of flames, the enhancement of mixing and stirring of the reacting species, all heretofore estab­ lished by empiricism become areas of increasing concern for the fluids engineer.