Showing papers in "Annual Review of Fluid Mechanics in 1994"

Dynamics of Drop Deformation and Breakup in Viscous Fluids

Abstract: This article describes the dynamics of drop deformation and breakup in viscous flows at low Reynolds numbers. An attempt has been made to bring together a wide range of studies in the drop deformation literature, as well as to provide a large number of references to potential applications. In particular, a summary is provided of experimental, numerical, and theoretical investigations that examine drop breakup in externally­ imposed flows, e.g. uniaxial extensional fluid motion or more complicated time-periodic flows. For well-characterized flow conditions that lead to breakup, the effects of flow and material parameters on the drop size distribution are summarized. Also, a short discussion is given of the stability of the shapes of translating drops. The subject of deformation of neutrally buoyant drops in viscous shear flows at low particle Reynolds numbers was summarized by Acrivos ( 1983) and was reviewed in this series by Rallison ( 1 984). The Acrivos and Rallison papers present (a) theoretical descriptions of steady, nearly spheri­ cal shapes and steady, long slender shapes, (b) a description of efficient boundary integral numerical methods, and (e) a summary of the experi­ mental work performed prior to 1984. As documented in these review articles, many of the important ideas necessary for understanding drop

High Rayleigh Number Convection

Abstract: Turbulent convection exemplifies many of the startling aspects of turbulent flows that have been uncovered in the past two decades, but frequently exhibits a novel twist. Thus, as in the case of free shear flows, convection can organize into large-scale vortical structures, but these then react back in subtle ways on the boundary layers which ultimately sustain them. Thermal plumes are a coherent mode of heat transport, analogous to boundary layer bursts, yet their overall effect can be surprisingly close to the structureless predictions of mixing length theory. Convection cells are closed, which facilitates their experimental control, but fluctuations never exit and there is a dynamically determined bulk forcing. While the single­ pass mode characteristic of wind tunnel experiments seems simpler, the convection cell is, in ways to be discussed, more constrained. This review aims to familiarize the turbulence researcher with con­ vergent lines of investigation in convection and also to remind those working in convection that turbulence is not a new subject. To situate convection within the gamut of other turbulent flows, let us by way of introduction contrast the directions in which convection has developed with research on the turbulent boundary layer. From the onset of convection up to Rayleigh numbers Ra � 1 0 times critical, there is a great wealth of information about flow structures (which can be visualized from above), and their relative stabilities (Busse 198 1 ) . Turbulence, in the sense of many coupled modes, and not just sensitive dependence on initial conditions, can arise for low Ra in large aspect ratio

Lagrangian PDF Methods for Turbulent Flows

Abstract: Lagrangian Probability Density Function (PDF) methods have arisen the past 10 years as a union between PDF methods and stochastic Lagrangian models, similar to those that have long been used to study turbulent dispersion. The methods provide a computationally-tractable way of calculating the statistics, of inhomogeneous turbulent flows of practical importance, and are particularly attractive if chemical reactions are involved. The information contained at this level of closure--equivalent to a multi-time Lagrangian joint pdf--is considerably more than that provided by moment closures. The computational implementation is conceptually simple and natural. At a given time, the turbulent flow is represented by a large number of particles, each having its own set of properties--position, velocity, composition etc. These properties evolve in time according to stochastic model equations, so that the computational particles simulate fluid particles. The particle-property time series contain information equivalent to the multi-time Lagrangian joint pdf. But, at a fixed time, the ensemble of particle properties contains no multi-point information: Each particle can be considered to be sampled from a different realization of the flow. (Hence two particles can have the same position, but different velocities and compositions.) It is generally acknowledged (e.g. Reynolds 1990) that many different approaches have important roles to play in tackling the problems posed by turbulent flows. Each approach has its own strengths and weaknesses.

Physical mechanisms of laminar-boundary-layer transition

Abstract: The problem of turbulence onset in shear flows has attracted the attention of investigators for more than a century. Despite its complexity, interest in the laminar-turbulent transition has increased during the past few decades owing to i ts importance in both fundamental and applied aspects of fluid mechanics . The physical mechanisms of the transition phenomenon depend essen­ tially on the specific type of flow and the character of environmental disturbances. For boundary-layer flows two main classes of transition are known (Morkovin 1 968, 1 984; Morkovin & Reshotko 1 990). The first of them is connected with boundary-layer instabilities (described initially by linear stability theories), amplification, and interaction of different instability modes resulting in the laminar flow breakdown. This class is usually observed when environmental disturbances are rather small. The second class of transition, usually called bypass, is connected with "direct" nonlinear laminar-flow breakdown under the influence of external dis­ turbances . This is observed when high enough levels of environmental perturbations (free-stream disturbances, surfacc roughness, etc) are pre­ sent. This article focuses on the first class of transition because of its fun­ damental and practical importance in problems involving moving vehicles

Double diffusion in oceanography

Abstract: The modern study of double-diffusive convection began with Melvin Stern's article on "The Salt Fountain and Thermohaline Convection" in 1960. In that paper, he showed how opposing stratifications of two component species could drive convection if their diffusivities differed. Stommel ct al (1956) had earlier noted that there was significant potential energy available in the decrease of salinity with depth found in much of the tropical and subtropical ocean. While they suggested that a flow (the salt fountain) would be driven in a thermally-conducting pipe, it was Stern who realized that the two orders of magnitude difference in heat and salt diffusivities allowed the ocean to form its own pipes. These later came to be known as "salt fingers." Stern also identified the potential for the oscillatory instability when cold, fresh water overlies warm, salty water in the 1960 paper, though only in a footnote. Turner & Stommel (1964) demonstrated the "diffusive-convection" process a few years later. From these beginnings in oceanography over three decades ago, double diffusion has come to be recognized as an important convection process in a wide variety of fluid media, including magmas, metals, and stellar interiors (Schmitt 1983, Turner 1985). However, it is interesting to note that about one hundred years before Stern's paper, W. S. Jevons (1857) reported on the observation of long, narrow convection cells formed when warm, salty water was introduced over cold, fresh water. He correctly attributed the phenomenon to a difference in the diffusivities for heat and

Wave evolution on a falling film

Abstract: Since the pioneering experiment by the father-son team of the Kapitza family during their house arrest in the late forties (Kapitza & Kapitza 1949), wave evolution on a falling film has intrigued many researchers. One of its main attractions is its simplicity-it is an open-flow hydrodynamic instability that occurs at very low flow rates. It can hence be studied with the simplest experimental apparatus, an obviously important factor for the Kapitzas. Yet, it yields a rich spectrum of fascinating wave dynamics, including a very unique and experimentally well-characterized sequence of nonlinear secondary transitions that begins with a selected monochromatic disturbance and leads eventually to nonstationary and broad-banded (in both frequency and wave number) "turbulent" wave dynamics. (Turbu­ lence here is used interchangeably with irregular spatio-temporal fluc­ tuations.) While this transition to "interfacial turbulence" or "spatio­ temporal chaos" seems to be quite analogous to other classical instabilities at first glance, there are subtle but important differences that have recently come to light. The pertinent nonlinear mechanisms behind these secondary transitions are the focus of the present review. We shall be mostly concerned with transitions on a free-falling vertical film. Wave dynamics on an inclined plane is quite analogous to the vertical limit and most experiments and theories have focused on the latter. For the vertical film, the problem is defined by two independent dimensionless parameters and we prefer the Russian convention of using the Reynolds

Vortex Interactions with Walls

Abstract: Situations where an effectively irrotational freest ream contains regions of concentrated vorticity are common in external aerodynamics, where vortices are known to play an important role in the flight of modern helicopters (Carr 1988) and aircraft (Cunningham 1989, Mabey 1989). Vortices may arise as a consequence of shedding from some upstream surface or near certain three-dimensional boundary geometries that act to promote vortex formation. Examples of the former type of vortex gen­ eration include: 1. vortices that trail from the tips of airfoils (Harvey & Perry 1971) and control surfaces on submarines (Lugt 1983), 2. transverse vortices shed from maneuvering airfoil surfaces and helicopter blades in a process known as dynamic stall (McCroskey 1982, Francis & Keesee 1985, Carr 1988), and 3. shedding from stationary obstacles. Geometry-induced creation can occur in any situation where a flow along a wall approaches a surface-mounted obstacle; examples include: 1. airframe features such as wing/body junctions, 2. conning towers on submarines, and 3 . computer chips mounted on electrical circuit boards. Similar geometries are en-

The Physics of Supersonic Turbulent Boundary Layers

Abstract: When a vehicle travels at Mach numbers greater than one, a significant temperature gradient develops across the boundary layer due to the high levels of viscous dissipation near the wall. In fact, the static-temperature variation can be very large even in an adiabatic flow, resulting in a low­ density, high-viscosity region near the wall. In turn, this leads to a skewed mass-flux profile, a thicker boundary layer, and a region in which viscous effects are somewhat more important than at an equivalent Reynolds number in subsonic flow. Intuitively, one would expect to see significant dynamical differences between subsonic and supersonic boundary layers. However, many of these differences can be explained by simply accounting for the fluid-property variations that accompany the temperature

Dynamics of Coupled Ocean-Atmosphere Models: The Tropical Problem

Abstract: Large-scale ocean-atmosphere interaction plays a crucial role in natural climate variability on a broad range of time scales and in anthropogenic climate change. The development of coupled ocean-atmosphere models is thus widely regarded as essential for simulating, understanding, and predicting the global climate system. Although these efforts typically benefit from years of previous work with atmospheric and oceanic models, coupling the two components represents a major step because of the new interactions introduced into the system. These can produce new phenomena, not found in either medium alone, the mechanisms for which present exciting theoretical problems. The removal of artificial negative feedbacks

Premixed combustion and gasdynamics

Abstract: Combustion science is a fascinating field of non equilibrium phenomena in complex systems. Although combustion processes are very diverse in nature, nevertheless, they have two fundamental characteristics: heat release by excess energy of chemical bonds and a strong temperature dependence of the chemical reaction rate. The basic laws of combustion may be obtained analytically by taking this thermal nonlinearity to its extreme limit. Yakov Borisovich Zeldovich is at the origin of this remark­ able asymptotic method and one is readily convinced by reading Volume I of his selected works (Ostriker 1 992), that nobody has contributed more than him to the understanding of combustion theory. The present paper will be restricted to combustion phenomena in pre­ mixed gases; detonations are not included. The theory of the thermal propagation mechanism of flames is briefly recalled in Section 2. New results on the intriguing cool flame phenomena are also presented in this section. Results obtained during this past decade on dynamics of flame fronts are outlined in Section 3. Flammability limits and ignition problems are considered in Sections 4 and 5. Section 6 presents the current status of turbulent flame theory. The rest of this paper is devoted to compressible effects. Recent theoretical results on sound generation by turbulent flames are presented in Section 7. The last section is devoted to acoustic insta­ bilities of combustion. Combustion in gases is governed by the following set of equations: mass and momentum conservation (inviscid approximation), equation of state (ideal-gas law), and energy and species conservation,

Climate dynamics and global change

Abstract: The question of global climate change has been a major item on the political agenda for several years now. Politically, the main concern has been the impact of anthropogenic increases in minor greenhouse gases (the major greenhouse gas is water vapor). The question is also an interesting scientific question. Restricting ourselves to issues of climate, the answer requires that we be able to answer at least two far more fundamental questions, both involving strong fluid mechanical components:

Three-Dimensional Long Water-Wave Phenomena

Abstract: Water-wave motion is a fascinating subject of fluid mechanics. Apart from being important in various branches of engineering and applied science, many water-wave phenomena are also familiar from everyday experience; obtaining a thorough understanding of the relevant physical mechanisms, however, presents fluid dynamicists with great challenges. Since the early work of Airy and Stokes in the middle of the previous century, it has been recognized that, even under the assumption of potential flow, the water-wave equations are analytically intractable in general. The main difficulty stems from the nonlinear boundary conditions that apply on the free surface, which itself is unknown and is to be determined as part of the solution. In recent years, considerable progress has been made in illuminating some aspects of water-wave propagation-most notably the interplay of weak finite-amplitude and dispersive effects-using approximate (model) equations, valid asymptotically in certain limits. Combined with experi­ mental observations, these asymptotic theories reveal useful insights into the relevant physics. Moreover, in many instances, they have provided the impetus for related computational efforts. Perhaps the most well known model equation for water waves, first proposed about a century ago [see Miles (1981) for a review including historical details], is the Korteweg-de Vries (KdV) equation (Korteweg & de Vries 1895):

Parallel simulation of viscous incompressible flows

Abstract: This article deals with the formulation, implementation, and application of parallel numerical algorithms for the simulation of incompressible viscous fluid flows.