Showing papers in "Annual Review of Fluid Mechanics in 1995"

Mixing enhancement in supersonic free shear flows

Abstract: Recent interest in supersonic combustion (scramjets) and noise reduction for the high speed civil transport (HSCT) plane prompted renewed research in supersonic mixing processes and means to control them. The scramjet propulsion concept requires rapid mixing between fuel and air in order to minimize the size of the combustor and affect the performance of the entire vehicle system. Also, accelerated mixing of exhaust plumes with coflowing air has been shown to lead to jet noise reduction. Other examples of technological applications requiring control of mixing in compressible flows include thrust augmenting ejectors, thrust vector control, metal deposition, and gas dynamic lasers. The technological challenge of mixing enhancement in compressible flows stems from the inherently low growth rates of supersonic shear layers. Many mixing augmentation methods employed efficiently in sub­ sonic flows failed to work at elevated Mach numbers, and some were inefficient because they were utilized outside their effective range. Never-

Continuum Deductions from Molecular Hydrodynamics

Abstract: Since a fluid is composed of molecules, one always has the option of calculating its static or dynamic properties by computing the motion of these constituents. For most purposes such a procedure is very inefficient, because it provides detailed information at molecular length scales, which are far beneath the usual realm of interest for continuum fluid mechanics. There are, however, situations where the microscopic details of a fluid flow are interesting if not crucial. For example, fluids in microscopic geometries or under high stress may exhibit deviations from the continuum equations, and one may wish to calculate such effects from first principles. Alternatively, in some problems the boundary conditions to be applied to the Navier-Stokes equations are not fully established or are unsatisfactory, as in the presence of moving contact lines or at the edge of a porous

Constitutive equations for polymeric liquids

Abstract: The origins, uses and evaluation of constitutive equations for the stress tensor of polymeric liquids are discussed.

Biological-Physical Interactions in the Upper Ocean: The Role of Vertical and Small Scale Transport Processes

Abstract: In a recent review of Lagrangian ocean studies, Davis ( 1 99 1) described physical oceanography as being a difficult and immature science, relative to other areas of fluid mechanics, because "First, the ocean is complex," "Second, the ocean cannot be controlled," and "Third, the ocean is logis­ tically difficult." Spatial scales of ocean motions span ten decades, from 1 mm (the viscous damping scale) to 10,000 km (the ocean basin scale), and associated temporal scales range from about 0.1 s to palaeoclimatic epochs. Imagine then the additional difficulties in acquiring a quantitative descrip­ tion and understanding of the dynamics of the oceanic food web, whose components exhibit varying degrees of mobility themselves in addition to being embedded in this continually changing complex of nested, inter­ acting oceanic motions. The food web comprises organisms ranging in size from less that 1 J.lm (bacteria) to greater than 10 m (whales). The smallest organisms are passive tracers of the flow, although some can control their buoyancy in response to external cues. Some phytoplankton (microscopic plants) under certain conditions exhibit directed motion (meters per day) along gradients of light, density, or chemical concentration. Zooplankton (mmto cm-scale animals that feed on plants or other smaller animals)

Convection instabilities in nematic liquid crystals

Abstract: Pattern formation in hydrodynamic instabilities has been studied intensely over the past few decades (Manneville 1990, Cross & Hohenberg 1993). Rayleigh-Benard convection (RBC) in simple fluids has been the prime example. Our goal in this review is to draw attention to the rich variety of scenarios found in nematic liquid crystals (LCs). Liquid crystals are materials made up of highly anisotropic organic molecules in a phase that reflects this anisotropy. The class of nematic LCs (nematics) is fully liquid without long-range translational, but with long-range uniaxial orienta tiona I ordering of the molecules. Thus in the well-established hydrodynamic description (Ericksen 1 976, Leslie 1 979, de Gennes 1974, Stephen & Straley 1974, Chandrasekhar 1977) the director n characterizing the preferred axis has to be included as an additional variable. One then has six shear viscosities lXI' • . • , 1X6 with 1X6 -1X5 = 1X3 + IXz (1X4/2 corresponds to the isotropic viscosity) in the momentum balance equation (generalized Navier-Stokes equation). In the director equation, which can be associated loosely with a balance of torque, there are two rotational viscosities, YI and Yz, which are expressible in terms of the shear viscosities. For the low-molecular-weight materials discussed here the vis­ cosities relevant in the following are of order 10-1 kg m -I S-I. One needs three orientational elastic modules, kl), k22' k33' to describe the three basic

Dynamics of Jovian atmospheres

Abstract: Earth's atmosphere receives more energy per unit area than any other planetary atmosphere (including Venus), and yet has the weakest winds in the solar system (Ingersoll 1 990). This is an indication that the terrestrial problem is complicated. Major factors that contribute to the complexity of Earth's weather are its irregular boundary conditions, i .e. its mountain ranges, and the fact that the atmospheric eddies and the planet are com­ parable in size. Apart from Mars, this size comparison does not hold for any other major atmosphere in the solar system. Venus and Titan rotate so slowly that they are significantly smaller than their atmospheres' Cori­ olis eddy sizes. In contrast, the giant, bottomless atmospheres of Jupiter, Saturn, Uranus, and Neptune offer us an opportunity to study geophysical fluid dynamics in a spacious setting that is similar to the roominess of Earth's oceans. In addition, these four atmospheres come pre-idealized, since they have no mountain ranges, air-sea interfaces, ocean basins, surface drag, or surface temperature gradients to complicate their dyna­ mics. Studying Jupiter's atmosphere is particularly rewarding because the planet's cloud-top circulations are easy to track from space, the jet streams flow in straight lines eastward or westward, and there is usually enough room for the vortices to keep out of each other's way. Earth, in contrast, is a planet with cloud-top circulations that are not easy to track from space, with jet streams that make wide, fluctuating arcs as they negotiate

The measurement of vorticity in turbulent flows

Abstract: with scalar components 01 == Ox, Oz == 0y, and 03 == Oz have been sought for a long time by turbulence experimentalists. (Here, Bijk is the alternating tensor and Vk is the velocity vector with scalar components VI == V, Vz == V, and V3 == W. Lower case variables indicate turbulent fluctuations with zero mean value.) The reason is rather obvious. Vorticity is a defining property of turbulence, i.e. the presence of vorticity in a flow is considered essential to identifying it as true turbulent motion. Furthermore, there are

Solitary waves and homoclinic orbits

Abstract: The notion that fluid motion often organizes itself into coherent structures has increasingly permeated modern fluid dynamics. Such localized objects appear in laminar flows and persist in turbulent states; from the water on windows on rainy days, to the circulations in planetary atmospheres. This review concerns solitary waves in fluids. More specifically, it centres around the mathematical description of solitary waves in a single spatial dimension. Moreover, it concentrates on strongly dissipative dynamics, rather than integrable systems like the KdV equation. One-dimensional solitary waves, or pulses and fronts as they are also called, are the simplest kinds of coherent structure (at least from a geometrical point of view). Nevertheless, their dynamics can be rich and complicated. In some circumstances this leads to the formation of spatio-temporal chaos in the systems giving birth to the solitary waves, and understanding that phenomenon is one of the major goals in the theory outlined in this review. Unfortunately, such a goal is far from achieved to date, and the author assess its current status and incompleteness.

High Angle-of-Attack Aerodynamics

Abstract: High angle-of-attack (high-IX) aerodynamics has been a key element in airplane design beginning with the first attempts at unpowered manned flight using gliders in the 1 800s and extending to the present day with civil and military airplanes. High-IX aerodynamics is commonly perceived as arising on an airplane at a physically large angle of attack with its leading­ edge vortex separating from highly swept wings. However, the underlying flow is that of a heavily loaded lifting surface, operating at other than optimum lift-to-drag ratio. This off-design or high-lift condition often includes regions of separated flow. In this regard, high-IX embraces a broader range of aerodynamic flows than is widely appreciated. For example, high-IX can be defined as any situation where an airplane or any of its components encounters off-design, high-lift flight, and includes attached flows, uncontrolled separated flows, and organized flow sep­ aration in the form of vortices, shock waves, and combinations of these flow conditions. The high-IX regime encompasses local and global flow fields that can occur at subsonic through hypersonic speeds. These flow fields can be highly interactive and either static or dynamic in nature. Examples of localized high-IX flows include the interaction of the propeller tip vortex system with the airframe of a light general aviation airplane;

Thermohaline Ocean Processes and Models

Abstract: Understanding the physical behavior of the ocean is of interest to scientists in a variety of disciplines because ocean dynamics interacts with atmo­ spheric processes to govern climatic and biological processes. For example, there is evidence that interactions between the ocean currents and tem­ perature fields and the atmospheric temperature and wind fields are pos­ sible mechanisms for the El Nino-Southern Oscillation (ENSO) (Neelin, Latif & Jin 1994), which influences global weather fluctuations and bio­ logical production over periods of years. For longer time scales, climate record studies reveal numerous oscillations in 180/160 ratios and for­ minifera populations (Broecker et a1 1985, Boyle 1990) which indicate that thermal and salinity distributions of past oceans differ significantly from the present ones. Such observations are qualitatively consistent with a relatively new but very simple idea (Stommel 1961)-that the combined heat and evapora­ tion boundary conditions imposed by the atmosphere can produce mul­ tiple states of ocean circulation. The states are thereby dependent on their initial condition. This causes them to exhibit catastrophic or discrete jumps as the boundary conditions are slowly varied owing to atmospheric changes. The governing equations are beautiful and simple examples of finite amplitude instability (also called catastrophic) transitions. Since records of the ice sheets indicate sudden melting and freezing events, it is

Numerical weather prediction

Abstract: This review highlights a number of current areas of emphasis in research and operational numerical weather prediction. Detailed accounts of each area of activity are not presented; some key references are provided within each section for interested readers who may wish to explore further. The review outlines the types of weather prediction models where the biggest contributions have emerged in recent years. The topics include an outline of such models, the data, their assimilation and initialization issues, model sensitivity to physical processes, tropical forecast advancements-mon­ soons and hurricanes, newer areas of thrust-use of adaptive grids for mesoscale forecasts of severe weather, and finally the recognition of current limits of predictability-chaos, i.e. the need for ensemble forecasts, via the probabilistic Monte Carlo type approach. We have currently reached roughly the halfway point towards the theor­ etical bound of predictability of two weeks, originally stated by Lorenz ( 1 963), for predicting the future state of the atmosphere using large-scale numerical weather prediction models. This limit is currently measured from correlations of observed versus predicted (massor motion-based) fields (generally from 200N to the North pole). The measure of useful skill has slowly increased from 2 days to roughly 7 days in the past 30 years as computing, modeling, and observational strategies have improved. Presently, the predictive skill over the southern hemisphere is roughly half