Boundary Layer

We develop a multiscale simulation method for dense granular drainage, based on the recently proposed spot model, where the particle packing flows by local collective displacements in response to diffusing "spots" of interstitial free volume. By comparing with discrete-element method (DEM) simulations of 55,000 spheres in a rectangular silo, we show that the spot simulation is able to approximately capture many features of drainage, such as packing statistics, particle mixing, and flow profiles. The spot simulation runs two to three orders of magnitude faster than DEM, making it an appropriate method for real-time control or optimization. We demonstrate extensions for modeling particle heaping and avalanching at the free surface, and for simulating the boundary layers of slower flow near walls. We show that the spot simulations are robust and flexible, by demonstrating that they can be used in both event-driven and fixed timestep approaches, and showing that the elastic relaxation step used in the model can be applied much less frequently and still create good results.

The present study reports the effect of momentum injection at the inlet on the performance of an S-shaped rectangular diffuser having an aspect ratio of 6 at inlet. A cylinder of diameter 3 cm was placed at the inflexion plane across the width of the diffuser and rotated at different speeds to inject momentum to the decelerating flow as a result of boundary layer separation. It was found that pressure recovery and flow distribution improved significantly. Improvement in coefficient of pressure recovery was about 24% for duct having an area ratio of 2 and nearly 22% for duct with an area ratio of 3. Simultaneously the values of the coefficient of total pressure loss decreased by 32% and 51% for ducts with area ratio of 2 and 3 respectively.

Keywords: S-shaped rectangular diffuser; rotating cylinder; momentum injection; boundary layer; CFD; pressure recovery coefficient

Separation control, by nominally two-dimensional periodic excitation, was studied experimentally by the authors and co-workers at Reynolds numbers ranging from 3 × 10 4 to 4 × 10 7 , including compressibility effects. The tests demonstrated that active control using oscillatory flow excitation can effectively delay flow separation from, and reattach separated flow to, aerodynamic surfaces at various flight conditions. At Reynolds number below 10 5 , where transition does not occur naturally and cannot be passively forced, active separation control may be the only effective method for delaying separation and generating useful lift. The essence of active separation control relies on exploiting instabilities that are inherent in the flow, generally requiring relatively small amplitude excitation. Effective excitation frequencies generate one to four vortices over the controlled region at all times, irrespective of Reynolds number, and perturbations should preferably be amplified over the region that is susceptible to separation. Periodic excitation is vastly superior to steady blowing in terms of performance benefits and eliminates abrupt flow responses, which are undesirable from a control point of view. The effects of compressibility in the absence of shocks are weak and undesirable effects accompanying separation, such as vortex-shedding and buffet, can be significantly reduced or completely eliminated. Separation resulting from shock-wave/boundary-layer interaction can be ameliorated, providing that excitation is introduced upstream of separation.  2004 Published by Elsevier SAS.

An approach for calculating turbulent flows in a wave-current boundary layer over a slowly varying bed is presented. Waves are periodic in time with several harmonics. In this paper, we adopt a time invariant eddy viscosity model, in which the eddy viscosity is linearly proportional to the distance from the bed. The boundary-layer flow field is solved analytically in terms of Fourier components. The approach allows fast computations and can be easily included in a phase resolving wave propagation model. As a part of the results, bottom shear stress and the spatial variation of the boundary layer thickness are also obtained. Present results compare well with experimental data and can explain the asymmetries in the bottom shear stress under sawtooth shaped waves.

Due to influence of compressibility, shock wave, instabilities, and turbulence on supersonic flows, current flow visualization and imaging techniques encounter some problems in high spatiotemporal resolution and high signal-to-noise ratio (SNR) measurements. Therefore, nanoparticle based planar laser scattering method (NPLS) is developed here. The nanoparticles are used as tracer, and pulse planar laser is used as light source in NPLS; by recording images of particles in flow field with CCD, high spatiotemporal resolution supersonic flow imaging is realized. The flow-following ability of nanoparticles in supersonic flows is studied according to multiphase flow theory and calibrating experiment of oblique shock wave. The laser scattering characteristics of nanoparticles are analyzed with light scattering theory. The results of theoretical and experimental studies show that the dynamic behavior and light scattering characteristics of nanoparticles highly enhance the spatiotemporal resolution and SNR of NPLS, with which the flow field involving shock wave, expansion, Mach disk, boundary layer, sliding-line, and mixing layer can be imaged clearly at high spatiotemporal resolution.

In this paper we investigate theoretically the unsteady boundary layer flow and heat transfer over a permeable shrinking sheet with non-uniform heat source. The nondimensional governing equations have been solved numerically using the bvp4c function from Matlab for different values of the pertinent parameters;

The low-latitude boundary layer (LBL) and its separation from the cusp have previously been identified using observations of particle precipitation at magnetosheath energies. Using $3-3 satellite observations, we have determined that these identifications can also be made from energetic particle observations on polar-orbiting satellites. It is found that the equatorward boundary of the LBL is identifiable as an approximately discontinuous decrease in 33-keV electron fluxes from low to high latitudes. Both the energetic ion and electron fluxes decrease discontinuously at the boundary between the LBL and the cusp or polar cap. A distinct LBL is nearly always identifiable in energetic particle measurements in the 10-14 MLT region when counting rates are statistically significant. The identifications obtained using the energetic particle measurements have been compared to those obtained using criteria developed by Newell and Meng (1988, 1989) for magnetosheath energy particle precipitation. In this way, we have evaluated the accuracy of both techniques and used the energetic particle measurements to supplement the identifications obtained using the Newell and Meng criteria. We propose that the Newell and Meng threshold on ion energy flux can be reduced by a factor of 6. This modification provides identification of the LBL for lower ion intensity levels than has previously [_een thought possible. Source, acceleration, and scattering processes have also been studied within _nd in the vicinity of the LBL. Observed trapped pitch angle distn'butions of energetic electrons imply that the LBL is at least partially on closed field lines. Strong scattering of energetic protons is found within and equatorward of the LBL and thus must occur at least partially along closed field lines. Field-aligned electron acceleration by parallel electric fields can be discerned within and poleward of the LBL, but a more detailed analysis is necessary for a statistical study. Conical ion acceleration was seen relatively frequently within the LBL and about half as often poleward of the LBL. Neither acceleration process could be identified anywhere equatorward of the LBL.

Numerical investigations on the turbulent fluid flow and the local heat transfer from rectangular bars for three different aspect ratios were carried out with Re=22000 and Pr=-0.71. The standard k-e turbulence model and a modified version were used in conjunction with the Reynolds-averaged momentum and energy equations for the simulations. The predictions of drag, lift, local and global heat transfer coefficients on the front, side and on the rear face of the rectangular bars are compared with available experimental results.

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The spectral values of the aerosol optical thickness t in the 400-670 nm band have been al determined from 500 solar direct irradiance spectra at normal incidence registered at Valencia (Spain) in the period from July 1993 to March 1997. The t values obtained from experimental measurements have been al compared with the boundary layer aerosol models implemented in the radiative transfer codes ZD-LOA and LOWTRAN 7. For the ZD-LOA code, the continental and maritime models have been considered and for the LOWTRAN 7 code the rural, maritime, urban and tropospheric models have been used. The obtained results show that the aerosol model that best represents the average turbidity of the boundary layer for the urban area of Valencia (Spain) is the continental model when the ZD-LOA code is used and the urban model when the LOWTRAN 7 code is used.

In magnetic fusion devices, radio frequency ͑rf͒ waves in the electron cyclotron ͑EC͒ and lower hybrid ͑LH͒ range of frequencies are being commonly used to modify the plasma current profile. In ITER, EC waves are expected to stabilize the neoclassical tearing mode ͑NTM͒ by providing current in the island region ͓R. Aymar et al., Nucl. Fusion 41, 1301 ͑2001͔͒. The appearance of NTMs severely limits the plasma pressure and leads to the degradation of plasma confinement. LH waves could be used in ITER to modify the current profile closer to the edge of the plasma. These rf waves propagate from the excitation structures to the core of the plasma through an edge region, which is characterized by turbulence-in particular, density fluctuations. These fluctuations, in the form of blobs, can modify the propagation properties of the waves by refraction. In this paper, the effect on rf due to randomly distributed blobs in the edge region is studied. The waves are represented as geometric optics rays and the refractive scattering from a distribution of blobs is formulated as a Fokker-Planck equation. The scattering can have two diffusive effects-one in real space and the other in wave vector space. The scattering can modify the trajectory of rays into the plasma and it can affect the wave vector spectrum. The refraction of EC waves, for example, could make them miss the intended target region where the NTMs occur. The broadening of the wave vector spectrum could broaden the wave generated current profile. The Fokker-Planck formalism for diffusion in real space and wave vector space is used to study the effect of density blobs on EC and LH waves in an ITER type of plasma environment. For EC waves the refractive effects become important since the distance of propagation from the edge to the core in ITER is of the order of a meter. The diffusion in wave vector space is small. For LH waves the refractive effects are insignificant but the diffusion in wave vector space is important. The theoretical model is general enough to study the effect of density blobs on all propagating cold plasma waves.

The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semiinfinite flat plate. The Blasius function is the solution to 2fxxx + ffxx = 0 on x ∈ [0, ∞] subject to f (0) = fx(0) = 0, fx(∞) = 1. We use this famous problem to illustrate several themes. First, although the flow solves a nonlinear partial differential equation (PDE), Toepfer successfully computed highly accurate numerical solutions in 1912. His secret was to combine a Runge-Kutta method for integrating an ordinary differential equation (ODE) initial value problem with some symmetry principles and similarity reductions, which collapse the PDE system to the ODE shown above. This shows that PDE numerical studies were possible even in the precomputer age. The truth, both a hundred years ago and now, is that mathematical theorems and insights are an arithmurgist's best friend, and they can vastly reduce the computational burden. Second, we show that special tricks, applicable only to a given problem, can be as useful as the broad, general methods that are the fabric of most applied mathematics courses: the importance of "particularity." In spite of these triumphs, many properties of the Blasius function f (x) are unknown. We give a list of interesting projects for undergraduates and another list of challenging issues for the research mathematician.

An experimental simulation of the interaction of vortex ring-like eddies with the sublayer of a turbulent boundary layer is investigated. An artificially generated vortex ring interacting with a Stokes' layer enables investigation of the interaction with reproducible initial conditions and in the absence of background turbulence. All of the observed features in the turbulent boundary layer production process such as the streaky structure, the pockets, the hairpin vortices, streak lift-up, oscillation, and breakup, have been observed to form. The model shows us that hairpin vortices can pinchoff and reconnect forming new vortex ring-like eddies. Interestingly, the model includes interactions that occur with low probability in the turbulent boundary layer, but which contribute significantly to transport, and may be the events most readily controllable. List of symbols D the diameter of a vortex ring R o Reynolds number based on momentum thickness T time to instability Tp average time between pockets U c convection velocity U r velocity of a vortex ring UTE convection velocity of a Typical eddy U w velocity of the moving belt ur friction velocity U~ freestream velocity x coordinate in the main flow direction y coordinate normal to the surface z spanwise coordinate the Stokes' layer thickness 0 momentum thickness of the shear layer v kinematic viscosity 2 streamwise wavelength shear stress co z spanwise vorticity Superscripts

The mass transfer around a rising bubble has been studied within the field of glass melting processes. Due to the large value of liquid viscosity, creeping flow was used. The rising bubble is assumed to have a clean interface with a total mobility and the exact solution of Hadamard or Rybczynski was used to define the velocity field around the bubble. The mass transfer of oxygen in the soda-lime-silica glass melt where oxidation-reduction reactions of iron oxides occur is also described. The dimensionless mass transfer coefficient, Sherwood number, was determined as a function of the Péclet number based on the terminal rise velocity of the bubble. Two different techniques have been used: the first based on the boundary layer theory and the second using a finite element method. In order to take into account the oxidation-reduction reaction in a unified framework, a modified Péclet number has been defined as a function of two dimensionless numbers. The first is strongly linked to the equilibrium constant of the chemical reaction and the second is the glass saturation, defined as the ratio of oxygen concentration in the bulk to that at the bubble surface. The Sherwood number, taking into account the chemical reactions, increases with iron content as well as with glass reduction (i.e. small saturation level). From an application point of view, the determination of a modified Péclet number is important because it is possible to use a similar expression (determined without the reaction) by replacing the classical Péclet number by the modified one proposed herewithin.

As a step toward an understanding of the mechanism of super cloud cluster (SCC), the effect of surface friction on the instability of Kelvin wave is discussed, together with the condition of the vertical profile of parameterized convective heating. In this paper (Part I), linear theory is developed with an equatorial beta-plane model in which the amount of convective heating is assumed to be proportional to the vertical velocity at the top of the boundary layer. Results from the eigenvalue problem suggest that the effect of surface friction is, at least under such parameterization, indispensable for essential understanding of SCC; this study is along the same line as Wang (1988) with respect to the importance of surface friction. Issue is focused on three unstable modes. One is a stationary mode excited with much heating at lower levels, and identified with conditional instability of the first kind (CIFK). The other two are Kelvin modes that contrast with each other; one is destabilized by enough heating at upper levels, even without surface friction (referred to as NFK: Non-Frictional Kelvin mode), and the other is destabilized by moderate heating at lower levels under the control of surface friction (FK: Frictional Kelvin mode). NFK has phase velocities of more than 10ms-1, and its growth rates are on the order of 10-3s-1 at small wavelengths. On the contrary, FK is characterized by smaller phase velocities of less than 10ms-l, and by only slight dependence of its growth rates on wavelength. In addition, the convergence in the boundary layer exhibits a phase shift slightly eastward relative to the convergence aloft; this is the key feature that induces effective feedback between convection and the wave. In view of the large phase velocity and the small preferred scale, NFK may be interpreted as a Kelvin mode of the type that has been treated in many previous studies on SCC. Difficulties in explaining the observed phase velocity and preferred scale of SCC are inherent in NFK. By contrast, FK can give a realistic phase velocity and preferred scale, and clear up major difficulties in the previous studies. Inclusion of surface friction is expected not only to serve as the missing link of the past linear theories of SCC, but also as a basis of future non-linear experiments with explicit moisture processes.

We carry out an analytical study of laminar circular hydraulic jumps, in generalized-Newtonian fluids obeying the two-parametric power-law model of Ostwald-de Waele. Under the boundary-layer approximation we obtained exact expressions determining the flow, an implicit relation for the jump radius is derived. Corresponding results for Newtonian fluids can be retrieved as a limiting case for the flow behavior index n=1, predictions are made for fluids deviating from Newtonian behavior.

Satellite measurements do not provide the vertical information needed to assess aerosol transport mechanisms. To supply this information, multiwavelength lidar measurements are needed to study the vertical structure of aerosol events. In support of NASA-INTEX and NOAA-NEAQS transport experiments; we present lidar retrievals, which identify multiple stratified particulate plumes occurring over NYC on July 21 in support of MODIS imagery. In particular, multiwavelength measurements at CCNY are used to determine the angstrom coefficient of the plumes that unambiguously identifies them as fine mode particulates and not cloud particles. A description of our Lidar system capabilities and processing algorithms used to process simultaneous backscatter Lidar measurements with Aeronet CIMEL Optical Depth (OD) data is presented and back trajectory analysis is used to confirm the source of the plumes to be from Alaskan wild fires. Finally, surface measurements from insitu particle counters are presented and show no enhanced PM2.5 loading. This result is supported by lidar measurements, which confirm that nearly all of the aerosol plumes are located above the normal aerosol boundary layer showing that satellite measurements are often incomplete and is not useful to assess surface air quality. In particular, we show that high PM2.5 events are triggered from more local sources such as the Ohio Basin and climatological conditions which drive the pollution to the surface.

VOL. 8. (I) The Laminar Boundary Layer (LBL) over a flat plate is a member of the family of similar flows over a wedge, which is famously known as Falkner-Skan Flows (FSF). Based on the available numerical results, this paper gives velocity distribution equations for LBL over a flat plate and FSF, which exhibit the influence of viscosity and external stream flow all over the depth of LBL. In the case of a Turbulent Boundary Layer (TBL), viscosity and boundary roughness affect lhe velocity distribution in the inner region, while the external stream flow influences the ollter region. The majority of TBL consists of the outer region in which the velocity saturates to external stream value. Available outer region models consist of superimposition of a wake function over the log-layer equation. The superimposed equation does not satisfy the boundary condition of free-stream velocity at infinite distance from the boundary. Presented herein is a generalized velocity distribution equation for both the inner and outer regions of the TBL. The equation is valid for both negative and positive pressure gradients. As the equation contains wall shear velocity, a generalized equation for wall shear velocity has also been given.

Observations of the tropical atmosphere are fundamental to the understanding of global changes in air quality, atmospheric oxidation capacity and climate, yet the tropics are under-populated with long-term measurements. The first three years (October 2006–September 2009) of meteorological, trace gas and particulate data from the global WMO/Global Atmospheric Watch (GAW) Cape Verde Atmospheric Observatory Humberto Duarte Fonseca (CVAO; 16° 51′ N, 24° 52′ W) are presented, along with a characterisation of the origin and pathways of air masses arriving at the station using the NAME dispersion model and simulations of dust deposition using the COSMO-MUSCAT dust model. The observations show a strong influence from Saharan dust in winter with a maximum in super-micron aerosol and particulate iron and aluminium. The dust model results match the magnitude and daily variations of dust events, but in the region of the CVAO underestimate the measured aerosol optical thickness (AOT) because of contributions from other aerosol. The NAME model also captured the dust events, giving confidence in its ability to correctly identify air mass origins and pathways in this region. Dissolution experiments on collected dust samples showed a strong correlation between soluble Fe and Al and measured solubilities were lower at high atmospheric dust concentrations. Fine mode aerosol at the CVAO contains a significant fraction of non-sea salt components including dicarboxylic acids, methanesulfonic acid and aliphatic amines, all believed to be of oceanic origin. A marine influence is also apparent in the year-round presence of iodine and bromine monoxide (IO and BrO), with IO suggested to be confined mainly to the surface few hundred metres but BrO well mixed in the boundary layer. Enhanced CO2 and CH4 and depleted oxygen concentrations are markers for air-sea exchange over the nearby northwest African coastal upwelling area. Long-range transport results in generally higher levels of O3 and anthropogenic non-methane hydrocarbons (NMHC) in air originating from North America. Ozone/CO ratios were highest (up to 0.42) in relatively fresh European air masses. In air heavily influenced by Saharan dust the O3/CO ratio was as low as 0.13, possibly indicating O3 uptake to dust. Nitrogen oxides (NOx and NOy) show generally higher concentrations in winter when air mass origins are predominantly from Africa. High photochemical activity at the site is shown by maximum spring/summer concentrations of OH and HO2 of 9 × 106 molecule cm−3 and 6 × 108 molecule cm−3, respectively. After the primary photolysis source, the most important controls on the HOx budget in this region are IO and BrO chemistry, the abundance of HCHO, and uptake of HOx to aerosol.

Evolution of sea fog has been investigated using three-dimensional Mesoscale Model 5 (MM5) simulations. The study focused on widespread fog-cloud layers advected along the California coastal waters during 14-16 April 1999. According to analysis of the simulated trajectories, the intensity of air mass modification during this advection significantly depended on whether there were clouds along the trajectories and whether the modification took place over the land or ocean. The air mass, with its trajectory endpoint in the area where the fog was observed and simulated, gradually cooled despite the gradual increase in sea-surface temperature along the trajectory. Modelling results identified cloud-top cooling as a major determinant of marine-layer cooling and turbulence generation along the trajectories. Scale analysis showed that the radiative cooling term in the thermodynamic equation overpowered surface sensible and latent heat fluxes, and entrainment terms in cases of the transformation of marine clouds along the trajectories. Transformation of air masses along the trajectories without clouds and associated cloud-top cooling led to fog-free conditions at the endpoints of the trajectories over the ocean. The final impact on cloud-fog transition was determined by the interaction of synoptic and boundary-layer processes. Dissipation of sea fog was a consequence of a complex interplay between advection, synoptic evolution, and development of local circulations. Movement of the high-pressure system over land induced weakening of the along-shore advection and synoptic-pressure gradients, and allowed development of offshore flows that facilitated fog dissipation.

The potential of a ground-based microwave temperature profiler to combine full tropospheric profiling with highresolution profiling of the boundary layer is investigated. For that purpose, statistical retrieval algorithms that incorporate observations from different elevation angles and frequencies are derived from long-term radiosonde data. A simulation study shows the potential to significantly improve the retrieval performance in the lowest kilometer by combining angular information from relatively opaque channels with zenith-only information from more transparent channels. Observations by a state-of-the-art radiometer employed during the International Lindenberg Campaign for Assessment of Humidity and Cloud Profiling Systems and Its Impact on High-Resolution Modeling (LAUNCH) in Lindenberg, Germany, are used for an experimental evaluation with observations from a 99-m mast and radiosondes. The comparison not only reveals the high accuracy achieved by combining angular and spectral observations (overall, less than 1 K below 1.5 km), but also emphasizes the need for a realistic description of radiometer noise within the algorithm. The capability of the profiler to observe the height and strength of low-level temperature inversions is highlighted.

We present an exact solution of Einstein's field equations in toroidal coordinates. The solution has three regions: an interior with a string equation of state; an Israel boundary layer; and an exterior with constant isotropic pressure and constant density, locally isometric to anti-de Sitter space-time. The exterior can be a cosmological vacuum with negative cosmological constant. The size and mass of the toroidal loop depend on the size of Lambda.

Laboratory experiments were performed to study the influence of density and viscosity layering on the formation and stability of plumes. Viscosity ratios ranged from 0.1 to 6400 for buoyancy ratios between 0.3 and 20, and Rayleigh numbers between 105 and 2.108. The presence of a chemically stratified boundary layer generates long-lived thermochemical plumes. These plumes first develop from the interface

We explore a numerical technique for determining the structure of the kinetic boundary layer of the Klein-Kramers equation for noninteracting Brownian particles in a fluid near a wall that absorbs the Brownian particles. The equation is of interest in the theory of diffusion-controlled reactions and of the coagulation of colloidal suspensions. By numerical simulation of the Langevin equation equivalent to the Klein-Kramers equation we amass statistics of the velocities at the first return to the wall and of the return times for particles injected into the fluid at the wall with given velocities. The data can be used to construct the solutions of the standard problems at an absorbing wall, the Milne and the albedo problem. We confirm and extend earlier results by Burschka and Titulaer, obtained by a variational method vexed by the slow convergence of the underlying eigenfunction expansion. We briefly discuss some further boundary layer problems that can be attacked by exploiting the results reported here.

With improved observation methods, increased winter navigation, and increased awareness of the climate and environmental changes, research on the Baltic Sea ice conditions has become increasingly active. Sea ice has been recognized as a sensitive indicator for changes in climate. Although the interannual variability in the ice conditions is large, a change towards milder ice winters has been detected from the time series of the maximum annual extent of sea ice and the length of the ice season. On the basis of the ice extent, the shift towards a warmer climate took place in the latter half of the 19th century. On the other hand, data on the ice thickness, which are mostly limited to the land-fast ice zone, basically do not show clear trends during the 20th century, except that during the last 20 years the thickness of land-fast ice has decreased. Due to difficulties in measuring the pack-ice thickness, the total mass of sea ice in the Baltic Sea is, however, still poorly known. The ice extent and length of the ice season depend on the indices of the Arctic Oscillation and North Atlantic Oscillation. Sea ice dynamics, thermodynamics, structure, and properties strongly interact with each other, as well as with the atmosphere and the sea. The surface conditions over the ice-covered Baltic Sea show high spatial variability, which cannot be described by two surface types (such as ice and open water) only. The variability is strongly reflected to the radiative and turbulent surface fluxes. The Baltic Sea has served as a testbed for several developments in the theory of sea ice dynamics. Experiences with advanced models have increased our understanding on sea ice dynamics, which depends on the ice thickness distribution, and in turn redistributes the ice thickness. During the latest decade, advance has been made in studies on sea ice structure, surface albedo, penetration of solar radiation, sub-surface melting, and formation of superimposed ice and snow ice. A high vertical resolution has been found as a prerequisite to successfully model thermodynamic processes during the spring melt period. A few observations have demonstrated how the river discharge and ice melt affect the stratification of the oceanic boundary layer below the ice and the oceanic heat flux to the ice bottom. In general, process studies on ice-ocean interaction have been rare. In the future, increasingly multidisciplinary studies are needed with close links between sea ice physics, geochemistry and biology.

The paper analytically investigated the double-diffusive natural convective boundarylayer flow of a nanofluid past a vertical plate with heat flux condition. The diffusive model used for nanofluid included the effects of Brownian motion and Thermophoresis. A similarity solution was presented and numerical calculations were performed by Maple software. The reduced Nusselt number as a function of a buoyancy-ratio number Nr, a Brownian motion number Nb, and a Thermophoresis number Nt was found with a various values of Prandtl number Pr and Lewis number Le.

Sediment entrainment and the initiation of bed defects has commonly been ascribed to the impact of high velocity sweeps upon mobile sand beds. Results of visualization experiments suggest that these sweep impacts are grouped and may define 'patches' of entrainment upon a mobile bed that may be wider than an individual sweep impact. Additionally, the presence of longitudinal ribs of sediment generated by sweep impacts may stabilize the position of sweeps and low speed streaks. These observations are interpreted in the light of recent boundary layer research which suggests the formation of multiple hairpin shaped vortices within turbulent flows: these are postulated to generate multiple sweeps that manifest themselves as entrainment patches on a mobile bed. These features of the turbulent boundary layer and its modification by sweep generated sediment ridges can be used to propose a model for bed defect formation and the subsequent development of current ripples.

We report on sizable antiferromagnetic interlayer exchange coupling (AFC) of Fe(001) layers across epitaxial Si spacers, for which epitaxial growth of a pseudomorphic phase stabilized by the interface is confirmed by low-energy electron diffraction and high-resolution transmission electron microscopy. The coupling strength decays with spacer thickness on a length scale of a few Å and shows a negative temperature coefficient. Transport measurements of lithographically structured junctions in current-perpendicular-to-plane geometry show the validity of the three “Rowell criteria” for tunneling: (i) exponential increase of resistance R with thickness of the barrier, (ii) parabolic dI/dV-V curves, and (iii) slight decrease of R with increasing temperature. Therefore, AFC is mediated by non-conductive spacers, which in transport experiments act as tunneling barriers with a barrier height of several tenths of an eV. We discuss our data — in particular the strength, thickness and temperature dependence — in the context of two previously proposed models for AFC across non-conducting spacers. We find that neither the molecular-orbital model for heat-induced effective exchange coupling nor the quantum interference model extended to insulator spacers by introducing complex Fermi surfaces can account for the strong AFC across epitaxial Si spacers and its negative temperature coefficient. The recently proposed defect-assisted interlayer exchange coupling model, however, yields qualitative agreement with the enhanced AFC and the temperature dependence.

In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade' approximant of order [m, m]. Some theoretical results are established and proved.

Similarity solutions of the laminar boundary-layer equations describing heat and flow in a quiescent fluid driven by a stretched surface subject to suction or injection are obtained herein. The surface is moving with a power-law velocity distribution, and its temperature has a power-law variation. The effect of various governing parameters, such as Prandtl number Pr, temperature exponent n, velocity exponent m, and the injection parameter d, which determine the temperature profiles and heat transfer coefficient are studied. Three boundary conditions of uniform temperature, variable temperature, and uniform heat flux at the surface have been investigated. The effect of decreasing d is found to be significant, particularly for high Prandtl numbers.

In this paper we present the results from a series of laboratory experiments on inclined negatively buoyant jets released in a receiving environment with waves. This simulates the case, typical of many practical applications, of the sea discharge of fluids denser than the receiving environment, as in the case of the brine from a desalination plant. The experiments were performed employing a Light Induced Fluorescence (LIF) technique, in order to measure the concentration fields. Both the jet and the wave motion features were varied, in order to simulate a typical discharge into the Mediterranean Sea. Reference discharges in a stagnant environment were performed as well. The jet behaviour was analyzed from a statistical point of view, both considering the global phenomenon and its single phases. The influence of the wave motion on the inclined negatively buoyant jet geometry and dilution turns out to be a combined action of a split into two branches of the jet and a rotation. Their combined action decreases the jet maximum height and the impact distance, and is the main cause for the higher dilution reached in a wavy environment.

This study is focused on the influences of secondary cooling rate (SCR) and solid fraction upon size of primary solid particles in Al-7.1 wt%Si slurries produced by semisolid rheocasting (SSR) process. SSR slurries with various solid fractions were poured into a wedge-shaped steel die to produce a range of SCRs. The extent of primary particle growth during secondary cooling at various cooling rates was estimated at these solid fractions using a 1/3-power law relationship. The results indicated that, at any given solid fraction, an increase in the SCR caused a smaller growth of primary particles during quench. Furthermore, for any given SCR, primary particles in low solid fraction SSR slurries grew more significantly during secondary cooling than those in high solid fraction slurries. These results were explained based on the effects of SCR and solid fraction on the overlap of solute boundary layers of the adjacent particles and the time available for the growth of the primary particles during secondary cooling stage.

An experimental investigation on natural convection in air in vertical convergent channels with wall uniform heat flux is presented. Wall temperatures show that by increasing the spacing the effect of the convergence angle decreases. For the lowest spacing, a significant decrease of maximum wall temperature occurs passing from the parallel vertical plate configurations to convergence angles h P 2 .

In the present paper different types of scramjet (supersonic combustion ramjet) combustors are investigated. Thereby the main difference between the combustors is the way of injecting the fuel into the combustion chamber. The first investigated concept of fuel injection is the injection by strut injectors. Here the injection of fuel is realized by a lobed strut that is located in the middle of the combustion chamber. The second concept for fuel supply is the wall injection of hydrogen. Here the fuel is injected by several holes in the wall of the combustor. Both concepts of fuel injection have different advantages and disadvantages which are explained in detail. Although different performance parameters for both scramjet combustors are introduced this paper will not compare the different techniques among each other. Because of the high Reynolds numbers in scramjet combustors, the need to resolve the boundary layers and the necessity of detailed chemistry, the simulation of scramjets is extremely CPU time demanding.

An intercomparison study for single column models (SCMs) of the diurnal cycle of shallow cumulus convection is reported. The case, based on measurements at the ARM Southern Great Plain site on 21 ¢ ¡ June 1997, has been used in an LES intercomparison study before. Results of the SCMs reveal the following general deficiencies: too large values of cloud cover and cloud liquid water, unrealistic thermodynamic profiles, and high amounts of noise. These results are analyzed in terms of the behavior of different parameterization schemes involved: the convection scheme, the turbulence scheme, and the cloud scheme. In general the behavior of the SCMs can be grouped in two different classes: one class with too strong mixing by the turbulence scheme, the other class with too strong activity by the convection scheme. In both classes high values of cloud cover and cloud liquid water content occur. Many of the SCMs suffer from a numerical instability in the cloud layer mainly due to the turbulence scheme. Results are also strongly dependent on vertical resolution, in particular caused by resolution dependencies in the mass flux scheme. The coupling between subcloud turbulence and the convection scheme plays a crucial role in determining the thermodynamic profiles. Finally, (in part) motivated by these results several models have been successfully updated with new parameterization schemes and/or their present schemes have been successfully modified. QJRMS 1

This paper is an application of the constructal method to the discovery of the optimal distribution of discrete heat sources cooled by laminar natural convection. The global objective is to maximize the global conductance between the wall and the fluid, or to minimize the hot-spot temperatures when the total heat generation rate and global system dimensions are specified. Two scenarios are investigated: (i) a large number of small heat sources mounted on a vertical wall facing a fluid reservoir, and (ii) a small number of finite-size heat sources mounted on the inside of the side wall of a two-dimensional enclosure. It is shown that the optimal distribution is not uniform (the sources are not equidistant), and that as the Rayleigh number increases the heat sources placed near the tip of a boundary layer should have zero spacings. In both (i) and (ii), the optimal configuration of the wall with discrete sources is generated by the pursuit of maximal global performance subject to global constraints.

This paper deals with inhomogeneous shearing deformation of an in"nite rubber-like slab under a temperature di!erence across its thickness. The deformation is analyzed within the context of "nite thermoelasticity with entropic origin for the stress. The isothermal strain energy functions of Mooney and of Yeoh are generalized by incorporating them into the thermoelastic model. The energy balance equation, which is decoupled from the linear momentum balance equations, is solved for the temperature "eld using the Fourier's law of heat conduction. The derived linear temperature "eld and the equations of the thermoelastic model are inserted into the linear momentum balance equations, thus yielding an ordinary di!erential equation for the shear strain. The shear strain, the degree of inhomogeneity in the shear strain, the stress "eld, and the principal stresses are then determined using a "nite di!erence method. The Mooney slab undergoes markedly greater shear strain near the colder boundary, thus exhibiting a boundary layer-like structure at higher temperature di!erences across the thickness. However, the Yeoh slab exhibits a relatively smaller variation of the shear strain even at the highest temperature di!erence. This di!erence in the behavior of the two slabs is attributed to the shear sti!ening of the Yeoh slab, which counteracts the formation of a boundary layer-like structure. Both slabs experience constant shear stresses across the thickness, whereas they experience much greater normal stress di!erences varying across the thickness. The values of the major principal stress turn out to be close to those of the "rst normal stress di!erence. The presence of a large normal stress di!erence compared with a relatively smaller shear stress in the slabs creates the possibility for Mode I type fracture propagation. (E. Bilgili). these materials when subjected to temperature gradients and "nite deformations. Rubber-like materials show non-linear stress}strain behavior, exhibit large deformation even under small loads, and have material parameters dependent on temperature . The coupling between the deformation and temperature increases the complexity of the non-linear equations that arise in "nite deformation of rubber-like materials.

In this paper, the decade of numerical and experimental investigations leading to the development of the authors' unique flapping-wing micro air vehicle is summarized. Early investigations included the study of boundary layer energization by means of a small flapping foil embedded in a flat-plate boundary layer, the reduction of the recirculatory flow region behind a backward-facing step by means of a small flapping foil, and the reduction or suppression of flow separation behind blunt or cusped airfoil trailing edges by flapping a small foil located in the wake flow region. These studies were followed by systematic investigations of the aerodynamic characteristics of single flapping airfoils and airfoil combinations. These unsteady flows were described using flow visualization, laser-Doppler velocimetry in addition to panel and Navier-Stokes computations. It is then shown how this flapping-wing database was used to conceive, design and develop a micro air vehicle which has a fixed wing for lift and two flapping wings for thrust generation. While animal flight is characterized by a coupled force generation, the present design appears to separate lift and thrust. However, in fact, the performance of one surface is closely coupled to the other surfaces.

The acoustic and fluid dynamic resonance in a two-dimensional cavity flow was investigated experimentally. In order to visualize a periodic oscillation of the shear layer and the behavior of vortices, the schlieren method was used with an ordinary CCD camera and a high-speed video camera. Particle image velocimetry (PIV) measurements were also carried out to obtain the vorticity distribution during the oscillation in the cavity flow. Shedding and interaction of vortices in the shear layer were observed near the trailing edge of the cavity, which causes the generation of pressure waves. The feedback process of the oscillation was determined using high-speed camera images. From these results, the x À t diagram for the oscillation cycle was obtained. Based on the flow visualization, for Rossiter's constants, it was confirmed that the dominant acoustic mode was m = 2 and that K c = 0.5 in the present experiment. Also, the pressure level for mode m = 2 was the most intense for a wide range of flow Mach numbers. The results obtained by PIV measurement show that there is outgoing and incoming flow near the trailing edge of the cavity. It was found that a very strong change of vorticity associated with the detachment and attachment of boundary layer was induced on the trailing edge due to the fluid dynamical instability.