Showing papers on "Boundary layer published in 1986"

A simple model of the atmospheric boundary layer; sensitivity to surface evaporation

Abstract: A simple formulation of the boundary layer is developed for use in large-scale models and other situations where simplicity is required. The formulation is suited for use in models where some resolution is possible within the boundary layer, but where the resolution is insufficient for resolving the detailed boundary-layer structure and overlying capping inversion. Surface fluxes are represented in terms of similarity theory while turbulent diffusivities above the surface layer are formulated in terms of bulk similarity considerations and matching conditions at the top of the surface layer. The boundary-layer depth is expressed in terms of a bulk Richardson number which is modified to include the influence of thermals. Attention is devoted to the interrelationship between predicted boundary-layer growth, the turbulent diffusivity profile, ‘countergradient’ heat flux and truncation errors. The model predicts growth of the convectively mixed layer reasonably well and is well-behaved in cases of weak surface heat flux and transitions between stable and unstable cases. The evolution of the modelled boundary layer is studied for different ratios of surface evaporation to potential evaporation. Typical variations of surface evaporation result in a much greater variation in boundary-layer depth than that caused by the choice of the boundary-layer depth formulation.

A new finite element formulation for computational fluid dynamics: II. Beyond SUPG

Abstract: A discontinuity-capturing term is added to the streamline-upwind/Petrov-Galerkin weighting function for the scalar advection-diffusion equation. The additional term enhances the ability of the method to produce smooth yet crisp approximations to internal and boundary layers.

Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parametrization

Abstract: Systematic westerly biases in the northern hemisphere wintertime flow of the Meteorological Office 15-layer operational model and 11-layer general circulation model are described. Evidence that the failure to parametrize subgrid-scale orographic gravity wave drag may account for such biases is presented. This evidence is taken from aircraft studies, surface pressure drag measurements, and studies of the zonally averaged momentum budget. A parametrization scheme is described in which the surface stress is proportional to the near-surface wind speed and static stability, and to the variance of subgrid-scale orography. The stress is absorbed in the vertical by considering the influence of such gravity wave activity on static stability and vertical wind shear. A Richardson-number-dependent wave breaking formulation is devised, and the vertical stress profile determined by a saturation hypothesis whereby the breaking waves are maintained at marginal stability. It is shown that wave breaking preferentially occurs in the boundary layer and in the lower stratosphere. Results from a simple zonally symmetric model show how the adjustment to thermal wind balance with a wave drag in the stratosphere, warms polar regions by adiabatic descent, and decelerates the mean westerlies in the troposphere. The influence of the parametrization scheme on integrations of the 11-layer model is described, and found to be generally beneficial. In a discussion of the reasons why this problem has only recently emerged, it is suggested that the satisfactory northern hemisphere winter circulations of previous, coarser general circulation models were due to a compensation implied by underestimating both the surface drag, and the horizontal flux of momentum by explicitly resolved large-scale eddies.

New pore-size parameter characterizing transport in porous media.

Abstract: We introduce a well-defined geometrical parameter, $\ensuremath{\Lambda}$, related to dynamically connected pore sizes in composite materials. $\ensuremath{\Lambda}$ describes the effects of an internal boundary layer on a variety of processes including electrical surface conduction, high-frequency viscous damping of acoustic waves, and healing length effects in fourth sound. We argue that $\ensuremath{\Lambda}$ is also related to the dc permeability to flow of a viscous fluid.

Structure of transitionally rough and fully rough turbulent boundary layers

Abstract: Structural characteristics of transitionally rough and fully rough turbulent boundary layers are presented. These were measured in flows at different roughness Reynolds numbers developing over uniform spheres roughness. Inner regions of the longitudinal component of normal Reynolds stress profiles and log regions of mean profiles continuously change in the transitionally rough regime, as the roughness Reynolds number, Rek, varies. These properties asymptotically approach fully rough behaviour as Rek increases, and smooth behaviour at low Rek Profiles of other Reynolds-stress tensor components, turbulence kinetic energy, turbulence-kinetic-energy production, and the turbulence-kinetic-energy dissipation are also given, along with appropriate scaling variables. Fully rough, one-dimensional spectra of longitudinal velocity fluctuations from boundary-layer inner regions are similar to smooth-wall results for k1 y > 0.2 when non-dimensionalized using distance from the wall y as the lengthscale, and (τ/ρ)½ as the velocity scale, where τ is local shear stress, ρ is static density, and k1 is one-dimensional wavenumber in the flow direction.

Experiments on scalar dispersion within a model plant canopy part I: The turbulence structure

Abstract: This is the first of a series of three papers describing experiments on the dispersion of trace heat from elevated line and plane sources within a model plant canopy in a wind tunnel. Here we consider the wind field and turbulence structure. The model canopy consisted of bluff elements 60 mm high and 10 mm wide in a diamond array with frontal area index 0.23; streamwise and vertical velocity components were measured with a special three-hot-wire anemometer designed for optimum performance in flows of high turbulence intensity. We found that: (i) The momentum flux due to spatial correlations between time-averaged streamwise and vertical velocity components (the dispersive flux) was negligible, at heights near and above the top of the canopy. (ii) In the turbulent energy budget, turbulent transport was a major loss (of about one-third of local production) near the top of the canopy, and was the principal gain mechanism lower down. Wake production was greater than shear production throughout the canopy. Pressure transport just above the canopy, inferred by difference, appeared to be a gain in approximate balance with the turbulent transport loss. (iii) In the shear stress budget, wake production was negligible. The role of turbulent transport was equivalent to that in the turbulent energy budget, though smaller. (iv) Velocity spectra above and within the canopy showed the dominance of large eddies occupying much of the boundary layer and moving downstream with a height-independent convection velocity. Within the canopy, much of the vertical but relatively little of the streamwise variance occurred at frequencies characteristic of wake turbulence. (v) Quadrant analysis of the shear stress showed only a slight excess of sweeps over ejections near the top of the canopy, in contrast with previous studies. This is a result of improved measurement techniques; it suggests some reappraisal of inferences previously drawn from quadrant analysis.

Length Scales in the Convective Boundary Layer

Abstract: We calculated integral scales for horizontal and vertical velocity components, temperature, humidity and ozone concentration, as well as for their variances and covariances from aircraft measurements in the convective atmospheric boundary layer over both ocean and land surfaces. We found that the integral scales of the second-order moment quantities are 0.67± 0.09 that of the variables themselves. Consequently, only the second-order moment integral scales are presented here. These results are used to calculate the averaging lengths necessary to measure second-order moment quantities to a given accuracy. We found that a measurement length of 10 to 100 times the boundary-layer height is required to measure variances to 10% accuracy, while scalar fluxes require a measurement length of 102 to 104 and stress a measurement length of 103 to 105 times the boundary layer height. We also show that the ratio of the wavelength of the spectral peak to the integral scale can be used to estimate the sharpness o...

The nonlinear development of Gortler vortices in growing boundary layers

Abstract: The Growth of Gortler vortices in boundary layers on concave walls is investigated. It is shown that for vortices of wavelength comparable to the boundary-layer thickness the appropriate linear stability equations cannot be reduced to ordinary differential equations. The partial differential equations governing the linear stability of the flow are solved numerically, and neutral stability is defined by the condition that a dimensionless energy function associated with the flow should have a maximum or minimum when plotted as a function of the downstream variable X. The position of neutral stability is found to depend on how and where the boundary layer is perturbed, so that the concept of a unique neutral curve so familiar in hydrodynamic-stability theory is not tenable in the Gortler problem, except for asymptotically small wavelengths. The results obtained are compared with previous parallel-flow theories and the small-wavelength asymptotic results of Hall (1982a, b), which are found to be reasonably accurate even for moderate values of the wavelength. The parallel-flow theories of the growth of Gortler vortices are found to be irrelevant except for the small-wavelength limit. The main deficiency of the parallel-flow theories is shown to arise from the inability of any ordinary differential approximation to the full partial differential stability equations to describe adequately the decay of the vortex at the edge of the boundary layer. This deficiency becomes intensified as the wavelength of the vortices increases and is the cause of the wide spread of the neutral curves predicted by parallel-flow theories. It is found that for a wall of constant radius of curvature a given vortex imposed on the flow can grow for at most a finite range of values of X. This result is entirely consistent with, and is explicable by the asymptotic results of, Hall (1982a).

The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities

Abstract: The flow-induced surface instabilities of Kramer-type compliant surfaces are investigated by a variety of theoretical approaches. This class of instability includes all those modes of instability for which the mechanism of generation involves essentially inviscid processes. The results should be applicable to all compliant surfaces that could be modelled theoretically by a thin elastic plate, with or without applied longitudinal tension, supported on a springy elastic foundation. with or without a viscous fluid substrate; material damping is also taken into account through the viscoelastic properties of the solid constituents of the coatings.The simple case of a potential main flow is studied first. The eigenmodes for this case are subjected to an energy analysis following the methods of Landahl (1962). Instabilities that grow both in space and time are then considered, and absolute and convective instabilities identified and analysed.The effects of irreversible processes on the flow-induced surface instabilities are investigated. The shear flow in the boundary layer gives rise to a fluctuating pressure component which is out of phase with the surface motion. This leads to an irreversible transfer of energy from the main stream to the compliant surface. This mechanism is studied in detail and is shown to be responsible for travelling-wave flutter. Simple results are obtained for the critical velocity, wavenumber and stability boundaries. These last are shown to be in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation. An analysis of the effects of a viscous fluid substrate and of material damping is then carried out. The simpler inviscid theory is shown to predict values of the maximum growth rate which are, again, in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation provided that the instability is fairly weak.Compliant surfaces of finite length are analysed in the limit as wave-length tends to zero. In this way the static-divergence instability is predicted. Simple formulae for critical velocity and wavenumber are derived. These are in exact agreement with the results of the simpler infinite-length theory. But, whereas a substantial level of damping is required for the instability on a surface of infinite length, static divergence grows fastest in the absence of damping on a surface of finite length.

Convectively forced internal gravity waves: Results from two-dimensional numerical experiments

Abstract: Two-dimensional numerical simulations were performed to investigate the nature of tropospheric internal gravity waves of the type which are observed to occur above active thermal convection over an unstable boundary layer. These gravity waves are believed to be excited by a combination of pure thermal forcing and by the boundary layer eddies and cumulus clouds acting as obstacles to the flow in the presence of mean environmental wind shear. Large amplitude internal gravity waves were obtained in the simulations with amplitudes and horizontal scales similar to the 12 June 1984 aircraft observations over western Nebraska. This was a day with strong wind shear in the lowest 3 km above the ground and with scattered cumulus clouds topping the boundary layer. The simulations show that there is significant difference between the early time solutions (as might be predicted by linear theory) and late time solutions for the boundary layer eddy structure. A layer interaction occurs in which gravity waves of the stable layer are excited by the boundary layer convection. There is evidence to suggest that this layer interaction occurs both with and without shear but that it is stronger in the presence of low-level shear. Results indicate that shear (or the obstacle) effect is a more efficient generator of gravity waves than is the pure thermal forcing. The simulations show that the gravity waves initially forced by the boundary layer eddies lead to a feedback mechanism that acts to organize the boundary layer eddies and the cumulus convection. The solutions suggest that the character of fair weather convection (moist or dry) is a non-local problem involving at times the full depth of the troposphere. The clouds produced in the simulations have very little influence on the wave field or boundary layer eddy structure as they are relatively small cumuli. On the other hand the clouds are strongly influenced by the interactions between the wave and eddy fields. Upshear growth of cumulus clouds similar to that which is frequently observed in nature is reproduced in the simulations. The development of feeder (‘feeder’ is used here in a dynamical sense only) clouds on (typically) the upshear side of the cloud is found to be a result of the interaction between the gravity wave field and the dry and moist convection. The relative phase velocity between the gravity waves and the cloud plays a crucial role in determining the character of the cumulus cloud growth in the present simulations. These simulations suggest that the dynamics both internal and external to the boundary of a cumulus cloud is a complicated mix between wave dynamics and the usually considered convection dynamics. A brief discussion of the implications of the present results to cloud boundary baroclinic instability dynamics is also presented.

Numerical study of sink-flow boundary layers

Abstract: Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 x 10 to the -6th and 3.0 x 10 to the -6th, are presented. The three-dimensional, time-dependent Navier-Stokes equations are solved numerically, using a spectral method, with about one million degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones and Launder (1972) is observed. The two effects of the favorable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of R(theta) for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 x 10 to the -6th, corresponding to a Reynolds number R(theta) of about 330.

The solar wind interaction with Venus

Abstract: The relation between Venus and the solar wind is analyzed. The effects of the intrinsic field, neutral atmosphere, and ionosphere of Venus on the solar wind are examined. The solar wind interaction phenomena is studied; consideration is given to the free-stream solar wind, bow shock, magnetosheath, boundary layer, ionospheric features, neutral atmosphere features, and wake and magnetotail. Further research on the boundary layer and tail formation, global models, and high-dynamic pressure interaction is proposed.

Vortex shedding and lock-on of a circular cylinder in oscillatory flow

Abstract: An experimental study has been made of a circular cylinder in steady and oscillatory flow with non-zero mean velocity up to a Reynolds number of 40000. The results for the stationary cylinder are in close agreement with previously published data. Skin-friction measurements revealed the amplitude of fluctuation of the boundary layer for different angular locations. It has been universally accepted that bluff bodies shed vortices at their natural frequency of shedding (Strouhal frequency), or, when synchronized with an external unsteadiness, at the frequency of the disturbance or half of it, depending of the direction of the unsteadiness. Our findings, instead, indicate that the shedding frequency may vary smoothly with the driving frequency before locking on its subharmonic. Moreover, the present results indicate that, at the lowest frequency limit of lock-on, vortices are shed simultaneously on both sides of the model. A more traditional alternate pattern of vortex shedding is then recovered at higher driving frequencies.

Lidar Measurements of Wind in the Planetary Boundary Layer: The Method, Accuracy and Results from Joint Measurements with Radiosonde and Kytoon.

Abstract: During the Central Illinois Rainfall Chemistry Experiment (CIRCE), the University of Wisconsin lidar measured wind and turbulence profiles through the planetary boundary layer for a 32-h period in conjunction with surface observations, radiosonde soundings and kytoon profiles made by Argonne National Laboratory. The lidar profiles were made using an advection model for aerosol inhomogeneities as described by Sroga et al. We discuss improvements to this model and explore the accuracy of the lidar wind and boundary layer depth measurements. In addition, the temporal variation of lidar data was utilized to measure boundary layer depth objectively. Cross sections of the speed, direction and rms variation of the wind for the 32-h period show the daytime convective layer, nocturnal stable layer and transitional periods.

A statistical study of the central plasma sheet: Implications for substorm models

Abstract: The University of Iowa Lepedea on board ISEE 1 is used to investigate the characteristics of the central plasma sheet under all levels of geomagnetic activity. Positive ion responses from 1 eV to 45 keV are used in this study. All the periods during 1978 when the central plasma sheet is encountered are included. This study excludes all boundary layer samples. The results of this study show that the central plasma sheet consists of plasma with high thermal energy (several keV) but low bulk speeds. This remains true even during high geomagnetic activity. The main effect of increasing activity is heating of the plasma sheet, preferentially at the high-latitude boundaries.

A simple model of neutrally stratified boundary-layer flow over complex terrain with surface roughness modulations (MS3DJH/3R)

Abstract: The MS3DJH series of simple models of flow over low hills and other terrain features described in earlier papers (see Taylor et al, 1983) required that the terrain was of uniform surface roughness In the present paper, we describe an approximate theory of flow above variations in surface roughness using a similar structure to that established by Jackson and Hunt (1975) for flow over hills This then allows us to include the calculation of flow perturbations due to roughness variations within a modified version of our model which we designate as MS3DJH/3R Comparisons are made with alternative calculations for simple two-dimensional flows; and sample three-dimensional calculations are presented The model retains its essential features of high spatial resolution and low computing cost

The effect of variable properties on laminar boundary layer flow

Abstract: The influence of temperature dependent fluid properties on laminar boundary layer flows is examined for wedge flows (Falkner-Skan). An asymptotic expansion for small heat transfer rates is applied under the boundary conditionsTw= const andqw=const. Linear deviations from the zero order solution (constant properties) can be given in a form known as the property ratio method. As a consequence this method is no longer an empirical one.

Aspherical structure of the core‐mantle boundary from PKP travel times

Abstract: Maps of aspherical structure in the vicinity of the core-mantle boundary have been constructed from a tomographic analysis of P′DF and P′AB travel times in the distance range 150°-180°. These maps reveal long-wavelength features not previously detected by mantle tomography. The peak-to-peak amplitude of these features is on the order of 1 s in vertical travel time, too large to be explained by conventional thermal boundary layer models or dynamically supported topography on the core-mantle boundary. We hypothesize the existence of one or more chemical boundary layers whose large-scale accumulations on the surface of the core may in some ways be analogous to continents at the earth's surface.

Aircraft measurements in the boundary layer

Abstract: Aircraft have had a long history of use for meteorological research. Indeed, the history of aircraft closely parallels the history of meteorology. This is not surprising, since flying requires accurate weather information and, conversely, aircraft provide a convenient and unique platform for collecting meteorological information. Thirty years ago, before the widespread use of pressurized aircraft, a large fraction of aircraft flight time was within the boundary layer. Even now, commercial jet aircraft must at least pass through the boundary layer on takeoff and landing. Thus, the structure of the boundary layer is still very relevant to the needs of aviation. At the same time, developments in aviation technology have led to improved tools for observing the boundary layer from aircraft.

Scrutinizing the k-ε Turbulence Model Under Adverse Pressure Gradient Conditions

Abstract: The k-e model and a one-equation model have been used to predict adverse pressure gradient boundary layers. While the one-equation model gives generally good results, the k-e model reveals systematic discrepancies, e.g. too high skin friction coefficients, for these relatively simple flows. These shortcomings are examined and it is shown by an analytical analysis for the log-law region that the generation term of the e-equation has to be increased to conform with experimental evidence under adverse pressure gradient conditions. A corresponding modification to the e-equation emphasizing the generation rate due to deceleration was employed in the present investigation and resulted in improved predictions for both moderately and strongly decelerated flows.

On similarity in the atmospheric boundary layer

Abstract: A similarity theory for the atmospheric boundary layer is presented. The Monin-Obukhov similarity theory for the surface layer is a particular case of this new theory, for the case of z → 0. Universal functions which are in agreement with empirical data are obtained for the stable and convective regimes.

Boundary-layer receptivity to unsteady pressure gradients: experiments and overview

Abstract: The experimental evidence on the mechanisms of forcing of unstable vorticity waves (the Tollmien–Schlichting–Schubauer or TS waves) of circular frequency ω and wavelength λTS in wall layers by unsteady pressure gradients of amplitude A and frequency ω is reviewed and found to be confused and contradictory. It is proposed that a likely effective receptivity mechanism rests on the fact that under realistic conditions A varies with distance x along any body of finite thickness, A(x), and introduces thereby additional characteristic lengths which can match λTS. Heuristic arguments suggest that through A(x) the pressure gradient infuses vorticity at the wall and forces spatial growth of the TS mean-square vorticity and is proportional to the imaginary part of κTSΔAF(KTS).The proposition is consistent in all currently verifiable respects with one numerical and a series of laboratory experiments. In the laboratory experiments, various configurations of a pulsating pressure source and shielding plates located in the free stream supplied the variable-amplitude pressure gradients over the nearby flat-wall boundary layer. Three of the cases presented here demonstrate that stationary unsteady pressure fields induce Stokes-like sublayers when the boundary layer is stable and self-excited vorticity waves when it is unstable. The results of a fourth experiment suggest that unsteady pressure sources in wakes near the boundary layer can force the growth of unstable wall waves at the wake frequencies even though their propagation speeds differ. Material is also presented on key Soviet experiments and views on receptivity. Finally, these experiments and ours are examined for consistency and complementarity.

Steady and Unsteady Boundary-Layer Separation

Abstract: The inspiring review oflaminar separation by Brown & Stewartson (1969) begins thus: "The phenomenon of separation is one of the most interesting features of the motion of an incompressible fluid past a bluff body at high Reynolds number. Here the main stream, which has hitherto been in close contact with the body, suddenly, and for no obvious reason, breaks away, and downstream a region of eddying flow, which is usually turbulent even if the flow elsewhere is laminar, is set up." These opening lines-which were followed by the above authors' brilliant and timely discourse emphasizing the difficulties associated with separation in classical boundary layers­ make an apt beginning for the present article on the current state of the art. The main feature, to which Brown & Stewarts on in fact alluded strongly, is that given the failure [due to singularities of the S. Goldstein (1948) type] in classical theory at separation, a fresh nonclassical start is necessary for high-Reynolds-number theory to encompass separating flow. This start was made by Stewartson & Williams (1969), Neiland (1969), and Messiter (1970). Our aim is to go from the significant advances made since 1969 to the recent developments and the possible areas of progress in the near future for the rational theory 'of steady and unsteady separation. The physical and theoretical understanding that can emerge from the study of flow structures at large characteristic Reynolds numbers Re is valuable for many reasons. Three major ones are the helpful comparisons with experiments and numerical results, the foundation such study gives to

A Model for Flow Over Two‐Dimensional Bed Forms

Abstract: When non‐cohesive sediment is set in motion by a unidirectional flow, waves of sand often result; moreover, these waves typically are asymmetrical with steep lee faces that produce flow separation. Behind each wave, a wake region forms which grows in height and decays in strength with distance downstream, producing a near‐bottom acceleration. The no‐slip condition at the bed, however, requires an internal boundary layer to form beneath the wake region which retards the flow there. The interaction of these flow processes produces a local maximum in the boundary shear stress downstream of a bump, even over an otherwise flat bed. Because the erosion rate is proportional to the stress divergence for bed load and weak suspended load transport, erosion will occur upstream of this point and desposition will occur downstream of it, thus influencing the bottom shape. Herein, the equations of motion are solved for the accelerating internal boundary layer beneath a wake. The resulting velocity and boundary shear str...

Interactions among Turbulence, Radiation and Microphysics in Arctic Stratus Clouds

Abstract: The Arctic Stratus Experiment, conducted during June 1980 over the Beaufort Sea, produced an extensive set of simultaneous measurements of boundary layer structure, radiation fluxes, and cloud microphysical properties. In this paper these data are used to determine the interactions between mixing, radiative transfer, and cloud microphysics for four cloud decks. The thermodynamic structure and fluxes of the thermodynamic quantities in the cloudy boundary layer are examined, including liquid water fluxes. Net radiative heating profiles are also determined. A detailed analysis of the fine-scale structure of the cloud microphysics is presented, including correlations between the cloud microphysical parameters (droplet concentration, liquid water content, mean radius, spectral dispersion, and the 95% volume liquid water drop radius), which are used to infer the nature of the mixing processes and the local effects of radiative heating/cooling. A comparison is then made with other observations and exist...

Large-Eddy Simulation of a Stratus-Topped Boundary Layer. Part I: Structure and Budgets

Abstract: The structure of a stratus-topped boundary layer is observed through large-eddy simulation which includes the interaction of longwave radiation and turbulence processes. This simulated boundary layer has a relatively warm and dry overlying inversion, a weak surface buoyancy flux, no solar heating, and an insignificant wind shear across the cloud top. The cloud top height and the layer-averaged buoyancy flux inside the cloud layer define a velocity scale appropriate for this of boundary layer. In the cloud layer, buoyancy generates the vertical component of the turbulent kinetic energy, while pressure effect transfer some of this energy into the horizontal components. In the subcloud layer, the only source of the vertical energy other than the surface buoyancy is import from above and the only source of the horizontal energy other than the mean shear is the vertical energy transferred through pressure effects. The profiles of the vertical velocity variance and kinetic energy flux in the stratus-to...

Mesoscale Indexing of the Distribution of Orographic Precipitation over High Mountains

Abstract: A simple analytical expression for indexing the orographic precipitation rate over high mountains is presented. The formula is based upon the assumption that the moisture convergence in the mountainous boundary layer approximately equals the precipitation. Realistic precipitation distributions are obtained when numerical advection is permitted for the Himalayas, Equadorian Andes and the Sierra Nevada Mountains in California. In the latter case the simulated distributions compete well with a fully two-dimensional precipitation model for some unusual stormy events. Following the model results over high mountains, it is suggested that for the distribution of precipitation, particularly over the high mountains, the detailed microphysical processes may play a lesser essential role than that for small to medium size mountains. The elevation of maximum orographic precipitation zm, is investigated and an analytical expression for zm is derived for a bell-shaped mountain. This expression predicts zm value...

Observations of supersonic free shear layers

Abstract: Visual spreading rates of turbulent shear layers with at least one stream supersonic were measured using Schlieren photography. The experiments were done at a variety of Mach number-gas combinations. The spreading rates are correlated with a compressibility-effect parameter called the convective Mach number. It is found that for supersonic values of the convective Mach number, the spreading rate is about one quarter that of an incompressible layer at the same velocity and density ratio. The results are compared with other experimental and theoretical results.

Numerical and Physical Aspects of Aerodynamic Flows

Abstract: Stewartson Memorial Lecture: Experiments are Telling You Something.- 1. Two- and Three-Dimensional Steady Flows.- 1. Predictions of Airfoil Aerodynamic Performance Degradation Due to Icing.- 2. VISTRAFS: A Simulation Method for Strongly Interacting Viscous Transonic Flow.- 3. Coupling Procedures for Viscous-Inviscid Interaction for Attached and Separated Flows on Swept and Tapered Wings.- 4. New Possibilities of Viscous-Inviscid Numerical Techniques for Solving Viscous Flow Equations with Massive Separation.- 5. Prediction of Post-Stall Flows on Airfoils.- 6. Turbulence Characteristics of Trailing-Edge Flows on Thick and Thin Hydrofoils.- 7. Computational Fluid Dynamics at NASA Ames Research Center.- 8. 3-D Composite Velocity Solutions for Subsonic/Transonic Flows.- 9. Calculation of Transonic Flows for Novel Engine-Airframe Installations.- 10. Calculation of Three-Dimensional Boundary Layers Including Hypersonic Flows.- 11. Supersonic/Hypersonic Euler Flowfield Prediction Method for Aircraft Configurations.- 12. Numerical Simulation of Separated and Vortical Flows on Bodies at Large Angles of Attack.- 2. Two- and Three-Dimensional Unsteady Flows.- 13. The Relevance of Unsteady Aerodynamics for Highly Maneuverable and Agile Aircraft.- 14. Experimental and Computational Studies of Dynamic Stall.- 15. A Critique of the Experimental Aerodynamic Data Base for an Oscillating Straked Wing at High Angles.- 16. On the Effects of Wind Tunnel Turbulence on Steady and Unsteady Airfoil Characteristics.- 3. Stability and Transition.- 17. Applications and Suggested Directions of Transition Research.- 18. Prediction of Transition on Airfoils with Separation Bubbles, Swept Wings, and Bodies of Revolution at Incidence.- 19. Transition in Hypersonic Boundary Layers.- 20. Transition Phenomena on Airfoils Operating at Low Chord Reynolds Numbers in Steady and Unsteady Flow.- 21. Disturbance Growth in an Unstable Three-Dimensional Boundary Layer.- 22. Experiments in Swept-Wing Transition.- 23. Experimental Transition and Boundary-Layer Stability Analysis for a Slotted Swept Laminar Flow Control Airfoil.- 24. Leading-Edge Contamination and Relaminarization on a Swept Wing at Incidence.- References.- Index of Contributors.