Showing papers on "Boundary layer published in 1972"

Numerical Investigation of Neutral and Unstable Planetary Boundary Layers

Abstract: Results of numerical integrations are presented for a neutrally stratified planetary boundary layer containing a passive scalar, and for three unstable cases with upward heat flux. The air is assumed unsaturated. A total of either 16,000 or 32,000 grid points was used in a three-dimensional region with length and width several times the height of the boundary layer. A key result is the irrelevance of the neutral height scale, u*/f, and its replacement by the height zi of the inversion base which confines the convective mixing when m and only for the two slightly unstable cases were the vertical velocity eddies distinctly elongated as in Ekman-layer theories. At large instabilities it is shown how the friction velocity u/* loses its influence upon the turbulence intensifies and a convective velocity wale becomes important. Vertical profiles of mean wind, potential tempe...

Structure of the reynolds stress near the wall

Abstract: Experimental studies of the flow field near the wall in a turbulent boundary layer using hot-wire probes are reported. Measurements of the product uv are studied using the technique of conditional sampling with a large digital computer to single out special events (bursting) when large contributions to turbulent energy and Reynolds stress occur. The criterion used to determine when the product uv is sampled is that the streamwise velocity at the edge of the sublayer should have attained a certain value. With this simple criterion we find that 60% of the contribution to is made during only 55% of the total time.

Atmosphere-ocean interaction

Abstract: Preface 1. Basic Concepts 1.1. Notation 1.2. Conservation equations 1.2.1. Conservation of matter 1.2.2. Conservation of momentum 1.2.3. Conservation of energy 1.3. Turbulence and turbulent transport 1.4. Statistical description of fluctuating quantities 1.4.1. Correlation functions and spectra 1.4.2. Isotropic turbulence 1.5. Scaling techniques and similarity relations 2. The State of Matter Near the Interface 2.1. Sea water 2.1.1. The equation of state 2.1.2. Latent heat and saturation vapour pressure of pure water 2.1.3. Colligative properties 2.1.4. Atmospheric gases in solution 2.1.5. Molecular transport coefficients 2.2 Moist air 2.2.1. The equation of state 2.2.2. Molecular transport coefficients 2.2.3. Isobaric mixing and fog formation 2.2.4. Adiabatic and pseudo-adiabatic changes of state 2.3. The liquid-gas interface 2.3.1. Laminar sublayers 2.3.2. Surface tension 2.3.3. Contamination 2.4. Bubbles and spray 2.4.1. Generation of bubbles and spray droplets 2.4.2. Equilibrium pressure in air bubbles and spray droplets 2.4.3. Terminal velocities of gas bubbles and spray droplets 2.4.4. The size and flux spectra of air bubbles in bubble clouds 2.4.5. Sea surface bubble spectra and whitecap coverage as a function of wind speed 2.4.6. The size and flux spectra of spray droplets 2.4.7. Environmental effects of bubbles and spray 2.5 Sea ice 2.5.1. Formation and growth 2.5.2. Physical properties of sea ice 3. Radiation 3.1. Definitions 3.2. Solar radiation 3.2.1. The net short-wave irradiance at the sea surface 3.2.2. Reflection at the sea surface 3.2.3. Absorption of solar radiation in the ocean 3.3. Terrestrial radiation 3.3.1. Long-wave emission from the sea surface 3.3.2. Radiative transfer in the lower atmosphere 3.4. Empirical formulas for estimating the surface radiation budget 3.4.1. Short-wave irradiance 3.4.2. Short-wave exitance 3.4.3. Long-wave irradiance and exitance 4. Surface Wind Waves 4.1. Basic dynamics of harmonic waves in fluids 4.2. Small amplitude waves at the air-sea interface 4.3. Second-order quantities and approximations 4.4. Sources and sinks of surface wave energy 4.4.1. Transfer of energy between waves 4.4.2. Dissipation and breaking 4.4.3. The generation of waves by the wind 4.5. The evolution and parameterization of surface wave spectra 5. Turbulent Transfer Near the Interface 5.1. The structure of the interface and adjacent layers 5.1.1. The profiles in the molecular sublayers 5.1.2. The matching of surface layers to molecular sublayers 5.1.3. Transition from smooth to rough flow 5.2. The effect of stratification 5.3. Dynamic interactions between wind and sea surface 5.3.1. Surface drift 5.3.2. Wind-wave interactions 5.4. Transport of trace gases across the interface 5.4.1. Application of the surface renewal model 5.4.2. The stagnant water film model 5.4.3. Experimental methods and results 5.5. The sea surface temperature (SST) and the energy budget 5.6. Methods to observe the fluxes in the atmospheric surface layer 5.6.1. The eddy correlation method 5.6.2. The eddy accumulation method and the conditional sampling method 5.6.3. The gradient method 5.6.4. The dissipation and inertial dissipation methods 5.6.5. Fluxes obtained with remote sensing techniques 5.6.6. The ageostrophic transport or momentum budget method 5.6.7. Bulk parameterizations 6. The Planetary Boundary Layer 6.1. The Ekman boundary layer 6.1.1. The stationary laminar Ekman layer 6.1.2. Transient Ekman layers and Ekman transports 6.1.3. The depth of the turbulent Ekman layer surface-waves effects 6.2. Coherent structures in the planetary boundary layer 6.2.1. Observations of oceanic longitudinal rolls 6.2.2. Observations of atmospheric longitudinal rolls 6.2.3. Laboratory experiments 6.2.4. Numerical simulations 6.2.5. Energetics of longitudinal rolls 6.2.6. Physical concepts and theories 6.3. Parametric representation of PBL fluxes and profiles 6.3.1. Diffusive models 6.3.2. The transilient scheme 6.3.3. Parametric representation of PBL profiles 6.4. Mixed-layer models 6.4.1. The oceanic mixed layer 6.4.2. The cloud-free atmospheric mixed layer 6.4.3. The cloud-topped convective marine boundary layer 6.5. Discussion and evaluation 7. Atmospherically-forced Perturbations in the Oceans 7.1. Perturbations of a shallow, homogeneous ocean 7.1.1. The different types of atmospheric forcing 7.1.2. The forced shallow water equation 7.1.3. Perturbations of different extent and duration 7.2. The two-layer ocean model 7.2.1. The governing equations 7.2.2. Gravity waves at an internal density discontinuity 7.2.3. The rigid-lid approximation 7.2.4. Ekman pumping 7.3. Internal inertio-gravity waves 7.3.1. Internal waves in a continuously-stratified ocean 7.3.2. Long-waves normal modes 7.3.3. Atmospheric forcing of inertio-gravity waves 7.4. The response of the open ocean to moving cyclonic storms 7.4.1. Observations 7.4.2. The simulated short-term oceanic response to moving storms 7.4.3. The long-term oceanic response to moving storms 7.5. The effect of lateral boundaries on wind-forced perturbations 7.5.1. Wind-forced upwelling and downwelling along a straight coast 7.5.2. Coastal Kelvin waves 7.5.3. Shelf waves 7.5.4. Storm surges 7.6. Rossby or planetary waves 7.6.1. Free planetary waves 7.6.2. Forced plantary waves 7.7. Equatorial currents and perturbations 7.7.1. Balanced equatorial currents 7.7.2. Equatorial perturbations 8. Large Scale Forcing by Sea Surface Buoyancy Fluxes 8.1. The predominant direction and variability of air-sea interactions 8.2. Deep convection 8.2.1. The general character and organization of deep convection 8.2.2. Laboratory experiments and dimensional analysis 8.2.3. Deep convection and bottom-water formation in the oceans 8.3. The tropical atmosphere 8.3.1. Deep convection in the presence of clouds and precipitation 8.3.2. The Inter-Tropical Convergence Zone (ITCZ) and the Hadley circulation 8.3.3. Hurricanes 8.4. Some low-frequency ocean-atmosphere feedback processes 8.4.1. El Nino and the Southern Oscillation (ENSO) 8.4.2. The Somali current and the Indian monsoon 8.4.3. Interactions between the hydrological cycle and the thermo-haline circulation

On the determination of the height of the Ekman boundary layer

Abstract: The heighth τ of the Ekman turbulent boundary layer determined by the momentum flux profile is estimated with the aid of considerations of similarity and an analysis of the dynamic equations. Asymptotic formulae have been obtained showing that, with increasing instability,h τ increases as ¦μ¦1/2 (where μ is the non-dimensional stratification parameter); with increasing stability, on the other hand,h decreases as μ−1/2. For comparison, a simple estimate of the boundary-layer heighth u determined by the velocity profile is given. As is shown, in unstable stratification,h u behaves asymptotically as ¦μ¦−1, i.e., in a manner entirely different from that ofh τ.

Mechanism by Which a Two‐Dimensional Roughness Element Induces Boundary‐Layer Transition

Abstract: An experimental investigation of the effect of two‐dimensional roughness elements on boundary‐layer transition is described. Primary emphasis is given to the nature of disturbances within the recovery zone, i.e., that region in the immediate downstream of the roughness where the mean flow has been distorted by the presence of the roughness. Detailed measurements of mean velocity distributions, of disturbance spectra, and intensity, growth, and decay of disturbances at discrete frequencies were made for a range of unit Reynolds numbers. The measurements demonstrate that the behavior can best be understood by considering wave‐type disturbances, and that the basic mechanism by which a two‐dimensional roughness element induces earlier transition to turbulent flow is by the destabilizing influence of the flow within the recovery zone. Comparison with the behavior expected from stability theory supports this conclusion.

Mechanism by which a two-dimensional roughness element induces boundary-layer transition: roughness induced transition

Abstract: An experimental investigation of the effect of two-dimensional roughness elements on boundary layer transition is described. Primary emphasis is given to the nature of disturbances within the recovery zone, i.e., that region in the immediate downstream of the roughness where the mean flow has been distorted by the presence of the roughness. Detailed measurements of mean velocity distributions, of disturbance spectra, and intensity, growth, and decay of disturbances at discrete frequencies were made for a range of unit Reynolds number. The measurements demonstrate that the behavior can best be understood by considering wave-type disturbances, and that the basic mechanism by which a two-dimensional roughness element induces earlier transition to turbulent flow is by the destabilizing influence of the flow within the recovery zone. Comparison with the behavior expected from stability theory supports this conclusion.

Theory of laminar boundary layer separation in supersonic flow

Abstract: A method of calculation is constructed for the Navier-Stokes equations using asymptotic expansions for high Reynolds numbers and matching techniques to join solutions (for example, [1]). The equations and boundary conditions for the first approximation, the method, and the results of numerical integration for the region lying above the separation point, including the separation point as well, are presented. A comparison is made with experimental data, and corrections corresponding to the second approximation are estimated. On the basis of these results, the limits of applicability of the approximate theories that utilize the boundary layer equations are discussed.

Time Scales and Correlations in a Turbulent Boundary Layer

Abstract: Space‐time correlations with large streamwise separation were obtained in a turbulent boundary layer with a zero‐pressure gradient. The auto and cross correlations of the velocities u and υ with streamwise spatial separation distances up to 20 boundary layer thicknesses revealed a difference in their structure and decay rate. Using conditional averaging techniques, the velocity product, uυ, was sampled in both the turbulent and nonturbulent zones. Further conditional sampling led to an average picture of the velocities in the interfacial bulges. Near the wall the space‐time correlation results are consistent with the idea of retarded fluid being ejected outward from the wall region and influencing the intermittent region.

A Theoretical and Experimental Study of the Internal Circulation in Water Drops Falling at Terminal Velocity in Air

Abstract: Four theoretical approaches are presented for quantitatively determining the intensity of the internal circulation and the flow patterns inside and outside liquid water spheres falling at terminal velocity in air. The first approach assumes creeping flow outside and inside a water sphere, the second assumes potential flow outside and inviscid motion inside a water sphere, the third makes use of boundary layer theory, and the fourth approach uses a numerical method to solve the full Navier-Stokes equation of motion inside and outside a water sphere. The theoretical predictions are compared with data obtained from new quantitative wind tunnel experiments on spherical and deformed water drops. The results show that the creeping flow analysis greatly underestimates the strength of the internal velocity while the inviscid flow analysis greatly overestimates it. On the other hand, the results of the boundary layer approach and of the numerical approach agree reasonably well with the experimental data f...

A Mesoseale Numerical Model of Lake-Fffect Storms

Abstract: The atmospheric structure upwind of the Great takes during arctic air outbreaks is represented by three layers: a lower constant flux layer in contact with the ground, a well-mixed planetary boundary layer surmounted by an inversion, and a deep stratum of overlying stable air. The set of primitive equations is averaged through the depth of the mixed layer to yield predictive equations for the horizontal components of velocity, potential temperature and specific humidity in the layer, and the height of the inversion. Interactions between the well-mixed convective layer and both the underlying and overlying layers are parameterized so that time-dependent calculations can be limited to a single layer. Precipitation from cumulus clouds within the layer is represented in terms of the mesoscale variables and latent heat is included. The equation set has been solved numerically for a 2000-point grid mesh centered on Lake Erie. Grid separation was 6 km in the cross-lake direction and 12 km along the lake...

Flow in a deep turbulent boundary layer over a surface distorted by water waves

Abstract: Linearized equations for the mean flow and for the turbulent stresses over sinusoidal, travelling surface waves are derived using assumptions similar to those used by Bradshaw, Ferriss & Atwell (1967) to compute boundary-layer development. With the assumptions, the effects on the local turbulent stresses of advectal, vertical transport, generation and dissipation of turbulent energy can be assessed, and solutions of the equations are expected to resemble closely real flows with the same conditions. The calculated distributions of surface pressure indicate rates of wave growth (expressed as fractional energy gain during a radian advance of phase) of about 15(ρ a /ρ w ) (τ o / c 2 ), where τ o is the surface stress, c o the phase velocity and ρ a and ρ w the densities of air and water, unless the wind velocity at height λ/2π is less than the phase velocity. The rates are considerably less than those measured by Snyder & Cox (1966), by Barnett & Wilkerson (1967) and by Dobson (1971), and arguments are presented to show that the linear approximation fails for wave slopes of order 0.1.

Shallow Water Waves on a Viscous Fluid—The Undular Bore

Abstract: A theory is presented for the surface profile above a fully developed Poiseuille channel flow. Small disturbances to this flow are examined, and it is shown that if the (channel depth)/(wavelength) ratio is small (shallow waves), and the Reynolds number large enough, these disturbances initially travel at the classical dynamic (Burns) wave speeds. However, by introducing appropriate far‐field coordinates it follows that the disturbance eventually travels at a different wave speed—the kinematic wave speed. To confirm this, the dynamic waves are shown to decay by using standard boundary layer techniques. This general result (of decay) agrees with previous one‐dimensional theories. The profile close to the kinematic wave front is examined and shown to satisfy an equation of the form ηT + ηηX + ηXXX = ΔηXX, where η(X, T) is the surface profile. This equation is called the Korteweg‐de Vries‐Burgers equation. The form of the steady solution of this equation exhibits all the characteristics of the undular bore. A bound on Δ agrees with stability requirements found by other authors using different methods.

Shock Wave Turbulent Boundary Layer Interaction in Hypersonic Flow

Abstract: : A study is presented of the characteristics of transitional and turbulent layers, and regions of shock wave-turbulent boundary layer interaction in high Reynolds number hypersonic flow. An examination and correlation of skin friction, heat transfer and pressure measurements in laminar, transitional and turbulent boundary layers on sharp flat plates and cones are presented for the Mach range from 3 to 13 at wall-to-free stream temperature ratios from 0.1 to 0. 4.

Some properties of sink-flow turbulent boundary layers

Abstract: An experimental study of asymptotic sink-flow turbulent boundary layers is reported. Three levels of acceleration corresponding to values of the acceleration parameter K of 1·5 × 10−6, 2·5 × 10×6 and 3·0 × 10×6 have been examined. In addition to mean velocity profiles, measurements have been obtained of the profiles of longitudinal turbulence intensity, and, for the lowest value of K, of the lateral and transverse components as well. Measurements at selected positions in the boundary layer of the power spectral density indicate that none of the boundary layers exhibit an inertial subrange; for the steepest acceleration, in particular, throughout the boundary layer the spectrum shapes are similar in form to those reported within the viscous sublayer of a high Reynolds number turbulent flow.

Calculation of Turbulent Shear Flows for Atmospheric and Vortex Motions

Abstract: Turbulent shear flows transport properties, computing atmospheric and vortex motions by invariant modeling of Reynolds stress term in boundary layer momentum equation

Large-scale motion of a turbulent boundary layer during relaminarization

Abstract: A fully developed turbulent boundary layer was subjected to a strongly favourable pressure gradient in order to investigate the role of the large eddy structure during ‘relaminarization’. Measurements of%he mean velocity profiles indicated that the ‘law of the wall’ disappeared in the region of the maximum pressure gradient. The three fluctuating velocity components and the tangential Reynolds stress were obtained to determine more precisely the nature of the decay of the turbulent structure. These measurements indicated that the absolute level of the velocities and stress were approximately constant along a mean streamline except near the wall. However, the relative levels were decreasing, as reported previously by several authors. The intermittency factor γ decreased along the mean streamlines until most of the boundary layer had only a negligible turbulence level. Space-time auto- and cross-correlations of u, v and I (the intermittency function) of the large-scale structure were obtained in the region of maximum pressure gradient and are compared with those measured in a zero pressure gradient flow.

Effect of nozzle boundary layers on rocket exhaust plumes.

Abstract: T expansion of a nozzle boundary layer into a vacuum has been treated numerically by Boynton. Following Weinbaum and Weiss and Weinbaum, Boynton treated the expansion as inviscid with the initial conditions specified by the viscous layer. Boynton demonstrated large differences in the plume properties when the influence of the supersonic portion of the nozzle boundary layer was included. In this Note, an effort is made to generalize Boynton's results and express the plume properties in terms of the boundary-layer thickness and nozzle exit conditions.

Separation Patterns of Boundary Layer over an Inclined Body of Revolution

Abstract: Based on recent symmetry-plane boundary-layer solutions, new separation patterns over an inclined body of revolution are presented. Support by experimental evidence as well as differences from other predictions in the literature are noted. Existing three-dimensional separation criteria are mostly inapplicable, and the resulting patterns found are compatible only with MaskelPs general description of separation—i.e., a combination of the free vortex layer type and a bubble type. For a not too blunt body, a bubble type prevails at low incidence, and a free vortex layer type dominates a high incidence. At extremely high incidence or for a more blunt body, a bubble type prevails again.

A Study of the Bottom Boundary Layer of the Florida Current

Abstract: This is a report of an experiment designed to study the bottom boundary layer of the Florida Current at a representative site in the Straits of Florida. The objectives of the experiment were 1) to ...

Spreading of a turbulent disturbance.

Abstract: The presented paper shows the effect of local Mach number on the turbulent disturbance spreading angle relative to the wall and on lateral disturbance spreading angles. Almost all the disturbances angles relative to the wall were determined from investigations where hot-wire contours or hot-film surveys of a 'laminar' boundary layer were obtained. Lateral disturbance spreading angles were obtained from investigations of various conditions including turbulent bursts, reported observations of transverse contamination, and observed transitional flow. It is noted that the disturbance spreading angle relative to the wall seems to remain essentially invariant with Mach number, while the lateral spreading angle decreases sharply with increasing Mach number up to about 6. The good agreement between lateral disturbance spreading angle data and data for the variation of turbulent jet spreading angle with Mach number implies that in the lateral dimension, turbulence in a boundary layer may develop essentially free of wall constraints (similar to a free shear layer).

Microscale pressure fluctuations measured within the lower atmospheric boundary layer

Abstract: Eulerian measurements of microscale fluctuations in static pressure are used, in conjunction with measurements of air velocity, to describe some of the properties of the static pressure fluctuations that occur within the turbulent flow of the lower atmospheric boundary layer. Using an instrument developed to measure the static pressure at a point within the boundary layer, data were collected at heights ranging from the surface up to about 6 m. The results are presented as power spectra, cross-spectra, coherence and phase. For all observations over a flat boundary the root-mean-square pressure produced by the boundary-layer turbulence is about 2.6 times the mean stress. The pressure spectra are found to have a, well-defined shape which does not change with height above the surface; at the higher frequencies the spectra show a power-law behaviour with a mean slope of −1·7. A number of observations with two pressure sensors are used to describe the structure and propagation velocity of individual pressure pulses.A dominant feature of the pressure-velocity relationship is that the large-scale pressure fluctuations are approximately in phase with the downstream velocity fluctuations; at small scales there is a large phase difference (∼−135°). These phase differences are interpreted to be the result of interaction of the large pressure-producing scales with the earth's surface, the small scales being ‘free’ of the surface. Prom the simultaneous measurements of pressure and downstream velocity the effect of pressure forces on the energy flux out of the downstream velocity fluctuations was evaluated. Typical values are about 0-45 of the net energy source to the downstream component. By means of pressure and vertical velocity measurements an estimate of the pressure divergence term in the net energy budget of a boundary layer is made. It was found to be about 1/10 of the energy feeding term.

On the Inflection Point Instability of a Stratified Ekman Boundary Layer.

Abstract: The neutral Ekman boundary layer is known to be dynamically unstable to infinitesimal perturbations under typical geophysical conditions. This paper discusses this instability to two-dimensional, simple-harmonic perturbations, for the stratified Ekman layer. While viscosity and Coriolis forces are generally important in setting up the basic mean profile, the inflection point instability can be investigated in the inviscid, non-rotating system limit. However, the singular nature of the resulting second-order characteristic equation makes it necessary to solve the non-singular sixth-order, viscous stratified equation. Since typically occurring Reynolds numbers are much larger than critical, emphasis has been placed on investigating the behavior of maximum growth rates versus stratification for large Re. The appropriate dimensionless parameters are found to be: ξ=(2/Ro Re)½, and Ra= gSδ4/KmmKh [where δ=(2K/ f)½, Re= Vgδ/Km, Ro=Vg/fδ and S=(z+g/ cp)/] for the general case, or ξ and RI=gS/Vz for the i...

A method for integrating the boundary-layer equations through a region of reverse flow

Abstract: Development of a procedure for numerically integrating the boundary-layer equations through a region of reverse flow which takes downstream influence into account. This method is applied to the problem of uniform flow past a parallel flat plate of finite length whose surface has a constant velocity directed opposite to that of the main stream. Although singularities occur at both the point of detachment (x sub s) and reattachment (x sub r) of the psi = 0 streamline, this integration technique provides a solution which ceases to apply only in the close proximity of these singular points. From this solution it is evident that, throughout a large portion of the separated region, the flow is strongly affected by conditions near x sub r, thereby demonstrating the importance of allowing information to be transmitted upstream in a region of backflow. Near x sub s, however, it is found that, in spite of the presence of reverse flow, the solution has a self-similar form in this particular example.