Abstract: ▪ Abstract The single-point statistics of turbulence in the ‘roughness sub-layer’ occupied by the plant canopy and the air layer just above it differ significantly from those in the surface layer. The mean velocity profile is inflected, second moments are strongly inhomogeneous with height, skewnesses are large, and second-moment budgets are far from local equilibrium. Velocity moments scale with single length and time scales throughout the layer rather than depending on height. Large coherent structures control turbulence dynamics. Sweeps rather than ejections dominate eddy fluxes and a typical large eddy consists of a pair of counter-rotating streamwise vortices, the downdraft between the vortex pair generating the sweep. Comparison with the statistics and instability modes of the plane mixing layer shows that the latter rather than the boundary layer is the appropriate model for canopy flow and that the dominant large eddies are the result of an inviscid instability of the inflected mean velocity profi...

Abstract: A new boundary layer turbulent mixing scheme has been developed for use in the UKMO weather forecasting and climate prediction models. This includes a representation of nonlocal mixing (driven by both surface fluxes and cloud-top processes) in unstable layers, either coupled to or decoupled from the surface, and an explicit entrainment parameterization. The scheme is formulated in moist conserved variables so that it can treat both dry and cloudy layers. Details of the scheme and examples of its performance in single-column model tests are presented.

Abstract: An investigation is made into the moving contact line dynamics of a Cahn–Hilliard–van der Waals (CHW) diffuse mean-field interface. The interface separates two incompressible viscous fluids and can evolve either through convection or through diffusion driven by chemical potential gradients. The purpose of this paper is to show how the CHW moving contact line compares to the classical sharp interface contact line. It therefore discusses the asymptotics of the CHW contact line velocity and chemical potential fields as the interface thickness e and the mobility κ both go to zero. The CHW and classical velocity fields have the same outer behaviour but can have very different inner behaviours and physics. In the CHW model, wall–liquid bonds are broken by chemical potential gradients instead of by shear and change of material at the wall is accomplished by diffusion rather than convection. The result is, mathematically at least, that the CHW moving contact line can exist even with no-slip conditions for the velocity. The relevance and realism or lack thereof of this is considered through the course of the paper.The two contacting fluids are assumed to be Newtonian and, to a first approximation, to obey the no-slip condition. The analysis is linear. For simplicity most of the analysis and results are for a 90° contact angle and for the fluids having equal dynamic viscosity μ and mobility κ. There are two regions of flow. To leading order the outer-region velocity field is the same as for sharp interfaces (flow field independent of r) while the chemical potential behaves like r−ξ, ξ = π/2/max{θeq, π − θeq}, θeq being the equilibrium contact angle. An exception to this occurs for θeq = 90°, when the chemical potential behaves like ln r/r. The diffusive and viscous contact line singularities implied by these outer solutions are resolved in the inner region through chemical diffusion. The length scale of the inner region is about 10√μκ – typically about 0.5–5 nm. Diffusive fluxes in this region are O(1). These counterbalance the effects of the velocity, which, because of the assumed no-slip boundary condition, fluxes material through the interface in a narrow boundary layer next to the wall.The asymptotic analysis is supplemented by both linearized and nonlinear finite difference calculations. These are made at two scales, experimental and nanoscale. The first set is done to show CHW interface behaviour and to test the qualitative applicability of the CHW model and its asymptotic theory to practical computations of experimental scale, nonlinear, low capillary number flows. The nanoscale calculations are carried out with realistic interface thicknesses and diffusivities and with various assumed levels of shear-induced slip. These are discussed in an attempt to evaluate the physical relevance of the CHW diffusive model. The various asymptotic and numerical results together indicate a potential usefullness for the CHW model for calculating and modelling wetting and dewetting flows.

Abstract: The dependence on initial conditions of the three-dimensional algebraic spatial instability of the Blasius boundary layer is examined by a recently developed method of receptivity analysis based on the upstream integration of adjoint equations. This method allows us to determine optimal perturbations, i.e. initial perturbations that maximize the energy growth, even in the wavenumber range where the problem is not amenable to a mode analysis, and thus to complement a previous paper in which the small-wavenumber regime was described.

Abstract: Direct numerical simulation of the incompressible Navier–Stokes equations is used to study flows where laminar boundary-layer separation is followed by turbulent reattachment forming a closed region known as a laminar separation bubble. In the simulations a laminar boundary layer is forced to separate by the action of a suction profile applied as the upper boundary condition. The separated shear layer undergoes transition via oblique modes and [Lambda]-vortex-induced breakdown and reattaches as turbulent flow, slowly recovering to an equilibrium turbulent boundary layer. Compared with classical experiments the computed bubbles may be classified as ‘short’, as the external potential flow is only affected in the immediate vicinity of the bubble. Near reattachment budgets of turbulence kinetic energy are dominated by turbulence events away from the wall. Characteristics of near-wall turbulence only develop several bubble lengths downstream of reattachment. Comparisons are made with two-dimensional simulations which fail to capture many of the detailed features of the full three-dimensional simulations. Stability characteristics of mean flow profiles are computed in the separated flow region for a family of velocity profiles generated using simulation data. Absolute instability is shown to require reverse flows of the order of 15–20%. The three-dimensional bubbles with turbulent reattachment have maximum reverse flows of less than 8% and it is concluded that for these bubbles the basic instability is convective in nature.

Abstract: The near-wall regions of high Reynolds numbers turbulent flows must be modelled to treat many practical engineering and aeronautical applications. In this review we examine results from simulations of both attached and separated flows on coarse grids in which the near-wall regions are not resolved and are instead represented by approximate wall boundary conditions. The simulations use the dynamic Smagorinsky subgrid-scale model and a second-order finite-difference method. Typical results are found to be mixed, with acceptable results found in many cases in the core of the flow far from the walls, provided there is adequate numerical resolution, but with poorer results generally found near the wall. Deficiencies in this approach are caused in part by both inaccuracies in subgrid-scale modelling and numerical errors in the low-order finite-difference method on coarse near-wall grids, which should be taken into account when constructing models and performing large-eddy simulation on coarse grids. A promising new method for developing wall models from optimal control theory is also discussed.

Abstract: Bed stresses in the bottom boundary layer of the York River estuary, Virginia, were estimated from three-dimensional near-bottom velocities measured by Acoustic Doppler Velocimeters (ADVs) and also by a profiling array of electromagnetic current meters. By assuming the measurements were made in a constant stress layer, four methods of stress estimation were evaluated using ADVs: direct covariance (COV) measurement, turbulent kinetic energy, inertial dissipation utilizing the Kolmogorov spectrum, and log profile. The four methods yielded similar estimates of frictional velocity (U*) based on ADV output from both 14 cm and 44 cm above bed. All eight estimates of average U* were consistent with the overall mean of 1.10 cm/s to within the 95% confidence interval for individual burst estimates. The COV method worked slightly better nearer the bed, possibly because of the sensitivity of COV to the upper limit of the constant stress layer. The inertial dissipation method performed marginally well at 14 cm above bed, likely because of sediment induced stratification and insufficient separation of turbulent production and dissipation scales. The log profile method was the most variable and appeared most sensitive to stratification and to the thickness of the constant stress layer. The turbulent kinetic energy method was the most consistent at both heights and appears most promising for further development. Results encourage future use of the ADV in estuarine environments but also favor the simultaneous use of several methods to estimate bottom stress.

Abstract: The MM5 mesoscale model is used to simulate Hurricane Bob (1991) using grids nested to high resolution (4 km). Tests are conducted to determine the sensitivity of the simulation to the available planetary boundary layer parameterizations, including the bulk-aerodynamic, Blackadar, Medium-RanGe Forecast (MRF) model, and Burk-Thompson boundary-layer schemes. Significant sensitivity is seen, with minimum central pressures varying by up to 17 mb. The Burk-Thompson and bulk-aerodynamic boundary-layer schemes produced the strongest storms while the MRF scheme produced the weakest storm. Precipitation structure of the simulated hurricanes also varied substantially with the boundary layer parameterizations. Diagnostics of boundary-layer variables indicated that the intensity of the simulated hurricanes generally increased as the ratio of the surface exchange coefficients for heat and momentum, C(sub h)/C(sub M), although the manner in which the vertical mixing takes place was also important. Findings specific to the boundary-layer schemes include: 1) the MRF scheme produces mixing that is too deep and causes drying of the lower boundary layer in the inner-core region of the hurricane; 2) the bulk-aerodynamic scheme produces mixing that is probably too shallow, but results in a strong hurricane because of a large value of C(sub h)/C(sub M) (approximately 1.3); 3) the MRF and Blackadar schemes are weak partly because of smaller surface moisture fluxes that result in a reduced value of C(sub h)/C(sub M) (approximately 0.7); 4) the Burk-Thompson scheme produces a strong storm with C(sub h)/C(sub M) approximately 1; and 5) the formulation of the wind-speed dependence of the surface roughness parameter, z(sub 0), is important for getting appropriate values of the surface exchange coefficients in hurricanes based upon current estimates of these parameters.

Abstract: Two independent experimental investigations of the behavior of turbulent boundary layers with increasing Reynolds number were recently completed. The experiments were performed in two facilities, the Minimum Turbulence Level (MTL) wind tunnel at Royal Institute of Technology (KTH) and the National Diagnostic Facility (NDF) wind tunnel at Illinois Institute of Technology (IIT). Both experiments utilized oil-film interferometry to obtain an independent measure of the wall-shear stress. A collaborative study by the principals of the two experiments, aimed at understanding the characteristics of the overlap region between the inner and outer parts of the boundary layer, has just been completed. The results are summarized here, utilizing the profiles of the mean velocity, for Reynolds numbers based on the momentum thickness ranging from 2500 to 27 000. Contrary to the conclusions of some earlier publications, careful analysis of the data reveals no significant Reynolds number dependence for the parameters desc...

Abstract: A direct numerical simulation of a supersonic turbulent boundary layer has been performed. We take advantage of a technique developed by Spalart for incompressible flow. In this technique, it is assumed that the boundary layer grows so slowly in the streamwise direction that the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for by a coordinate transformation and a multiple-scale analysis. The result is a modified system of equations, in which the flow is homogeneous in both the streamwise and spanwise directions, and which represents the state of the boundary layer at a given streamwise location. The equations are solved using a mixed Fourier and B-spline Galerkin method.Results are presented for a case having an adiabatic wall, a Mach number of M = 2.5, and a Reynolds number, based on momentum integral thickness and wall viscosity, of Reθ′ = 849. The Reynolds number based on momentum integral thickness and free-stream viscosity is Reθ = 1577. The results indicate that the Van Driest transformed velocity satisfies the incompressible scalings and a small logarithmic region is obtained. Both turbulence intensities and the Reynolds shear stress compare well with the incompressible simulations of Spalart when scaled by mean density. Pressure fluctuations are higher than in incompressible flow. Morkovin's prediction that streamwise velocity and temperature fluctuations should be anti-correlated, which happens to be supported by compressible experiments, does not hold in the simulation. Instead, a relationship is found between the rates of turbulent heat and momentum transfer. The turbulent kinetic energy budget is computed and compared with the budgets from Spalart's incompressible simulations.

Abstract: Turbulent boundary layers near the trailing edge of a lifting surface are known to generate intense, broadband scattering noise as well as surface pressure e uctuations. Numerically predicting the trailing-edge noise requires that the noise-generating eddies over a wide range of length scales be adequately represented. The large-eddy simulation (LES) technique provides a promising tool for obtaining the unsteady wall-pressure e elds and the acousticsourcefunctions. An LES iscarried out forturbulent boundary-layere ow pastan asymmetrically beveled trailing edge ofa e at strut at a chord Reynolds number of 2 :15 £ 10 6 . The computed velocity and surface pressure statistics compare reasonably well with previous experimental measurements. The far-e eld acoustic calculation is facilitated by the integral solution to the Lighthill equation derived by Ffowcs-Williams and Hall. Computations havebeen carried outto determine thefar-e eld noisespectra,thesource-term characteristics, and therequirement for the integration domain size. It is found that the present LES domain is adequate for predicting noise radiation over a range of frequencies. At the low-frequency end, however, the spanwise source coherenceestimated based on surface pressure e uctuations does not decay sufe ciently, suggesting the need for a wider computational domain.

Abstract: Using the large eddy simulation (LES) technique, the authors study a clear-air, stably stratified atmospheric boundary layer (ABL) as it approaches a quasi-steady state. The Beaufort Sea Arctic Stratus Experiment (BASE) dataset is used to impose initial and boundary conditions. The authors explore the parameter space of the boundary layer by varying latitude, surface cooling rate, geostrophic wind, inversion strength, and surface roughness. Recognizing the critical dependence of the results of LES on the subgrid-scale (SGS) model, they test and use a nonlinear SGS model, which is capable of reproducing the effects of backscatter of turbulent kinetic energy (TKE) and of the SGS anisotropies characteristic for shear-driven flows. In order to conduct a long-term LES so that an ABL can reach a quasi-steady state, a parallel computer code is developed and simulations with a spatial domain of up to 963 grid points are performed. The authors analyze the evolution of the mean wind, potential temperature,...

Abstract: The use of a discontinuous control law (typically, sign functions) in a sampled-data system will bring about chattering phenomenon in the vicinity of the sliding manifold, leading to a boundary layer with thickness O(T), where T is the sampling period. However, by proper consideration of the sampling phenomenon in the discrete-time sliding mode control design, the thickness of the boundary layer can be reduced to O(T/sup 2/). In contrast to discontinuous control for continuous-time VSS, the discrete-time sliding mode control need not be of switching type.

Abstract: The authors examine measurements of boundary layer height zi and entrainment zone thickness observed with two lidars and with a radar wind profiler during the Flatland96 Lidars in Flat Terrain experiment. Lidar backscatter is proportional to aerosol content (and some molecular scatter) in the boundary layer, and wind profiler backscatter depends on the refractive index structure (moisture gradients and turbulence strength). Although these backscatter mechanisms are very different, good agreement is found in measurements of zi at 1-h resolution. When the dataset is limited to daytime convective conditions (times between 1000 and 1700 LT), correlation coefficients between the profiler and each lidar are 0.87 and 0.95. Correlation between the two lidars is 0.99. Comparisons of entrainment zone thickness show less agreement, with correlation coefficients of about 0.6 between the profiler and lidars and 0.8 between the two lidars. The lidar measurements of zi make use of coefficients of a Haar continu...

Abstract: The laminar boundary layer on a flat surface is made to separate by way of aspiration through an opposite boundary, causing approximately a 25% deceleration. The detached shear layer transitions to turbulence, reattaches, and evolves towards a normal turbulent boundary layer. We performed the direct numerical simulation (DNS) of this flow, and believe that a precise experimental repeat is possible. The pressure distribution and the Reynolds number based on bubble length are close to those on airfoils; numerous features are in agreement with Gaster's and other experiments and correlations. At transition a large negative surge in skin friction is seen, following weak negative values and a brief contact with zero; this could be described as a turbulent re-separation. Temperature is treated as a passive scalar, first with uniform wall temperature and then with uniform wall heat flux. The transition mechanism involves the wavering of the shear layer and then Kelvin–Helmholtz vortices, which instantly become three-dimensional without pairing, but not primary Gortler vortices. The possible dependence of the DNS solution on the residual incoming disturbances, which we keep well below 0.1%, and on the presence of a ‘hard’ opposite boundary, are discussed. We argue that this flow, unlike the many transitional flows which hinge on a convective instability, is fully specified by just three parameters: the amount of aspiration, and the streamwise and the depth Reynolds numbers (heat transfer adds the Prandtl number). This makes comparisons meaningful, and relevant to separation bubbles on airfoils in low-disturbance environments. We obtained Reynolds-averaged Navier–Stokes (RANS) results with simple turbulence models and spontaneous transition. The agreement on skin friction, displacement thickness, and pressure is rather good, which we attribute to the simple nature of ‘transition by contact’ due to flow reversal. In contrast, a surge of the heat-transfer coefficient violates the Reynolds analogy, and is greatly under-predicted by the models.

Abstract: The turbulent boundary layer along a compression ramp with a deflection angle of 18° at a free-stream Mach number of M = 3 and a Reynolds number of Reθ = 1685 with respect to free-stream quantities and mean momentum thickness at inflow is studied by direct numerical simulation. The conservation equations for mass, momentum, and energy are solved in generalized coordinates using a 5th-order hybrid compact- finite-difference-ENO scheme for the spatial discretization of the convective fluxes and 6th-order central compact finite differences for the diffusive fluxes. For time advancement a 3rd-order Runge–Kutta scheme is used. The computational domain is discretized with about 15 × 106 grid points. Turbulent inflow data are provided by a separate zero-pressure-gradient boundary-layer simulation. For statistical analysis, the flow is sampled 600 times over about 385 characteristic timescales δ0/U∞, defined by the mean boundary-layer thickness at inflow and the free-stream velocity. Diagnostics show that the numerical representation of the flow field is sufficiently well resolved.Near the corner, a small area of separated flow develops. The shock motion is limited to less than about 10% of the mean boundary-layer thickness. The shock oscillates slightly around its mean location with a frequency of similar magnitude to the bursting frequency of the incoming boundary layer. Turbulent fluctuations are significantly amplified owing to the shock–boundary-layer interaction. Reynolds-stress maxima are amplified by a factor of about 4. Turbulent normal and shear stresses are amplified differently, resulting in a change of the structure parameter. Compressibility affects the turbulence structure in the interaction area around the corner and during the relaxation after reattachment downstream of the corner. Correlations involving pressure fluctuations are significantly enhanced in these regions. The strong Reynolds analogy which suggests a perfect correlation between velocity and temperature fluctuations is found to be invalid in the interaction area.

Abstract: In this paper a new analysis is proposed for the driving mechanisms and the statistics for turbulent boundary layers at very high Reynolds numbers. It differs from theories for moderate to low Reynolds numbers and is based on the results of (linear) rapid distortion theory, and both laboratory and field experimental data. The large-scale eddy structure near the wall in boundary layers is distorted in several ways: by the strong mean shear, by the blocking of the normal velocity component and by the moving internal shear layers produced by large eddies as they impinge and scrape along the wall. Elongated streamwise vortices are formed with length scales that are several times the boundary layer height. An approximate stability argument suggests that if the Reynolds number for the turbulence, Re τ ≫10 4 , these internal layers are fully turbulent and that the large eddies can burst upward where the vortical eddies interact. The forms of the main statistical quantities, such as variances, spectra, length scales, are derived in terms of outer layer quantities using surface similarity and inhomogeneous linear theory. These `top-down' eddy-impingement, inner-layer/eddy-interaction/ejection mechanisms at very high Reynolds number are sensitive to changes in surface conditions and to variations in pressure gradients. They may therefore require different techniques for their control from those used at lower Reynolds number when boundary layers are driven by `bottom-up' instability/surface-interaction mechanisms. Furthermore, accurate numerical modelling of boundary layers at high Reynolds number requires resolving surface processes at very fine resolution. By inference, it is likely that there is some residual `top-down' influence, even at low Re τ .

Abstract: Direct numerical simulations (DNS) of a turbulent channel flow at low Reynolds number (Reτ=100,200,400, where Reτ is the Reynolds number based on the wall-shear velocity and channel half-width) are carried out to examine the effectiveness of using the Lorentz force to reduce skin friction. The Lorentz force is created by embedding electrodes and permanent magnets in the flat surface over which the flow passes. Both open-loop and closed-loop control schemes are examined. For open-loop control, both temporally and spatially oscillating Lorentz forces in the near-wall region are tested. It is found that skin-friction drag can be reduced by approximately 40% if a temporally oscillating spanwise Lorentz force is applied to a Reτ=100 channel flow. However, the power to generate the required Lorentz force is an order of magnitude larger than the power saved due to the reduced drag. Simulations were carried out at higher Reynolds numbers (Reτ=200,400) to determine whether efficiency, defined as the ratio of the p...

Abstract: A method for the theoretical determination of the wall shear stress under impinging jets of various congurations is presented. Axisymmetric and two-dimensional incompressible jets of a wide range of Reynolds numbers and jet heights are considered. Theoretical predictions from this approach are compared with available wall shear stress measurements. These data are critically evaluated based on the method of measurement and its applicability to the boundary layer under consideration. It was found that impingement-region wall shear stress measurements using the electrochemical method in submerged impinging liquid jets provide the greatest accuracy of any indirect method. A unique wall shear stress measurement technique, based on observing the removal of monosized spheres from well-characterized surfaces, was used to conrm the impinging jet analysis presented for gas jets. The technique was also used to determine an empirical relation describing the rise in wall shear stress due to compressibility eects in impinging high-velocity jets.

Abstract: A new concept for boundary layer separation control has been developed that is a derivative of the synthetic jet concept (being used primarily for virtual shape control) which converts acoustic oscillations into mean fluid motions. The new concept, the so-called “directed synthetic jet”, has an acoustically excited neck like the synthetic jet, however the neck is curved in the downstream tangential direction. In this manner, the boundary layer flowing over the neck or slot is energized via suction removal of the approaching low momentum fluid on the in-stroke and tangential blowing of high momentum on the out-stroke, thereby making it in the time average more resistant to separation. The concept has been demonstrated to be energy efficient comparing input power to system benefit, yielding a net power gain and also potent enough to completely suppress boundary layer separation. An electroacoustic model is presented which describes the actuator characteristics and enables realistic application analysis.

Abstract: The application of pulsed vortex generator jets to control separation on the suction surface of a low-pressure turbine blade is reported. Blade Reynolds numbers in the experimental, linear turbine cascade match those for high-altitude aircraft engines and aft stages of industrial turbine engines with elevated turbine inlet temperatures. The vortex generator jets have a 30 deg pitch and a 90 deg skew to the free-stream direction. Jet flow oscillations up to 100 Hz are produced using a high-frequency solenoid feed valve. Results are compared to steady blowing at jet blowing ratios less than 4 and at two chordwise positions upstream of the nominal separation zone. Results show that pulsed vortex generator jets produce a bulk flow effect comparable to that of steady jets with an order of magnitude less massflow. Boundary layer traverses and blade static pressure distributions show that separation is almost completely eliminated with the application of unsteady blowing. Reductions of over 50 percent in the wake loss profile of the controlled blade were measured. Experimental evidence suggests that the mechanism for unsteady control lies in the starting and ending transitions of the pulsing cycle rather than the injected jet stream itself. Boundary layer spectra support this conclusion and highlight significant differences between the steady and unsteady control techniques. The pulsed vortex generator jets are effective at both chordwise injection locations tested (45 and 63 percent axial chord) covering a substantial portion of the blade suction surface. This insensitivity to injection location bodes well for practical application of pulsed VGJ control where the separation location may not be accurately known a priori.

Abstract: In this work, we study the characteristics of a stably stratifiedatmospheric boundary layer using large-eddy simulation (LES).In order to simulate the stable planetary boundary layer, wedeveloped a modified version of the two-part subgrid-scalemodel of Sullivan et al. This improved version of themodel is used to simulate a highly cooled yet fairly windy stableboundary layer with a surface heat flux of(Wθ)o = -0.05 m K s-1and a geostrophic wind speed of Ug = 15 m s-1.Flow visualization and evaluation of the turbulencestatistics from this case reveal the development ofa continuously turbulent boundary layer with small-scalestructures. The stability of the boundary layercoupled with the presence of a strong capping inversionresults in the development of a dominant gravity wave atthe top of the stable boundary layer that appears to be relatedto the most unstable wave predicted by the Taylor–Goldsteinequation. As a result of the decay of turbulence aloft,a strong-low level jet forms above the boundary layer.The time dependent behaviour of the jet is compared with Blackadar'sinertial oscillation analysis.

Abstract: It is well known that a boundary layer of air is entrained around a rotating grinding wheel. The effects of the boundary layer have been under some scrutiny in recent years with most research being based on trying to overcome the boundary layer. The current investigation aims to show through experiment and modelling, the effects of the boundary layer on cutting fluid application and how it can be used to aid delivery by increasing flow rate beneath the wheel. Results from three experiments with different quantities of cutting fluid passing through the grinding zone are presented.