Response Of Boundary Layer Research Articles

Flow control with active dimples

AbstractThe long-term goal is to design and manufacture optimal ‘on-demand’ vortex generators, ‘dimples’ that can produce vortices of prescribed strength and duration for the real-time control of aerodynamic flows that are either undergoing transition or are fully turbulent, attached or separating. Electro-active polymers (EAP) are ideal for a dimple control surface, offering high strain rate, fast response, and high electromechanical efficiency. EAP can also be used as the basis of a resistanc – or capacitance – change pressure sensor, development of which has just begun. In terms of manufacture, inkjet printing of EAP also offers a paradigm shift such that a monolithic control surface is a very real possibility. Important features for integration into a control system are robustness and a predictable, repeatable motion. With these objectives in mind, the suitability of EAP-based actuators is assessed both mechanically and aerodynamically. The ultimate goal is to integrate these devices, along with shear-stress and pressure sensors and distributed control, also under development, into a flexible ‘smart skin’ which could be incorporated into an airframe structure. The response of a laminar boundary layer to forcing is investiagted using mechanical dimples.

Response of a compressible laminar boundary layer to free-stream vortical disturbances

As a first step towards understanding the role of free-stream turbulence in laminar–turbulent transition, we calculate the fluctuations induced by free-stream vortical disturbances in a compressible laminar boundary layer. As with the incompressible case investigated by Leibet al. (J. Fluid Mech. vol. 380, 1999, p. 169), attention is focused on components with long streamwise wavelength. The boundary-layer response is governed by the linearized unsteady boundary-region equations in the typical streamwise region where the local boundary-layer thickness δ* iscomparable with the spanwise length scale Λ of the disturbances. The compressible boundary-region equations are solved numerically for a single Fourier component to obtain the boundary-layer signature. The root-mean-square of the velocity and mass-flux fluctuations induced by a continuous spectrum of free-stream disturbances are computed by an appropriate superposition of the individual Fourier components.Low-frequency vortical disturbances penetrate into the boundary layer to form slowly modulating streamwise-elongated velocity streaks. In the compressible regime, vortical disturbances are found to induce substantial temperature fluctuations so that ‘thermalstreaks’ also form. They may have a significant effect on the secondary instability. The calculations indicate that for a vortical disturbance with a relatively large Λ, the induced boundary-layer fluctuation ultimately evolves into an amplifying wave. This is due to a receptivity mechanism, in which a vortical disturbance first excites a decaying quasi-three-dimensional Lam–Rott eigensolution. The latter then undergoes wavelength shortening to generate a spanwise pressure gradient, which eventually converts the Lam–Rott mode into an exponentially growing mode. The latter is recognized to bea highly oblique Tollmien–Schlichting wave. A parametric study suggests that this receptivity mechanism could be significant when the free-stream Mach number is larger than 0.8.

Cancellation of Aerosol Indirect Effects in Marine Stratocumulus through Cloud Thinning

Abstract Applying perturbation theory within a mixed layer framework, the response of the marine boundary layer (MBL) cloud thickness h to imposed increases of the cloud droplet concentration Nd as a surrogate for increases in cloud condensation nuclei (CCN) concentrations is examined. An analytical formulation is used to quantify the response and demonstrate theoretically that for the range of environmental conditions found over the subtropical eastern oceans, on time scales of less than a day, the cloud thickness feedback response is largely determined by a balance between the moistening/cooling of the MBL resulting from the suppression of surface precipitation, and the drying/warming resulting from enhanced entrainment resulting from increased turbulent kinetic energy. Quantifying the transient cloud response as a ratio of the second to the first indirect effects demonstrates that the nature of the feedback is critically dependent upon the nature of the unperturbed state, with the cloud-base height zcb being the single most important determinant. For zcb < 400 m, increasing Nd leads to cloud thickening in accordance with the Albrecht hypothesis. However, for zcb > 400 m, cloud thinning occurs, which results in a feedback effect that increasingly cancels the Twomey effect as zcb increases. The environmental conditions favoring an elevated cloud base are relatively weak lower-tropospheric stability and a dry free troposphere, although the former is probably more important over the subtropical eastern oceans. On longer time scales an invariable thickening response is found, and thus accurate quantification of the aerosol indirect effects will require a good understanding of the processes that control the time scale over which aerosol perturbations are modified.

Conjugate response of a thermal boundary layer with reverse flow

The full numerical solutions of the heat transfer from a flush mounted wall hot-film is carried to investigate its response in reversing flow by taking into account both the axial diffusion and the conduction to the substrate. It is shown that the axial diffusion affects considerably the heat transfer at the reversal points. The numerical results are in good agreement with the experiments conducted in an unsteady water channel. When the conductivity ratio of the substrate to the fluid is high, the response of the film is considerably attenuated, and it is hard to detect the flow reversal phase from the cyclic variations of the global heat flux. The direct flux from the film to the film is relatively less dependent on the conductivity ratio and follows reasonably well the flow reversal.

The Scripps Coupled Ocean–Atmosphere Regional (SCOAR) Model, with Applications in the Eastern Pacific Sector

AbstractA regional coupled ocean–atmosphere model is introduced. It is designed to admit the air–sea feedbacks arising in the presence of an oceanic mesoscale eddy field. It consists of the Regional Ocean Modeling System (ROMS) and the Regional Spectral Model (RSM). Large-scale forcing is provided by NCEP/DOE reanalysis fields, which have physics consistent with the RSM. Coupling allows the sea surface temperature (SST) to influence the stability of the atmospheric boundary layer and, hence, the surface wind stress and heat flux fields. The system is denominated the Scripps Coupled Ocean–Atmosphere Regional (SCOAR) Model.The model is tested in three scenarios in the eastern Pacific Ocean sector: tropical instability waves of the eastern tropical Pacific, mesoscale eddies and fronts of the California Current System, and gap winds of the Central American coast. Recent observational evidence suggests air–sea interactions involving the oceanic mesoscale in these three regions. Evolving SST fronts are shown to drive an unambiguous response of the atmospheric boundary layer in the coupled model. This results in significant model anomalies of wind stress curl, wind stress divergence, surface heat flux, and precipitation that resemble the observations and substantiate the importance of ocean–atmosphere feedbacks involving the oceanic mesoscale.

Modeling of Wake-Induced Transition in Linear Low-Pressure Turbine Cascades

An unsteady Reynolds-averaged Navier-Stokes (URANS) strategy is applied to the problem of wake-induced transition at high freestream turbulence on the suction side of two blades representative of those used in low-pressure turbines. Experimentally, the blades are arranged in high-aspect-ratio linear cascades, with upstream circular bars generating passing wakes, and two-dimensional flow conditions are, thus, assumed. The strategy combines an explicit algebraic Reynolds-stress turbulence model with transition-specific modifications targeted at capturing the effects of high freestream turbulence and of pretransitional laminar fluctuations. Close attention is paid to numerical accuracy, and grids of up to 140,000 cells are used in combination with 800 time steps per pitchwise traverse to resolve small-scale features in the blade boundary layers that are associated with the unsteady interaction. The computational results demonstrate that the combined model returns a good representation of the response of the suction-side boundary layer to the passing wakes in both blades. Specifically, in the boundary layer of one of the two blades, the wakes are observed to cause a periodic upstream shift in the transition onset and, thus, correspondingly periodic attachment and calming. In the other, no separation occurs, and the wakes are shown to produce a significant periodic reduction in shape factor and increase in skin friction in the blade boundary layer, again as a consequence of the upstream shift in the transition location.

Transition length in turbine/compressor blade flows

High Reynolds number mathematical models for convected vortex impinging against a local hump and sound scattering into Tollmien–Schlichting eigenmodes are introduced to simulate basic mechanisms of the disturbance excitation typical of turbomachinery environments. The streamwise dimension of the transitional flow on the suction side of a blade is evaluated on the assumption that the transition length is of equal order with the extent of viscous/inviscid interaction controlling the boundary-layer response. The triple-deck theory gives a simple power law correlation to express a value of the Reynolds number based on the transition length in terms of the Reynolds number calculated with the blade cord. Precisely the same correlation stems from processing experimental data for both smooth and rough surfaces. The computation shows the explosive development of highly modulated wave packets and their rapid breakdown brought about by erratic short-scaled wiggles riding on the primary long-scaled oscillation cycles. The filling-up of distant parts of the wavenumber spectrum is at the heart of the signal distortion. This process heralds the start of deep transition terminating in fully developed turbulent flow well before reaching the upper stability branch. With the time-harmonic excitation broadly used in experiments, transition requires a much longer distance to complete. An agreement between theoretical predictions based on the assumption of indefinitely large Reynolds numbers and experimental findings from wind-tunnel observations at finite Reynolds numbers is encouraging.

Contrasts between the summertime surface energy balance and boundary layer structure at Dome C and Halley stations, Antarctica

The Antarctic research stations of Dome C and Halley lie at similar latitudes (∼75°S) and are thus subject to similar diurnal variation of solar radiation at the top of the atmosphere. However, the response of the atmospheric boundary layer to this diurnally varying forcing differs greatly at the two stations. At Dome C during summer there is a strong diurnal cycle in near‐surface temperature and wind speed, and a shallow (∼350 m) convective boundary layer is observed to grow in response to diurnal heating. At Halley, diurnal variations in temperature and wind speed are smaller than those at Dome C, and there is no clear diurnal variability in boundary layer depth. Analysis of the summertime surface energy budget for both stations indicates that the main reason for the different diurnal variability at the two stations is the greater partitioning of available energy into latent heat flux at the warmer Halley station. We argue that the diurnally varying convective boundary layer observed at Dome C will not be typical of the whole of the East Antarctic plateau.

Response of the bottom boundary layer over a sloping shelf to variations in alongshore wind

Rapidly repeated transects of currents, density, and turbulence through the bottom boundary layer across a relatively uniform stretch of the continental shelf off Oregon reveal the response to a sequence of strong upwelling followed by relaxation and thence a resumption of upwelling. Several definitions of boundary layer thickness are employed to describe the evolution of the bottom boundary layer. Well‐mixed and turbulent layers were typically confined to 10 m from the bottom. However, boundary layer thicknesses were greatest during relaxation from upwelling (when mixed layer and turbulent layer thicknesses exceeded 20 m), and turbulence in the bottom boundary layer was most intense at this time. Dense, near‐bottom fluid was observed to move upslope with upwelling and back down the slope with relaxation from upwelling. By tracking the intersection of near‐bottom isopycnals with the bottom over successive transects, we estimate the cross‐shore speed of fluid in the bottom boundary layer. Cross‐shore speed agrees well with dynamical estimates of cross‐shore velocity in the bottom Ekman layer derived from bottom stress measurements. This leads to a confirmation of the Ekman balance of alongshore momentum in the bottom boundary layer across the full width of the shelf. Good correlation exists between alongshore velocity at the top of the bottom boundary layer and cross‐shore velocity of dense fluid in the bottom boundary layer. Application of a derived proxy for bottom stress to moored velocity observations indicates Ekman balance of alongshore momentum at a midshelf location (81 m depth) for a 3 month period in spring/summer 2001.

Effects Of Changing Surface Heat Flux On Atmospheric Boundary-Layer Flow Over Flat Terrain

We examine the unsteady response of a neutral atmospheric boundary layer (ABL) of depth h and friction velocity u * when a uniform surface heat flux is applied abruptly or decreased rapidly over a time scale t thetas less than about h /(10u *). Standard Monin–Obukhov (MO) relationships are used for the perturbed eddy viscosity profile in terms of the changes to the heat flux and mean shear. Analytical solutions for changes in temperature, mean wind and shear stress profile are obtained for the surface layer, when there are small changes in h /|LMO| over the time scale tMO~|L MO|/(10u*) (where L MO and t MO are the length and time scales, respectively). They show that a maximum in the wind speed profile occurs at the top of the thermal boundary layer for weak surface cooling, i.e. a wind jet, whereas there is a flattening of the profile and no marked maximum for weak surface heating. The modelled profiles are approximately the same as those obtained from the U.K. Met Office Unified Model when operating as a mesoscale model at 12-km horizontal resolution. The theoretical model is modified when strong surface heating is suddenly applied, resulting in a large change in h /|L MO| (>>1), over the time scale t MO. The eddy structure is predicted to change significantly and the addition of convective turbulence increases the shear turbulence at the ground. A low-level wind jet can form, with convective turbulence adding to the mean momentum of the flow. This was verified by our laboratory experiment and direct numerical simulations. Additionally, it is shown that the effects of Coriolis acceleration diminish (rather than as suggested in the literature, amplify) the formation of the wind jets in the situations considered here. Hence, only when the surface heat flux changes over time scales greater than 1/f (where f is the Coriolis parameter) does the ABL adjust monotonically between its equilibrium states. These results are also applicable to the ABL passing over spatially varying surface heat fluxes.

High-Resolution Satellite Measurements of the Atmospheric Boundary Layer Response to SST Variations along the Agulhas Return Current

Abstract The marine atmospheric boundary layer (MABL) response to sea surface temperature (SST) perturbations with wavelengths shorter than 30° longitude by 10° latitude along the Agulhas Return Current (ARC) is described from the first year of SST and cloud liquid water (CLW) measurements from the Advanced Microwave Scanning Radiometer (AMSR) on the Earth Observing System (EOS) Aqua satellite and surface wind stress measurements from the QuikSCAT scatterometer. AMSR measurements of SST at a resolution of 58 km considerably improves upon a previous analysis that used the Reynolds SST analyses, which underestimate the short-scale SST gradient magnitude over the ARC region by more than a factor of 5. The AMSR SST data thus provide the first quantitatively accurate depiction of the SST-induced MABL response along the ARC. Warm (cold) SST perturbations produce positive (negative) wind stress magnitude perturbations, leading to short-scale perturbations in the wind stress curl and divergence fields that are linearly related to the crosswind and downwind components of the SST gradient, respectively. The magnitudes of the curl and divergence responses vary seasonally and spatially with a response nearly twice as strong during the winter than during the summer along a zonal band between 40° and 50°S. These seasonal variations closely correspond to seasonal and spatial variability of large-scale MABL stability and surface sensible heat flux estimated from NCEP reanalysis fields. SST-induced deepening of the MABL over warm water is evident in AMSR measurements of CLW. Typical annual mean differences in cloud thickness between cold and warm SST perturbations are estimated to be about 300 m.

Mixing within the interior of the Faeroe-Shetland Channel

Observations of the distribution of the density field, the dissipation rate of turbulent kinetic energy, e, the vertical diffusivity, Kz, and optical backscatter over a repeated cross-section of the FaeroeShetland Channel (FSC) are presented within the context of ocean mixing. Turbulence in the permanent pycnocline occurs in discrete vertical patches of thickness 20‐50 m coincident with layers of elevated vertical current shear magnitude, S 10 2 s 1 . The layers of elevated shear result from high-wavenumber internal waves which may break through shear instabilities as indicated by critical Richardson numbers, Ri 1. The internal waves are ubiquitous features of strong boundary currents flowing along continental shelves and are likely generated here by geostrophic adjustment of the pycnocline in response to lateral excursions of the boundary current over the Shetland slope or by the scattering of internal tide energy. The pycnocline as a whole exhibits Kz 10 4.5 m 2 s 1 , a factor of 3 larger than typical open ocean thermoclines but still implying a weak exchange of water mass properties across the density interface despite the confined and isolated patches of enhanced turbulence which elevate Kz by an order of magnitude. Both the boundary current and the deep interior are typified by weak stratification and locally high Kz 10 3 m 2 s 1 , but low turbulent buoyancy fluxes. The strongest observed turbulence and mixing in the channel, e O(10 7 Wk g 1 ) and Kz 10 3 m 2 s 1 respectively, is observed in the near-bed region over the Shetland slope and results from solibore propagation up the slope and the asymmetric response of the bottom boundary layer to the tidal currents. The overall contribution of the FSC to oceanic mixing would appear to be about half of the required canonical value of Kz 10 4 m 2 s 1 given the observed short duration and/or infrequent occurrence of the processes generating turbulence in the near-bed region, the spatially confined sporadic mixing patches in the pycnocline, and the low turbulent buoyancy fluxes in the interior and slope current.

Response of the atmospheric boundary layer to a mesoscale oceanic eddy in the northeast Atlantic

Fields of air‐sea turbulent fluxes and bulk variables were derived from satellite sensor data from February to April 2001, over a region of the northeast Atlantic where a field experiment, Programme Océan Multidisciplinaire Meso Echelle (POMME), was conducted. The satellite products are in good agreement with in situ data in terms of heat fluxes, sea surface temperature, and wind speed. The central part of the experimental domain presented a cyclonic eddy in the ocean, which corresponded to a cold sea surface temperature (SST) anomaly. Winds were weaker within the eddy than outside of it, with lower latent and sensible heat loss. In order to analyze the relationship between the SST and wind anomalies, three numerical experiments were conducted with a regional atmospheric model. Three 3‐month runs of the model were performed, using a realistic SST field, a smoothed SST field in which the cold SST was not present (reference run), and an SST field where the cold anomaly was increased by two degrees, successively. The fields simulated with the realistic SST were consistent with satellite sensor derived observations. In particular, the weak wind area over the cold SST anomaly was successfully rendered, whereas it was not present in the forcing fields. Taken individually, the three runs did not reveal the presence of secondary circulations. However, anomalous secondary circulations were clearly identified with respect to the reference run. The origin of the latter circulations was investigated with the Giordani and Planton generalization of the Sawyer‐Eliassen equations. According to our results, differential heating induced by the cold SST anomaly mostly altered the vertical wind through the effect of friction and only marginally through pressure gradient forces. In the upper part of the boundary layer, the wind speed increased (decreased) over (downstream) the cold SST. We found that stability was the main factor that induced the simulated patterns of the friction term in the diagnostic equations. Therefore our results show that mesoscale wind patterns were significantly affected by SST gradients through the effect of stability, in a region of low oceanic eddy activity.

Development of low-frequency streaks in Blasius boundary layer

A response of flat plate boundary layer to a single free-stream axial vortex of limited spanwise extent with periodically modulated strength is investigated. The response is dominated by a streamwise velocity perturbation (streak), whose characteristics are in agreement with data of previous experiments performed with natural streaks developed under the effect of free-stream turbulence. This confirms that the experimental approach used is suitable for an accurate modeling of the low-frequency natural streaks in controlled conditions. A quantitative comparison of the observed streak characteristics with available theoretical approaches is performed.

A Comparison between Observations and MM5 Simulations of the Marine Atmospheric Boundary Layer across a Temperature Front

Simulations, made with the fifth-generation Pennsylvania State University (PSU)‐National Center for Atmospheric Research (NCAR) Mesoscale Model (MM5), of the response of the marine atmospheric boundary layer (MABL) as air moves over a sharp SST front are compared with observations made during the Frontal Air‐Sea Interaction Experiment (FASINEX) in the North Atlantic subtropical convergence zone. The purpose of undertaking these comparisons was to evaluate the performance of MM5 in the vicinity of an SST front and to determine which of the planetary boundary layer (PBL) parameterizations available best represents MABL processes. FASINEX provides an ideal dataset for this work in that it contains detailed measurements for scenarios at the two extremes: wind blowing from warm to cold water normal to a 28C SST front and the converse, wind blowing from cold to warm water. For the wind blowing from warm to cold water, there is a pronounced modification of the near-surface wind field over the front, in both model results and aircraft observations. The decrease of near-surface wind speed and stress is due to a stable internal boundary layer (IBL) induced by the SST front, restricting exchange of mass and momentum between the surface and upper part of the MABL. For the cold-to-warm case, the relatively strong vertical mixing through the entire MABL over warm water dampens the response of the near-surface winds and surface stress to the SST front. The properties observed by the aircraft are simulated quite well in both cases, suggesting that MM5 captures the appropriate boundary layer physics at the mesoscale or regional scale.

Unique bending boundary layer behaviors in a composite non-circular cylindrical shell

A cylindrical composite shell with a non-circular, symmetric cross-section of flat sides and circular arc corners is analyzed using the abaqus finite element program. A trade study on the effects of various corner radii and shell lengths is performed. The response of the shell to constant internal pressurization is studied, with particular attention given to the bending boundary layer (BBL) near the ends. It is found that the extent of the BBL in the non-circular case is 2.5–4 times longer than that predicted by the classical equation, however, the ‘intensity’ of the bending boundary layer is reduced. An unusual ‘compounding’ effect in boundary layer response for short non-circular shells is described.

Vertical mixing schemes in the coastal ocean: Comparison of the level 2.5 Mellor‐Yamada scheme with an enhanced version of the K profile parameterization

The performance of two vertical mixing parameterizations in idealized continental shelf settings is analyzed to assess in what aspects and under what conditions they differ. The level 2.5 Mellor‐Yamada turbulence closure (M‐Y) is compared with an enhanced version of the K profile parameterization (KPP), which has been appended to include a representation of the bottom boundary layer. The two schemes are compared in wind‐driven one‐ and two‐dimensional shallow ocean settings to examine differences in (1) the surface boundary layer response, (2) the response when surface and bottom boundary layers are in close proximity, and (3) the response when the horizontal advective effects of a coastal upwelling circulation compete with the vertical mixing processes. The surface boundary layer experiments reveal that M‐Y mixes deeper and entrains more than KPP when the pycnocline beneath the wind‐mixed layer is highly stratified and mixes less when it is weaker. This is related to the role of vertical diffusion of turbulent kinetic energy in M‐Y and the nature of the interior shear mixing parameterization of KPP. In shallow water when surface and bottom boundary layers impinge on each other, the stronger mixing at the interface produced by KPP can lead to much more rapid disintegration of the pycnocline. The two‐dimensional upwelling circulation experiments show that the two schemes can produce quite similar or significantly different solutions in the nearshore region dependent on the initial stratification. The differences relate to the stronger suppression of turbulence by M‐Y under the restratifying influence of horizontal advection of denser water in the bottom boundary layer.

Numerical Simulation of Atmospheric Response to Pacific Tropical Instability Waves*

Tropical instability waves (TIWs) are 1000-km-long waves that appear along the sea surface temperature (SST) front of the equatorial cold tongue in the eastern Pacific. The study investigates the atmospheric planetary boundary layer (PBL) response to TIW-induced SST variations using a high-resolution regional climate model. An investigation is made of the importance of pressure gradients induced by changes in air temperature and moisture, and vertical mixing, which is parameterized in the model by a 1.5-level turbulence closure scheme. Significant turbulent flux anomalies of sensible and latent heat are caused by changes in the air‐sea temperature and moisture differences induced by the TIWs. Horizontal advection leads to the occurrence of the air temperature and moisture extrema downwind of the SST extrema. High and low hydrostatic surface pressures are then located downwind of the cold and warm SST patches, respectively. The maximum and minimum wind speeds occur in phase with SST, and a thermally direct circulation is created. The momentum budget indicates that pressure gradient, vertical mixing, and horizontal advection dominate. In the PBL the vertical mixing acts as a frictional drag on the pressure-gradient-driven winds. Over warm SST the mixed layer deepens relative to over cold SST. The model simulations of the phase and amplitude of wind velocity, wind convergence, and column-integrated water vapor perturbations due to TIWs are similar to those observed from satellite and in situ data.

The response of a turbulent boundary layer to different shaped transverse grooves

The response of a turbulent boundary layer to three different shaped transverse grooves was investigated at two values of momentum thickness Reynolds numbers ( R θ =1000 and 3000). A 20-mm wide square, semicircular and triangular groove with depth to width ( d / w) ratio of unity was used. In general, the effects of the grooves are more significant at the higher R θ , with the most pronounced effects caused by the square groove. An increase in wall shear stress τ w was observed just downstream of the groove for all three shapes. The increase in τ w is followed by a small decrease in τ w below the smooth-wall value before it relaxes back to the corresponding smooth-wall value at x / δ 0≈3. At the higher R θ , the maximum increase in τ w for the square groove is about 50% higher than for the semicircular groove and almost twice that for the triangular groove. The effect of the square groove on U / U 0, u ′/ U 0 and v ′/ U 0 is much more significant than the effect of the semicircular and triangular grooves. There is an increase in the bursting frequency ( f B +) on the grooved-wall compared to the smooth-wall case. The distribution of f B + downstream of the different shaped grooves is similar to the τ w distribution.

Unsteady mixed convection due to time-dependent free stream velocity

An analysis has been presented to study the unsteady combined convection from a horizontal circular cylinder to a transverse flow. A perturbation method is used to transform the governing set of partial differential equations, representing the constitutive laws, into a system of ordinary differential equations. For the case of sinusoidal variation of the free stream velocity, the boundary layer response is estimated due to both low frequency as well as high frequency oscillation. Numerical solutions are presented for the distribution of unsteady Nusselt number and friction factor.