Showing papers on "Drag coefficient published in 1996"
TL;DR: In this article, a general classification of two-phase flows and a number of possible ways to formulate two-fluid models are discussed, and a general procedure to develop such a model is presented.
522 citations
TL;DR: In this article, the authors defined accumulation parameter Cd drag coefficient Ci = lift coefficient Cm = moment coefficient Cp = pressure coefficient c = specific heat at constant pressure, J/(kg-K); airfoil chord, m D = propeller diameter, m; flexural stiffness, N-m D drag force, N d = droplet diameter, E = total collection efficiency / = freezing fraction g = acceleration caused from gravity, m/s Hi = ice thickness, m Hp = plate thickness.
Abstract: Nomenclature Ac = accumulation parameter Cd drag coefficient Ci = lift coefficient Cm = moment coefficient Cp = pressure coefficient c = specific heat at constant pressure, J/(kg-K); airfoil chord, m D = propeller diameter, m; flexural stiffness, N-m D drag force, N d = droplet diameter, m E = total collection efficiency / = freezing fraction g = acceleration caused from gravity, m/s Hi = ice thickness, m Hp = plate thickness, m h = airfoil projected height, m hc = convective heat transfer coefficient, W/(m-K) hfg = heat of vaporization, J/kg hsi = heat of fusion, J/kg / = airfoil drag constant K = thermal conductivity, W/(m-K); inertia parameter K0 = modified inertia parameter k = roughness diameter, m LWC = liquid water content, kg/m M = local Mach number MVD = median volume droplet diameter, m m = mass, kg ra = mass flow rate, kg/s m' = mass flow rate per unit width, kg/(m-s) m" = mass flux, kg/(m-s) n = normal direction P = pressure, Pa p spatial pressure distribution, N/m <2 = heat rate, W q = normal pressure distribution, N/m
335 citations
TL;DR: In this paper, the effects of Reynolds number and angle of attack on boundary-layer separation from an Eppler 387 airfoil at low Reynolds number were investigated numerically.
Abstract: Unsteady boundary-layer separation from an Eppler 387 airfoil at low Reynolds number is studied numerically. Through a series of computations, the effects of Reynolds number and angle of attack are investigated. For all cases, vortex shedding is observed from the separated shear layer. From linear stability analysis, a KelvinHelmholtz instability is identified as causing shear layer unsteadiness. The low-turbulence wind-tunnel tests of the Eppler 387 airfoil are used to compare with the time-averaged results of the present unsteady computations. The favorable comparison between computational and experimental results strongly suggests that the unsteady largescale structure controls the low-Reynolds-number separation bubble reattachment with small-scale turbulence playing a secondary role. Nomenclature C = chord length CD - drag coefficient CL = lift coefficient Cp = pressure coefficient / = shedding frequency Re = chord Reynolds number R P - reattachment point S P = separation point Sr = Strouhal number U = velocity 9 = momentum thickness Subscripts sep = conditions at separation oo = freestream conditions
233 citations
TL;DR: In this paper, the electro-osmotic drag coefficient of water in two polymer electrolytes was experimentally determined as a function of water activity and current density for temperatures up to 200 C.
Abstract: The electro-osmotic drag coefficient of water in two polymer electrolytes was experimentally determined as a function of water activity and current density for temperatures up to 200 C. The results show that the electro-osmotic drag coefficient varies from 0.2 to 0.6 in Nafion{reg_sign}/H{sub 3}PO{sub 4} membrane electrolyte, but is essentially zero in phosphoric acid-doped PBI (polybenzimidazole) membrane electrolyte over the range of water activity considered. The near-zero electro-osmotic drag coefficient found in PBI indicates that this electrolyte should lessen the problems associated with water redistribution in proton exchange membrane fuel cells.
232 citations
15 Jan 1996
TL;DR: It is shown that a reasonable estimate of the fluid drag force on a fractal aggregate may be obtained by assigning a constant volume-averaged porosity to the aggregate and using any of the expressions available in the literature for aggregates with uniform permeability.
Abstract: Hydrodynamic properties of fractal aggregates with radially varying permeability are investigated in terms of two parameters: radius of equivalent solid sphere experiencing the same drag as the aggregate (Ω*radius of aggregate) and fluid collection efficiency (η) of the aggregate. Resistance to the fluid flow through the aggregate is predicted to increase with increasing fractal dimension, while the fluid collection efficiency is expected to decrease. It is shown that a reasonable estimate of the fluid drag force on a fractal aggregate may be obtained by assigning a constant volume-averaged porosity to the aggregate and using any of the expressions available in the literature for aggregates with uniform permeability. The two hydrodynamic parameters, Ω and η, are used to modify the existing expressions for interactions between solid spheres to account for the porous nature of aggregates and thus calculate the collision rate kernels for interacting aggregates. The ratio of hydrodynamic radius of an aggregate to its radius of gyration predicted by the proposed model was in reasonable agreement with an experimental value reported in the literature.
226 citations
TL;DR: In this paper, a phenomenological description of the high-frequency vortex dynamics in and discuss the main parameters related to vortex motion, namely the viscous drag coefficient, the pinning constant (Labusch parameter) and the depinning frequency.
Abstract: We present a phenomenological description of the high-frequency vortex dynamics in and discuss the main parameters related to vortex motion, namely the viscous drag coefficient , the pinning constant (Labusch parameter) and the depinning frequency . We demonstrate experimental results on the angular and temperature dependence of , and in and compare these results with existing models. We show how studies of the vortex viscosity may yield information on the superclean limit. This limit corresponds to the formation of the discrete excitation spectrum in the vortex core due to quantum confinement and small coherence length. From the low-temperature viscosity data we conclude that the superclean limit in is reached for magnetic field perpendicular to the c-axis.
216 citations
TL;DR: In this article, a cyclic spanwise oscillation of the wall with a proper frequency and amplitude is imposed, allowing a reduction of the turbulent drag of up to 40% in turbulent boundary layers and channel flows.
Abstract: In the present work a technique is numerically investigated, which is aimed at reducing the friction drag in turbulent boundary layers and channel flows. A cyclic spanwise oscillation of the wall with a proper frequency and amplitude is imposed, allowing a reduction of the turbulent drag of up to 40%. The present work is based on the numerical simulation of the Navier-Stokes equations in the simple geometry of a plane channel flow. The frequency of the oscillations is kept fixed at the most efficient value determined in previous studies, while the choice of the best value for the amplitude of the oscillations is evaluated not only in terms of friction reduction, but also by taking into consideration the overall energy balance and the power spent for the motion of the wall. The analysis of turbulence statistics allows to shed some light on the way oscillations interact with wall turbulence, as illustrated by visual inspection of some instantaneous flow fields. Finally, a simple explanation is proposed for this interaction, which leads to a rough estimate of the most efficient value for the frequency of the oscillations.
167 citations
TL;DR: It is suggested that birds of any size that have well-streamlined bodies can achieve minimum body drag coefficients of around 0.05 if the feet can be fully retracted under the flank feathers, and field observations of flight speeds may need to be reinterpreted in the light of higher estimates of Vmp.
Abstract: A teal (Anas crecca) and a thrush nightingale (Luscinia luscinia) were trained to fly in the Lund wind tunnel for periods of up to 3 and 16 h respectively. Both birds flew in steady flapping flight, with such regularity that their wingbeat frequencies could be determined by viewing them through a shutter stroboscope. When flying at a constant air speed, the teal's wingbeat frequency varied with the 0.364 power of the body mass and the thrush nightingale's varied with the 0.430 power. Both exponents differed from zero, but neither differed from the predicted value (0.5) at the 1 % level of significance. The teal continued to flap steadily as the tunnel tilt angle was varied from -1 ° (climb) to +6 ° (descent), while the wingbeat frequency declined progressively by about 11 %. In both birds, the plot of wingbeat frequency against air speed in level flight was U-shaped, with small but statistically significant curvature. We identified the minima of these curves with the minimum power speed (Vmp) and found that the values predicted for Vmp, using previously published default values for the required variables, were only about two-thirds of the observed minimum-frequency speeds. The discrepancy could be resolved if the body drag coefficients (CDb) of both birds were near 0.08, rather than near 0.40 as previously assumed. The previously published high values for body drag coefficients were derived from wind-tunnel measurements on frozen bird bodies, from which the wings had been removed, and had long been regarded as anomalous, as values below 0.01 are given in the engineering literature for streamlined bodies. We suggest that birds of any size that have well-streamlined bodies can achieve minimum body drag coefficients of around 0.05 if the feet can be fully retracted under the flank feathers. In such birds, field observations of flight speeds may need to be reinterpreted in the light of higher estimates of Vmp. Estimates of the effective lift:drag ratio and range can also be revised upwards. Birds that have large feet or trailing legs may have higher body drag coefficients. The original estimates of around CDb=0.4 could be correct for species, such as pelicans and large herons, that also have prominent heads. We see no evidence for any progressive reduction of body drag coefficient in the Reynolds number range covered by our experiments, that is 21 600215 000 on the basis of body cross-sectional diameter.
165 citations
TL;DR: In this paper, the authors measured the impact and drag forces for disks dropped into water at low Froude numbers (u2/gr=1-80) and measured the period during which the air cavity behind the disk remains open to atmospheric air.
Abstract: As basilisk lizards (Basiliscus basiliscus) and shore birds run along the water surface they support their body weight by slapping and stroking into the water with their feet. The foot motions exploit the hydrodynamic forces of low‐speed water entry. To determine the forces that are produced during water entry at low speeds, we measured directly the impact and drag forces for disks dropped into water at low Froude numbers (u2/gr=1–80). Also, we measured the period during which the air cavity behind the disk remains open to atmospheric air. We found that the force impulse produced during the impact phase is due to the acceleration of the virtual mass of fluid associated with a disk at the water surface. A dimensionless virtual mass M, defined as M=mvirtual/(4/3)πρr3, has a value near 1/π for disks. After impact, as penetration depth of the disk increases, the drag force can rise by as much as 76% even though the downward velocity is steady. However, a dimensionless force which includes the contribution fro...
164 citations
TL;DR: In this article, the feasibility of using free-settling test for estimating activated sludge floc density was discussed and the results showed that floc permeability depends strongly on the models or parameter sets applied.
158 citations
TL;DR: In this article, a spectral collocation technique has been developed to simulate the full three-dimensional incompressible flow over elliptic cylinders and, unlike spectral element and spectral multidomain techniques, here the flow is solved in a single domain.
TL;DR: In this article, the drag force of a single particle in the presence of other equal-sized particles arranged in specific configurations is measured directly for Re from 30 to 106, and the measured drag force, expressed in terms of the drag ratio, is compared with the theoretical values at zero Re and the experimental values for 100 < Re < 103 reported in the literature.
TL;DR: In this article, the authors present a review of the developments that have taken place on the use of passive techniques or devices for axisymmetric base and net afterbody drag reduction in the absence of jet flow at the base.
TL;DR: In this article, the steady flow of a power-law fluid past a stationary circular cylinder was considered and the governing nonlinear equations, expressed in terms of a stream function and vorticity, were solved by finite differences for Reynolds numbers (based on the radius of the cylinder)R=5,20, 40 for various power law indices,n.
Abstract: Considered in this paper is the two-dimensional steady flow of a power-law fluid past a stationary circular cylinder. The governing nonlinear equations, expressed in terms of a stream function and vorticity, were solved by finite differences for Reynolds numbers (based on the radius of the cylinder)R=5,20, 40 for various power-law indices,n. Parameters such as the drag coefficient, separation angle, wake length and critical Reynolds number are presented and contrasted with those of a Newtonian fluid (n=1) to illustrate the non-Newtonian effects. For a given-Reynolds number a consistent behaviour withn was observed in the parameters for the ranges considered. The results obtained for the Newtonian case agree well with documented results.
TL;DR: In this article, it is shown that the long-term zonally symmetric response to an imposed extratropical local force or diabatic heating is shown to induce a drag force in the sponge that modifies the response expected from the "downward control" arguments of Haynes et al.
Abstract: Middle-atmosphere models commonly employ a sponge layer in the upper portion of their domain. It is shown that the relaxational nature of the sponge allows it to couple to the dynamics at lower levels in an artificial manner. In particular, the long-term zonally symmetric response to an imposed extratropical local force or diabatic heating is shown to induce a drag force in the sponge that modifies the response expected from the “downward control” arguments of Haynes et al. [1991]. In the case of an imposed local force the sponge acts to divert a fraction of the mean meridional mass flux upward, which for realistic parameter values is approximately equal to exp(−Δz/H), where Δz is the distance between the forcing region and the sponge layer and H is the density scale height. This sponge-induced upper cell causes temperature changes that, just below the sponge layer, are of comparable magnitude to those just below the forcing region. In the case of an imposed local diabatic heating, the sponge induces a meridional circulation extending through the entire depth of the atmosphere. This circulation causes temperature changes that, just below the sponge layer, are of opposite sign and comparable in magnitude to those at the heating region. In both cases, the sponge-induced temperature changes are essentially independent of the height of the imposed force or diabatic heating, provided the latter is located outside the sponge, but decrease exponentially as one moves down from the sponge. Thus the effect of the sponge can be made arbitrarily small at a given altitude by placing the sponge sufficiently high; e.g., its effect on temperatures two scale heights below is roughly at the 10% level, provided the imposed force or diabatic heating is located outside the sponge. When, however, an imposed force is applied within the sponge layer (a highly plausible situation for parameterized mesospheric gravity-wave drag), its effect is almost entirely nullified by the sponge-layer feedback and its expected impact on temperatures below largely fails to materialize. Simulations using a middle-atmosphere general circulation model are described, which demonstrate that this sponge-layer feedback can be a significant effect in parameter regimes of physical interest. Zonally symmetric (two dimensional) middle-atmosphere models commonly employ a Rayleigh drag throughout the model domain. It is shown that the long-term zonally symmetric response to an imposed extratropical local force or diabatic heating, in this case, is noticeably modified from that expected from downward control, even for a very weak drag coefficient.
TL;DR: In this article, the authors examined the dependence of the computed drag coefficient on wind speed, stability, fetch, flux sampling problems, and method of calculation of the drag coefficient, and applied to data collected at a tower 2 km off the coast of Denmark during the Riso Air Sea Experiment (RASEX).
Abstract: This study examines the dependence of the computed drag coefficient on wind speed, stability, fetch, flux sampling problems, and method of calculation of the drag coefficient. The analysis is applied to data collected at a tower 2 km off the coast of Denmark during the Riso Air Sea Experiment (RASEX). Various flux sampling problems are evaluated to eliminate unreliable fluxes. Large drag coefficients are observed with weak large-scale flow. However, the value of the computed drag coefficient at weak wind speeds is sensitive to flux sampling problems and the method of calculation of the drag coefficient, which might be a general characteristic of weak winds. The drag coefficient is significantly larger for short fetch conditions, particularly at strong wind speeds.
TL;DR: In this paper, a numerical analysis of forced-convection heat transfer from a horizontal stationary circular cylinder dissipating a uniform heat flux in a crossflow of air is conducted by solving the full two-dimensional steady-state Navier-Stokes and energy equations in the range of the Reynolds numbers from 100 to 500 (based on diameter).
Abstract: A numerical analysis of forced-convection heat transfer from a horizontal stationary circular cylinder dissipating a uniform heat flux in a crossflow of air is conducted by solving the full two-dimensional steady-state Navier-Stokes and energy equations in the range of the Reynolds numbers from 100 to 500 (based on diameter). A numerical study by this author for Reynolds numbers less than 100 was previously conducted and therefore is not repeated here. Dependence on the Reynolds number of the flow and thermal fields, vorticity and pressure distributions, separation angle, drag coefficient, and local and average Nusselt number around the cylinder are shown. Correlations for the separation angle and drag coefficient as functions of Reynolds number are suggested. Quantities such as vorticity, pressure, and Nusselt number at the forward and rear (base) stagnation points are also calculated and correlated as functions of Reynolds number. The local and average values of the Nusselt numbers are shown to be in go...
TL;DR: In this paper, the concentration dependence of drag reduction for these systems was shown to obey an empirical drag reduction equation which has been previously applied to describe flow in circular pipes, and linear correlation between polymer concentration and drag reduction was also obtained for different molecular weights of PEO and PIB.
Abstract: Turbulent drag reduction induced by dilute solutions of both water-soluble poly(ethylene oxide) (PEO) and oil-soluble polyisobutylene (PIB) under turbulent flow in a rotating disk apparatus was investigated. The concentration dependence of drag reduction for these systems was shown to obey an empirical drag reduction equation which has been previously applied to describe flow in circular pipes. Linear correlation between polymer concentration and drag reduction for different molecular weights of PEO and PIB was also obtained. The intrinsic concentration [C] was found to be very useful in normalizing the drag reduction data for different types of polymers, polymer molecular weights, concentrations, and rotational disk velocities. Explanation of the drag reduction phenomenon on a molecular level can be obtained from intrinsic drag reduction and [C].
TL;DR: In this article, the impact of sea waves on sensible heat and momentum fluxes is described, which is based on the conservation of energy and momentum in the marine atmospheric surface layer, and the experimental fact that the drag coefficient above the sea increases considerably with increasing wind speed, while the exchange coefficient for sensible heat remains virtually independent of wind speed.
Abstract: The impact of sea waves on sensible heat and momentum fluxes is described. The approach is based on the conservation of heat and momentum in the marine atmospheric surface layer. The experimental fact that the drag coefficient above the sea increases considerably with increasing wind speed, while the exchange coefficient for sensible heat (Stanton number) remains virtually independent of wind speed, is explained by a different balance of the turbulent and the wave-induced parts in the total fluxes of momentum and sensible heat.
TL;DR: In this paper, a plume with a mushroom-shaped front forms above the sphere whose length and thickness decrease with increasing Gr. The vortex size increases with Gr and the local Nusselt number along the sphere surface first decreases, reaches a minimum, and then increases steeply at the rear of the sphere.
TL;DR: In this paper, the authors investigated the effect of stable stratification on the aerodynamic force induced by turbulent boundary-layer flow over two-dimensional hills using both analytical and numerical models.
Abstract: We investigate how stable stratification affects the aerodynamic force, or form drag, induced by turbulent boundary-layer flow over two-dimensional hills. Both analytical and numerical models are used to calculate the flow and thence the form drag on the hill. In the analytical model we use a two-layer, truncated mixing-length, turbulence model, which is consistent with scaling arguments and which produces reliable estimates of the form drag for the neutral flow. The form drag is also calculated analytically using an eddy-viscosity model, and the results compare well with values computed with the nonlinear numerical model that uses a similar turbulence model.
The leading-order contribution to the form drag is from a non-separated sheltering mechanism, which is similar to the mechanism in neutral flow. Stable stratification changes the magnitude of this mechanism through several effects. For weak stratification the predominant effect is an increase in shear in the upstream wind profile across a middle layer, which increases the form drag by a factor of two or more. There is indirect experimental evidence to support this finding. If the stratification is more stable, then the shear across the middle layer becomes limited because the boundary layer has a finite depth. Then the dynamical effect of buoyancy on the pressure perturbation becomes important and reduces the form drag, eventually to zero.
For still more stable stratification, gravity waves and associated wave drag are produced. The analysis shows that the appropriate scaling velocity for wave drag is the approach-flow wind speed evaluated at the middle-layer height. The relationship between the form and wave drag components is investigated by evaluating the analytical formula for the drag on isolated hills of two idealized shapes. For weak stratification the form drag dominates, but as the stratification becomes more stable the wave drag increases and first equals the form drag, at a value that depends on the hill shape, and then dominates.
TL;DR: In this article, a simple and precise explicit correlation can be developed if CD is related to the Archimedes instead of the Reynolds number, which is similar to that of the Turton and Levenspiel (1986) while it is explicit in the terminal velocity.
Abstract: An analysis of the correlations proposed in the literature for calculation of the drag coefficient (CD ) and the terminal velocity of a falling rigid sphere has been made. Among the correlations describing CD vs. Re, that of Turton and Levenspiel fits the experimental data almost perfectly. However, it is not explicit in the terminal velocity. The available explicit correlations do not fit the experimental data well. The present paper shows that a simple and precise explicit correlation can be developed if CD is related to the Archimedes instead of the Reynolds number. The precision of the correlation proposed is similar to that of the Turton and Levenspiel (1986), while it is explicit in the terminal velocity. On the basis of this correlation, a model is proposed to calculate the drag coefficients and the terminal velocities of free falling or rising spherical particles in an infinite fluid as well as gas bubbles with any volume and shape rising in a contaminated liquid.
TL;DR: In this article, a series of polystyrene-based Boger fluids were used to investigate how the drag behavior of a sphere falling in a Boger fluid is affected by the fluid's extensibility, solvent quality and chain molecular weight.
Abstract: This study experimentally investigates how the drag behavior of a sphere falling in a Boger fluid is affected by the fluid's extensibility, solvent quality and chain molecular weight. By means of terminal velocity measurements under conditions of creeping flow, deviations from Newtonian drag behavior in a homologous series of three polystyrene-based Boger fluids were measured as a function of Weissenberg number ( We ). The polymer-solvent quality and polymer molecular weight of each of the Boger fluids were manipulated in a manner that produced a systematic variation in the degree of extensibility of the fluids. Here, we define extensibility in terms of the FENE model parameter L , the ratio of a fully extended coil length to an equilibrium coil length. It is expected that L varies by nearly a factor of three over this series of Boger fluids. The compositions and ranking of the degree of extensibility of the three Boger fluids are the following: a high extensibility fluid of 2.0 × 10 7 g mol −1 polystyrene in a poor, dioctyl phthalate (DOP)-based solvent, a medium extensibility fluid of 2.0 × 10 7 g mol −1 polystyrene in a good, tricresyl phosphate (TCP)-based solvent and a low extensibility fluid of 2.0 × 10 6 g mol −1 polystyrene in a poor DOP-based solvent. The principal result of the falling sphere experiments is that while the low extensibility fluid shows only small deviations from Newtonian behavior at all tested We , the two fluids of greater extensibility show drag enhancement of more than 300% for We > 1. These experiments are in agreement with the earlier work of Tirtaatmadja et al. and Chmielewski et al., indicating that the drag does not correlate with We alone. Here, by using monodisperse polymers and systems in which the polymerssolvent interactions have been characterized, we are also able to determine the sensitivity of the dimensionless drag to polymer molecular weight and polymer-solvent quality.
17 Jun 1996
TL;DR: In this paper, the variations of flow, drag force, permeability, and pressure perturbation for shelterbelts of different widths and different horizontal structures are numerically studied, and their influences on shelter efficiency are discussed.
Abstract: Natural shelterbelts, unlike planar barriers, have a certain width, within which interactions among wind speed, drag force and pressure perturbations create a net sheltering effect. The variations of flow, drag force, permeability, and pressure perturbation for shelterbelts of different widths and different horizontal structures are numerically studied, and their influences on shelter efficiency are discussed. Comparisons are made of fourteen medium-dense shelterbelts, with the same overall leaf-area, that differ only in width or horizontal distribution of leaf-area density. The simulated results are consistent with both field observations and wind-tunnel measurements.
TL;DR: In this article, a conceptually new and highly sensitive method for determining the shear surface viscosity of adsorbed or spread surfactant monolayers at a gas−liquid interface is presented.
Abstract: A conceptually new and highly sensitive method for determining the shear surface viscosity of adsorbed or spread surfactant monolayers at a gas−liquid interface is presented. The surface viscosity is calculated from the drag coefficient of a small spherical particle floating at the interface under the action of an external capillary force. In this respect the method resembles the known Stokes method for measuring the bulk shear viscosity of liquids. The shear viscosity of adsorbed monolayers from sodium dodecyl sulfate and hexadecyltrimethylammonium bromide was measured. The sensitivity of the method is of the order of 10-8 Pa m s.
TL;DR: The cardiovascular system presented here can also be simulated at higher and varying heart rates--up to 200 beats per minute and the results of calculations for some pathological changes are discussed.
TL;DR: In this article, the authors investigated uniform flow past one (or two in tandem formation) finite length circular cylinder(s) and found that the flow that separates from the free end interacts strongly with those that separate from the sides and results in a three-dimensional flow.
TL;DR: In this paper, the results of viscous drag reduction using riblets from 3M on a NACA 0012 airfoil model up to moderate angles of attack are presented.
Abstract: Results of viscous drag reduction using riblets from 3M on a NACA 0012 airfoil model up to moderate angles of attack are presented. Measurements made consisted of model surface pressure distributions, mean velocity and streamwise turbulence intensity profiles in the boundary layer (just ahead of the trailing edge), and total airfoil drag for two riblet heights of 0.152 and 0.076 mm. Results show significantly higher skin friction drag reduction with incidence compared to plat plate flows; the reduction was as high as 16% at ? = 6 deg. Results of mean velocity profiles show that a larger contribution to drag reduction results from the suction side of the airfoil, indicating increased effectiveness of riblets in adverse pressure gradients. Examination of turbulence intensity profiles in the wall region indicates an appreciable reduction in the presence of riblets; correspondingly, the spectra show reduced energy levels at low frequencies.