Inactive Motion Research Articles

Nonsmooth modal analysis of a varying cross-sectional area bar in unilateral contact

Nonsmooth modes of vibration allow for identification of resonant behaviours and attendant vibratory frequencies in structures prone to unilateral contact conditions on the boundary. The prominent approach for finding nonsmooth modes of vibration entails finding continua of periodic solutions to the system in question. In this paper, nonsmooth modes of a one-dimensional bar of varying cross-sectional area prone to unilateral contact with a rigid obstacle are determined. While numerical and analytical techniques were previously proposed, they were limited to constant cross section bar and could not be applied on the varying area bar for which the classical d’Alembert solution no longer exists. In this article, nonsmooth modal analysis of the varying area bar is performed via a novel treatment of the Signorini conditions within the finite element framework: the nodal boundary method. The nodal boundary method solves the Signorini problem by switching between two sets of shape functions describing either (1) inactive contact motion (motion away from the rigid obstacle) or (2) active contact motion (bar in contact with the rigid obstacle). In the proposed nodal boundary method, the motion of the contacting node does not participate in the resulting governing Ordinary Differential Equation (ODE). Instead, its motion is prescribed by the boundary conditions and is dictated by the motion of internal nodes. The nodal boundary method results in a discontinuous ODE in the internal nodes which can be solved both analytically and via numerical techniques. Solutions obtained by the nodal boundary method exhibit several advantages over existing numerical techniques: no chattering at contact, no penetration of the rigid obstacle, and existence of periodic solutions. Specifically, these periodic solutions are readily detectable via the shooting method with sequential continuation. The nodal boundary method is used successfully for the nonsmooth modal analysis of different models of the varying area bar. Besides, application of the nodal boundary method for nonsmooth modal analysis of the uniform area cantilever bar in Dirichlet or Robin boundary conditions is also demonstrated for comparison with existing literature.

Revealing the mechanisms for inactive rolling and wear behaviour on chemical mechanical planarization

The paper examines the influences of abrasive conditions, silica thickness, and motion parameters on the polishing process of a silicon substrate covered by a thin silica film. The silica film minimizes the direct collision of the abrasive on the silicon substrate. During the polishing process, the adhesion phenomenon plays the main role in atomic removal. Notably, the abrasive sliding motion can generate an inactive rolling motion. The inactive rolling motion can be used to explain the stick-slip motion by showing the system of periodic high-strain marks. In rolling, the deformation behaviors of the workpiece rely on the correspondence between the rolling and the moving speeds. In the fixed diamond abrasive (FDA) cases, the atomic sticking rate is lower but the workpiece deformation is higher than the loose diamond abrasive (LDA) cases. Besides, the FDA cannot create the inactive rolling motion and the stick-slip motion as the LDA. In general, the paper points out the existence of the inactive rolling motion and its role in the atomic removal process through the stick-slip motion phenomenon at the nanoscale, the advantage of this type of motion in a conventional chemical mechanical polishing (CMP) process, and the padding role of the silica layer.

On exactly self-similar turbulent boundary layers and single-layer scaling

Turbulent boundary layers are traditionally thought to obey two layer scaling. However, it was shown by Dixit and Ramesh [J. Fluid Mech. 615, 445–475 (2008)] that the so-called sink flow turbulent boundary layer obeys a Blasius-like scaling all through the boundary layer. We make this single layer scaling as an operational definition for perfectly equilibrium flow and derive equations for a general class of equilibrium flows with permeable walls allowing suction and blowing of fluid. Using the above definition, constraints required to be satisfied by such equilibrium turbulent boundary layers are derived and discussed in detail. Using direct numerical simulations (DNS), we demonstrate the existence of such turbulent boundary layers, and various properties of these boundary layers are studied in detail. In particular, it is shown that the mean velocity profiles and other turbulent statistics display excellent similarity, and various boundary layer parameters in such boundary layers vary systematically with the magnitude of blowing/suction parameter. By extension, it is also demonstrated by DNS that higher order moments (up to third order moments) also display streamwise self-similarity. We believe that this is an important result where self-similarity is demonstrated for the first time for higher moments of fluctuating velocity. The non-universality of the log-law coefficients in favorable pressure gradient flows is already known [S. A. Dixit and O. N. Ramesh, J. Fluid Mech. 615, 445–475 (2008) and Chauhan et al., in Proceedings of 11th EUROMECH European Turbulence Conference on Turbulence, Porto, Portugal (Springer Proceedings in Physics, 2007), pp. 239–241]. We demonstrate their non-universal nature in equilibrium boundary layers with suction and blowing using the present direct numerical simulations. Remarkably, the ratio of Reynolds shear stress (u′v′¯) to streamwise (u′2¯) and spanwise turbulent intensity (w′2¯) in these boundary layers is constant over the log-region in the mean velocity profile even though u′2¯, w′2¯, and u′v′¯ by themselves show variation with y+ in the log region, indicative of the absence of inactive motion in these flows. It is shown that the dominance of active motion and more importantly the absence of inactive motion leads to a universality of scaling that manifests as a single layer Blasius scaling with self-similarity in such flows. Equivalently, it could also be seen as a single layer scaling with all variables all through the boundary layer. This would mean that the friction velocity scales the entire boundary layer, which could be taken to suggest equivalence of attached eddies with the active component of motion.

Active and inactive components of the streamwise velocity in wall-bounded turbulence

Abstract

Modelling of Quadratic-Surface Sludge Digesters by Smoothed Particle Hydrodynamics (SPH) – Finite Element (FE) Methods

Abstract The quadric-surfaced sludge digester (QSD), also known as the egg-shaped sludge digester, has proven its advantages over traditional cylindrical digesters recently. A reduction in operational cost is the dominant factor. Its shell can be described as a revolution of a parabola with the apex and base being either tapered or spherical. This shape provides a surface free of discontinuities, which is advantageous regarding the efficiency during mixing. Since the shape does not produce areas of inactive fluid motion within the tank, sludge settlement and an eventual grit build-up are avoided. The stresses developed in the shell of the sludge digester, vary along the meridian and equatorial diameters. A non-dimensional parameter, ξ, defines the height-to-diameter aspect ratio which is used to delineate the parametric boundary conditions of the shell’s surface. Three groups of analyses were conducted to determine the orthogonal stresses in the shell of the QSD. The first-principles numerical models ran reasonably quickly, and many simulations were made during the study. The results showed that they were in within the range 5.34% to 7.2% to 2D FEA results. The 3D FEA simulation results were within the range of 8.3% to 9.2% to those from the MATLAB time-history models. This is a good indicator that the first principles numerical models are an excellent time-saving method to predict the behaviour of the QSD under seismic excitation. Upon examining the criteria for the design, analysing the results for the 2D FEA simulations showed that the fill height is not a significant variable with sloshing however the 3D FEA showed that the hydrostatic pressure is a significant variable. With the maximum tensile stress of the 3D-printed Acrylonitrile Butadiene Styrene (ABS)-a common thermoplastic polymer typically used for injection molding applications, being 24.4 MPa, the overall maximum stress of 5.45 MPa, the material can be a viable option for the use of QSD construction in small island developing states (SIDS).

Video Key Frame Monitoring Algorithm and Virtual Reality Display Based on Motion Vector

In this article, a motion vector-based video key frame detection algorithm is proposed to solve the problem of miss election and missing selection caused by the difficulty in detecting the moving target characteristics of the video key frame. Firstly, the entropy of adjacent frame difference and the two-dimensional entropy of image are introduced, and the combination of the two is taken as the measurement of the difference between video frames. Secondly, outliers are detected by statistical tools to obtain the lens boundary, thus realizing the adaptive lens detection of video content. Then, ViBe algorithm is used to detect the foreground object in the video sequence and extract the scale-invariant feature transformation features of the foreground moving object. Finally, the motion vector is introduced, and the sum of the block matching results is motion vector by partitioning the two adjacent frames and performing block matching. The magnitude of motion vector reflects the intensity of motion in the video, so active and inactive motion regions are obtained, and the similarity of video frames is calculated according to the defined formula, and key frames are extracted in these regions respectively. The experimental results show that the detection algorithm proposed in this article improves the video results with rich motion information obviously, and the objective indexes and subjective scores are improved to some extent, which improves the universality of the algorithm. In addition, this article also studies the display mode of key frame extraction results in virtual reality environment. The key frame display mode of video in virtual reality is optimized mainly by changing the display mode of information and changing the scene and testing the result of user task execution.

Modulation of the regeneration cycle by neutrally buoyant finite-size particles

Direct numerical simulations of turbulent suspension flows are carried out with the force-coupling method in plane Couette and pressure-driven channel configurations. Dilute to moderately concentrated suspensions of neutrally buoyant finite-size spherical particles are considered when the Reynolds number is slightly above the laminar–turbulent transition. Tests performed with synthetic streaks, in both turbulent channel and Couette flows, show clearly that particles trigger the instability in channel flow whereas the plane Couette flow becomes laminar. Moreover, we have shown that particles have a pronounced impact on pressure-driven flow through a detailed temporal and spatial analysis whereas they have no significant impact on the plane Couette flow configuration. The substantial difference between the two flow configurations is related to the spatial preferential distribution of particles in the large-scale rolls (inactive motion) in Couette flow, whereas they are accumulated in the ejection (active motion) regions in pressure-driven flow. Through investigation of particle modification in two distinct flow configurations, we were able to show the specific response of turbulent structures and the modulation of the fundamental mechanisms composing the regeneration cycle in the buffer layer of the near-wall turbulence. Especially for pressure-driven flow, the particles enhance the lift-up and let it act continuously whereas the particles do not significantly alter the streak breakdown process. The reinforcement of the streamwise vortices is attributed to the vorticity stretching term by the wavy streaks. The smaller and more numerous wavy streaks enhance the vorticity stretching and consequently strengthen the circulation of large-scale streamwise vortices in suspension flow.

Synchronized Intermittent Motion Induced by the Interaction between Camphor Disks

A new mode of collective motion was discovered in a system of camphor disks floating on the water surface in a circular chamber. The mode was induced by tuning the number of the disks. A single or few disks are known to continuously move on the water surface. Conversely, when many disks are present, motion comes to a stop and the disks form ordered spatial patterns by repulsive interaction. Here we found the third mode that emerged at an intermediate disk number, in which inactive and active motion phases alternated non-periodically. This new mode exhibited synchronization as the disk number increased.

Statistical structure of self-sustaining attached eddies in turbulent channel flow

AbstractThe linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend’s attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend’s attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length ${\it\lambda}_{z}$ between ${\it\lambda}_{z}^{+}=100$ and ${\it\lambda}_{z}\simeq 1.5h$, where $h$ is half the height of the channel, the former is found to be self-similar along $y\simeq 0.1{\it\lambda}_{z}$ and ${\it\lambda}_{x}\simeq 10{\it\lambda}_{z}$, while the latter is self-similar along $y\simeq 0.5{\it\lambda}_{z}\sim 0.7{\it\lambda}_{z}$ and ${\it\lambda}_{x}\simeq 2{\it\lambda}_{z}\sim 3{\it\lambda}_{z}$ where $y$ is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of $k_{x}^{-1}$ spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend’s inactive motion and several recent theoretical findings.

Scaling and correlation of vorticity fluctuations in turbulent channels

Data from direct numerical simulations have been correlated to examine the effects of Reynolds number on vorticity fluctuation profiles. Three different scalings are found: two in the inner region and the third in the outer region. In the inner region a two-term asymptotic expansion is required to represent the mean square vorticity profiles; ⟨ωω⟩#=⟨ωω⟩0#+⟨ωω⟩1+u∗/U0. The first scaling ⟨ωω⟩0#=⟨ωω⟩0/(u∗3U0/ν2) is for inactive motions that do not generate Reynolds shear stress. It applies to the streamwise and spanwise components. However, the zero-order term is zero for the normal vorticity component. The scrubbing of the inactive motions over the wall generates vorticity, which is a maximum at the wall, and diffuses out to about y+=50 before it decays. The fluctuating viscous wall shear stress is due entirely to this motion, and as a result the stress ratio (rms/mean) τ′/τ0=CU0/u∗ depends on the Reynolds number. The second scaling ⟨ωω⟩1+=⟨ωω⟩1/(u∗4/ν2), the same scaling as the Reynolds shear stress, is active motions. All three components participate in these motions, which are zero at the wall, rise to a peak at about y+=13–20, and fall to zero at about y+=400. This is consistent with the fact that the Reynolds shear stress is identically zero at the wall. The third scaling correlates data in the outer region using the Kolmogorov time scale ⟨ωω⟩/(u∗3/hν). Matching between the inner and outer regions has a common part (the equivalent of the log law) of ∼C/y+ or ∼C/Y for all three components. All components decrease further and become isotropic as the centerline is approached. Scaling with the Kolmogorov scale implies that dissipation is the important activity. The correlated data are fitted to simplified equations that can be formed into composite expansions to predict profiles at any Reynolds number.

The interaction between inner and outer regions of turbulent wall-bounded flow

The nature of the interaction between the inner and outer regions of turbulent wall-bounded flow is examined. Townsend's theory of inactive motion is shown to be a first-order, linear approximation of the effect of the large eddies at the surface that acts as a quasi-inviscid, low-frequency modulation of the shear-stress-bearing motion. This is shown to be a 'strong' asymptotic condition that directly expresses the decoupling of the inner-scale active motion from the outer-scale inactive motion. It is further shown that such a decoupling of the inner and outer vorticity fields near the wall is inappropriate, even at high Reynolds numbers, and that a 'weak' asymptotic condition is required to represent the increasing effect of outer-scale influences as the Reynolds number increases. High Reynolds number data from a fully developed pipe flow and the atmospheric surface layer are used to show that the large-scale motion penetrates to the wall, the inner-outer interaction is not describable as a linear process and the interaction should more generally be accepted as an intrinsically nonlinear one.

Structure of Turbulent Flow in a Shallow Tidal Estuary

A high-resolution current profiler (HRCP), which belongs to a pulse-to-pulse coherent Doppler sonar, has been used to measure vertical profiles of turbulence parameters, such as the Reynolds stresses, eddy viscosity, production and dissipation rates, etc., and to test the parametrization of dissipation rate and eddy viscosity. The HRCP and automatic ascending/descending CTD are deployed during the autumn of 2001 for 24 h in a tidal estuary. Reliable velocities along the beams with HRCP are collected with 3 s intervals and a vertical resolution as fine as 0.03 m in the range 0.02–0.98 m above the bottom. Density profiles with the CTD are taken nominally every 30 sec. The turbulent velocity variables depend largely on the tidal phase; the variables during the ebb deviate from those in neutral equilibrium boundary layer. This deviation during the ebb presumably arises from the “inactive motion.” The stability function SM in the Mellor–Yamada (M–Y) model is smaller than 0.39 even when the stratification is negligible during the flood. The constant of proportionality B1 in the dissipation model is larger than 16.6 used in M–Y model. There is room for improving some of the mixing parametrizations in estuarine tidal flows.

Townsend's Hypothesis, Coherent Structures And Monin–Obukhov Similarity

Townsend's hypothesis states that turbulence near a wall can be divided into an active part that transports momentum, and an inactive part that does not, and that these two kinds of turbulence do not interact. Active turbulence is generated by wind shear and has properties that scale on local parameters of the flow, while inactive turbulence is the product of energetic processes remote from the surface and scales on outer-layer parameters. Both kinds of motion can be observed in the atmospheric surface layer, so Monin-Obukhov similarity theory, which is framed in terms of local parameters only, can apply only to active motions. If Townsend's hypothesis were wrong, so that active and inactive motions do interact in some significant way, then transport processes near the ground would be sensitive to outer-layer parameters such as boundary-layer depth, and Monin-Obukhov theory would fail. Experimental results have shown that heat transport near the ground does depend on processes in the outer layer. We propose a mechanism for this whereby inactive motions initiate active, coherent ejection/sweep structures that carry much of the momentum and heat. We give evidence that the inactive motions take the form of streak patterns of faster and slower air, and argue that these are induced by the pressure effects of large eddies passing overhead. The streak pattern includes regions where faster streams of air overtake and engulf slower-moving streaks. Transverse vortices form across the spines of the streaks at these places and some of them develop into horseshoe vortices. These horseshoe vortices grow rapidly and are rotated forward in the sheared flow so they soon contact the ground, squirting the air confined between the legs of the horseshoe vortex outwards as a forceful ejection. This model is consistent with a wide range of results from the field and laboratory experiments. Heat transport is significantly affected, so undermining the dimensional assumptions of Monin-Obukhov similarity theory.

Compressibility and structure of turbulence in supersonic shear flows

In this paper, different aspects of supersonic turbulent flows are discussed, in connection with some properties of compressible turbulence. The discussion is based on experiments, in which particular features have been found. The first point is the influence of density gradients. It is shown that changing the density gradient in a boundary layer does not change the particularly small size of the energetic scales. This effect is attributed to compressibility and not to density stratification, probably by modifying the `inactive motions'. The second point is about the importance of acoustics in a mixing layer. The results show that turbulent transport of momentum and heat follows the same analogy as in boundary layers, and that the energy losses by acoustic radiation are too weak to explain the reduction of the spreading rate, which is the major global effect of compressibility.

Active Turbulence and Scalar Transport near the Forest–Atmosphere Interface

Turbulent velocity, temperature, water vapor concentration, and other scalars were measured at the canopy‐ atmosphere interface of a 13‐14-m-tall uniform pine forest and a 33-m-tall nonuniform hardwood forest. These measurements were used to investigate whether the mixing layer (ML) analogy of Raupach et al. predicts eddy sizes and flow characteristics responsible for much of the turbulent stresses and vertical scalar fluxes. For this purpose, wavelet spectra and cospectra were derived and analyzed. It was found that the ML analogy predicts well vertical velocity variances and integral timescales. However, at low wavenumbers, inactive eddy motion signatures were present in horizontal velocity wavelet spectra, suggesting that ML may not be suitable for scaling horizontal velocity perturbations. Momentum and scalar wavelet cospectra of turbulent stresses and scalar fluxes demonstrated that active eddy motion, which was shown by Raupach et al. to be the main energy contributor to vertical velocity (w) spectral energy (Ew), is also the main scalar flux‐transporting eddy motion. Predictions using ML of the peak Ew frequency are in excellent agreement with measured wavelet cospectral peaks of vertical fluxes ( Kh 5 1.5, where K is wavenumber and h is canopy height). Using Lorentz wavelet thresholding of vertical velocity time series, wavelet coefficients associated with active turbulence were identified. It was demonstrated that detection frequency of organized structures, as predicted from Lorentz wavelet filtering, relate to the arrival frequency ^U&/h and integral timescale, where ^U& is the mean horizontal velocity at height z 5 h. The newly proposed wavelet thresholding approach, which relies on a ‘‘global’’ wavelet threshold formulation for the energy in w, provides simultaneous energy‐covariance-preserving characterization of ‘‘active’’ turbulence at the canopy‐atmosphere interface.

Skin temperature perturbations induced by surface layer turbulence above a grass surface

High‐frequency (5 Hz) atmospheric surface layer (ASL) turbulent velocity (u′) and infrared skin temperature perturbations (T′s) were measured above a grass‐covered forest clearing and analyzed for cloud free conditions. These measurements were used to investigate mechanisms responsible for the production of large short‐lived T′s perturbations caused by rapid excursions in u′. To quantify the effects of u′ on rapid surface cooling, wavelet spectra of u′ and T′s and cospectra of u′T′s were computed. The u′ wavelet power spectra were then analyzed using Townsend's [1961, 1976] hypothesis. Townsend's hypothesis states that ASL eddy motion can be decomposed into an active component, which is a function of the ground shear stress (u*) and height (z) above the zero plane displacement, and an inactive component, which is produced in the atmospheric boundary layer (ABL) outer region. A −1 power law in the u′ power spectrum was used as a signature for inactive eddy motion. Therefore the −1 power law was used to identify wavenumber ranges (about 1.5 decades) associated with inactive eddy motion. The measured T′s wavelet spectra and u′T′s cospectra identified with this wavenumber range demonstrate that much of the T′s energy and 〈u′T′s〉 are due to inactive eddy motion, where the angle brackets indicate time averaging. Hence, in contrast to the laboratory experiments of Owen and Thomson [1963], it is argued that skin temperature perturbations at the canopy‐atmosphere interface of a grass‐covered surface (small thermal inertia) are strongly dependent on the inactive eddy motion produced in the outer layer of the ABL.

A Theoretical and Experimental Investigation of Energy-Containing Scales in the Dynamic Sublayer of Boundary-Layer Flows

The existence of universal power laws at low wavenumbers (K) in the energy spectrum (Eu) of the turbulent longitudinal velocity (u) is examined theoretically and experimentally for the near-neutral atmospheric surface layer. Newly derived power-law solutions to Tchen's approximate integral spectral budget equation are tested for strong- and weak-interaction cases between the mean flow and turbulent vorticity fields. To verify whether these solutions reproduce the measured Eu at low wavenumbers, velocity measurements were collected in the dynamic sublayer of the atmosphere at three sites and in the inner region of a laboratory open channel. The atmospheric surface layer measurements were carried out using triaxial sonic anemometers over tall corn, short grass, and smooth desert-like sandy soil. The open channel measurements were performed using a two-dimensional boundary-layer probe above a smooth stainless steel bed. Comparisons between the proposed analytical solution for Eu, the dimensional analysis by Kader and Yaglom, and the measured Haar wavelet Eu spectra are presented. It is shown that when strong interaction between the mean flow and turbulent vorticity field occurs, wavelet spectra measurements, predictions by the analytical solution, and predictions by the dimensional analysis of Kader-Yaglom (KY) are all in good agreement and confirm the existence of a -1 power law in Eu(= Cuuu2* K-1, where Cuu is a constant and u* is the friction velocity). The normalized upper wavenumber limit of the -1 power law (Kz = 1, where z is the height above the zero-plane displacement) is estimated using two separate approaches and compared to the open channel and atmospheric surface-layer measurements. It is demonstrated that the measured upper wavenumber limit is consistent with Tchen's budget but not with the KY assumptions. The constraints as to whether the mean flow and turbulent vorticity strongly interact are considered using a proposed analysis by Panchev. It is demonstrated that the arguments by Panchev cannot be consistent with surface-layer turbulence. Using dimensional analysis and Heisenberg's turbulent viscosity model, new constraints are proposed. The new constraints agree with the open channel and atmospheric surface-layer measurements, Townsend's ‘inactive eddy motion hypothesis’, and the Perry et al. analysis.

Perspectives on wall turbulence: The use of complementary techniques

The concept of “inactive” motion (originally put forward by Townsend and subsequently refined and extended by Bradshaw) is examined and its relevance to our present understanding of near-wall turbulence is illustrated. Bradshaw's seminal papers of the 1960s are revisited, and the ideas put forward in them are examined in the light of recent data analyzed with the benefit of newer techniques, including conditional sampling, wave-number/phase-velocity spectra and continuous wavelet transforms. Bradshaw's basic ideas (perhaps best exemplified by the “Friday morning discussions” with Kline and others during the Stanford '68 meeting) are used as a point of departure for examining the distinction between inactive and active motion, as well as the appropriateness of “wall scaling” for the latter. In particular, the role of “ejections” and “sweeps” within the context of the theory is examined. Recent results show that Bradshaw's initial ideas are still valid and that they are a lasting tribute to his insight and his gift of devising the “right” experiment. However, the importance of viscous scaling for ejection and sweep lengths in smooth-wall boundary layers is demonstrated, while the importance of the roughness length scale in rough-wall boundary layers also is apparent. It is clear that more detailed experiments are required, using data from direct numerical simulations.

The “Inactive” Eddy Motion and the Large-Scale Turbulent Pressure Fluctuations in the Dynamic Sublayer

Abstract The statistical structure of the turbulent pressure fluctuations was measured in the dynamic sublayer of a large grass-covered forest clearing by a free air static pressure probe and modeled using Townsend's hypothesis. Townsend's hypothesis states that the eddy motion in the equilibrium layer can be decomposed into an active component, which is only a function of the ground shear stress and height, and an inactive component, which is produced by turbulence in the outer region. It is demonstrated that the inactive eddy motion contributes significantly to the pressure and longitudinal velocity power spectra for wavenumbers much smaller than that corresponding to the height above the ground surface. Because of the importance of this inactive eddy motion contribution, it was possible to derive and validate a scaling law for the pressure power spectrum at low wavenumbers. The root-mean-square pressure was derived from the ground shear stress using simplifications to the Poisson equation that relate t...

The structure and development of a wing-tip vortex

Experiments have been performed on the tip vortex trailing from a rectangular NACA 0012 half-wing. Preliminary studies showed the vortex to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful velocity measurements could therefore be made using hot-wire probes.Detailed analysis of the effects of wandering was performed to properly reveal the flow structure in the core region and to give confidence in measurements made outside the core. A theory has been developed to correct mean-velocity profiles for the effects of wandering and to provide complete quantitative estimates of its amplitude and contributions to Reynolds stress fields. Spectral decomposition was found to be the most effective method of separating these contributions from velocity fluctuations due to turbulence.Outside the core the flow structure is dominated by the remainder of the wing wake which winds into an ever-increasing spiral. There is no large region of axisymmetric turbulence surrounding the core and little sign of turbulence generated by the rotational motion of the vortex. Turbulence stress levels vary along the wake spiral in response to the varying rates of strain imposed by the vortex. Despite this complexity, the shape of the wake spiral and its turbulent structure reach an approximately self-similar form.On moving from the spiral wake to the core the overall level of velocity fluctuations greatly increases, but none of this increase is directly produced by turbulence. Velocity spectra measured at the vortex centre scale in a manner that implies that the core is laminar and that velocity fluctuations here are a consequence of inactive motion produced as the core is buffeted by turbulence in the surrounding spiral wake. Mean-velocity profiles through the core show evidence of a two-layered structure that dies away with distance downstream.