Perturbations In Boundary Layer Research Articles

What Is the Main Cause of Diurnal Variation and Nocturnal Peak of Summer Precipitation in Sichuan Basin, China? The Key Role of Boundary Layer Low‐Level Jet Inertial Oscillations

AbstractThe precipitation in Sichuan Basin (SB), China, exhibits pronounced diurnal variation, including minimum rainfall in daytime and a prominent peak near midnight. This study investigates the primary mechanism of precipitation diurnal variation in SB using forecasts from three summer months of 2013 produced at a 4‐km grid spacing. The model forecasts reproduce the observed spatial distributions and diurnal cycles well, including the peak precipitation in SB at around 02 local solar time (LST). Contrary to the common belief that emphasizes the solenoidal effects associated with the Tibetan and Yunnan‐Guizhou Plateaus, prominent diurnal inertial oscillations of boundary layer south‐southwesterly low‐level jet into SB are shown to play more important roles in modulating the diurnal cycles of precipitation in SB. A basinwide moisture budget analysis is performed to reveal that the moisture flux from the southeast side of the basin dominates within the diurnal oscillations of the net moisture flux into the basin, and the much enhanced nocturnal low‐level jet plays a crucial role in the formation of nocturnal precipitation within the basin. The net moisture flux into SB reaches maximum at around 22 LST, the time boundary layer perturbation winds from the daily mean in the direction normal to the southeastern boundary of SB reach maximum, which is about 4 hr before precipitation peak at around 02 LST. Shallow thermally forced nighttime downslope flows and daytime upslope flows on the Tibetan Plateau and Yunnan‐Guizhou Plateau slopes contribute only a small portion of moisture fluxes through the basin boundaries.

Effect of a Roughness Element on the Hypersonic Boundary Layer Receptivity Due to Different Types of Free-Stream Disturbance with a Single Frequency.

The hypersonic flow field around a blunt cone was simulated using a high-order finite difference method. Fast acoustic waves, slow acoustic waves, entropy waves, and vortical waves were introduced into the free-stream to determine the influence of a free-stream with disturbances on the hypersonic flow field and boundary layer. The effect of disturbance type on the evolution of perturbations in the hypersonic boundary layer was analyzed. Fast Fourier Transform was adopted to analyze the effect of the disturbance type on the evolution of different modes in the boundary layer. A roughness element was introduced into the flow field to reveal the impact of the roughness element on hypersonic boundary layer receptivity. The results showed that a free-stream with disturbances affected the hypersonic flow field and boundary layer; acoustic waves had the greatest influence. The impact of slow acoustic waves on the flow field was mainly concentrated in the region between the shock and the boundary layer, whereas the influence of fast acoustic waves was mainly concentrated in the boundary layer. Multi-mode perturbations formed in the boundary layer were caused by the free-stream with disturbances, wherein the fundamental mode was the dominant mode of the perturbations in the boundary layer caused by fast acoustic waves, entropy waves, and vortical waves. The dominant modes of the perturbations in the boundary layer caused by slow acoustic waves were both the fundamental mode and the second harmonic mode. The roughness element changed the propagation process of different modes of perturbations in the boundary layer. In the downstream region of the roughness element, perturbations in the boundary layer caused by the slow acoustic waves had the greatest influence. The second harmonic mode in the boundary layer was significantly suppressed, and the fundamental mode became the dominant mode. The effects of fast acoustic waves and entropy waves on the boundary layer receptivity were similar, except the amplitude of the perturbations in the boundary layer caused by the fast acoustic waves was larger.

Renormalization group approach to boundary layer problems

Renormalization group(RG) method in the singular perturbation theory, originally introduced by Chen et al, has been proved to be very practicable in a large number of singular perturbed problems. In this paper, we firstly reconsider the RG method and give a new formulation of the renormalized procedure. Then we apply our strategy to investigate several kinds of singular perturbed boundary layer problems, our results show that the RG method has the same efficiency as the classical matched asymptotic expansion method, and can be viewed as a preliminary answer to the open problem proposed by Kirkinis.

Influence of the viscous boundary layer perturbations on single-mode panel flutter at finite Reynolds numbers

Panel flutter is an aeroelastic instability of aircraft skin panels, which can lead to a reduction in service life and panel destruction. Despite the existence of many studies related to panel flutter, the influence of the boundary layer on the panel stability has been considered in only a few of them. Up to the present day, most papers on the boundary layer effect consider only a zero-pressure-gradient boundary layer over a flat plate. The only studies of a boundary layer of arbitrary form were conducted in our previous papers (Vedeneev, J. Fluid Mech., vol. 736, 2013, pp. 216–249 and Bondarev & Vedeneev, J. Fluid Mech., vol. 802, 2016, pp. 528–552), where the boundary layer was represented as an inviscid shear layer (the Reynolds number $R=\infty$). In this paper we investigate the problem, taking viscosity into account, at large but finite Reynolds numbers. As before, we assume that the panel length is large and use Kulikovskii’s global instability criterion to analyse the panel eigenmodes and consider two different types of boundary layer profiles: a generalised convex profile and a profile with a generalised inflection point. Results show that viscous perturbations can, in general, have both stabilising and destabilising effects on the system, depending on the velocity and temperature profiles of the boundary layer and on its thickness. However, surprisingly, we prove that if the boundary layer yields a significant growth rate in the inviscid approximation, then the viscosity always produces an even larger growth rate.

Standard and boundary layer perturbation approaches to predict nonlinear axisymmetric behavior of cylindrical shells

The feasibility and performance of standard and boundary layer perturbation techniques in nonlinear analyses of cylindrical shells are investigated. To this end, the nonlinear axisymmetric behavior of short and long functionally graded (FG) cylindrical shells is considered. The nonlinear governing equations of shell theory with first-order approximation and the von Karman nonlinearity are decoupled. This uncoupling makes it possible to present an analytical solution. A new boundary layer perturbation solution is presented by reducing the governing equations to a normalized form of boundary-layer type. Also, the uncoupled governing equations are solved using standard one-, two-, and three-parameter expansions. Findings indicate that the boundary layer technique cannot predict the post-buckling behavior of cylindrical shells for any geometric ratios R/h andL/R, since after occurrence of instability, the behavior of shell is not boundary-layer type and it is impossible to satisfy the matching conditions. Hence, this technique is only valid for the analysis of long shells before buckling occurs. Furthermore, the standard perturbation series in terms of output parameters can predict the buckling load and the static equilibrium path with acceptable accuracy only under consideration of the deflection of points at an area near enough to the ends of the shell. On the other hand, the standard expansions in loading parameters are able to predict the snap-through post-buckling behavior accurately by considering higher-order terms (around 30th order) in expansion series.

Flow structure generated by laser-induced blast wave propagation through the boundary layer of a flat plate

Laser energy deposition generates localized flow structures that can be used as flow control devices in high-speed flows. In the present study, the interaction between a laser-induced blast wave and an incoming laminar boundary layer on a flat plate was experimentally investigated at a Mach 5 flow with three different unit Reynolds numbers. A hemispherical laser-induced blast wave (LIBW) is induced by focusing a 532 nm pulsed Nd:YAG laser beam on the surface of the plate. The hemispherical shaped fore wave front of the LIBW is locally transformed to an oblique shape, which results in a laser-induced oblique shock wave (LIOSW). As LIOSW propagates through the laminar boundary layer increases its thickness. With laser energy deposition near the leading edge of the flat plate, the LIOSW interacts and influences the leading edge shock wave (LSW). This interaction could contribute to the modulation of the LSW in scramjet intakes. A weak shock limb generated at the shape transition point of the LIBW or thermal spot due to laser-induced gas breakdown causes the boundary layer perturbation. The geometrical pattern produced due to the interaction between the LIOSW and the disturbed boundary layer remains similar to itself as it grows with time as well as at different local Reynolds numbers, 2.2×105 to 5.7×105.

Variability and Clustering of Midlatitude Summertime Convection: Testing the Craig and Cohen Theory in a Convection-Permitting Ensemble with Stochastic Boundary Layer Perturbations

Abstract The statistical theory of convective variability developed by Craig and Cohen in 2006 has provided a promising foundation for the design of stochastic parameterizations. The simplifying assumptions of this theory, however, were made with tropical equilibrium convection in mind. This study investigates the predictions of the statistical theory in real-weather case studies of nonequilibrium summertime convection over land. For this purpose, a convection-permitting ensemble is used in which all members share the same large-scale weather conditions but the convection is displaced using stochastic boundary layer perturbations. The results show that the standard deviation of the domain-integrated mass flux is proportional to the square root of its mean over a wide range of scales. This confirms the general applicability and scale adaptivity of the Craig and Cohen theory for complex weather. However, clouds tend to cluster on scales of around 100 km, particularly in the morning and evening. This strongly impacts the theoretical predictions of the variability, which does not include clustering. Furthermore, the mass flux per cloud closely follows an exponential distribution if all clouds are considered together and if overlapping cloud objects are separated. The nonseparated cloud mass flux distribution resembles a power law. These findings support the use of the theory for stochastic parameterizations but also highlight areas for improvement.

Growth mechanisms of perturbations in boundary layers over a compliant wall

The temporal modal and nonmodal growth of three-dimensional perturbations in the boundary-layer flow over an infinite compliant flat wall is considered. Using a wall-normal velocity/wall-normal vorticity formalism, the dynamic boundary condition at the compliant wall admits a linear dependence on the eigenvalue parameter, as compared to a quadratic one in the canonical formulation of the problem. This greatly simplifies the accurate calculation of the continuous spectrum by means of a spectral method, thereby yielding a very effective filtering of the pseudospectra as well as a clear identification of instability regions. The regime of global instability is found to be matching the regime of the favorable phase of the forcing by the flow on the compliant wall so as to enhance the amplitude of the wall. An energy-budget analysis for the least-decaying hydroelastic (static-divergence, traveling-wave-flutter and near-stationary transitional) and Tollmien--Schlichting modes in the parameter space reveals the primary routes of energy flow. Moreover, the flow exhibits a slower transient growth for the maximum growth rate of a superposition of streamwise-independent modes due to a complex dependence of the wall-boundary condition with the Reynolds number. The initial and optimal perturbations are compared with the boundary-layer flow over a solid wall; differences and similarities are discussed. Unlike the solid-wall case, viscosity plays a pivotal role in the transient growth. A slowdown of the maximum growth rate with the Reynolds number is uncovered and found to originate in the transition of the fluid-solid interaction from a two-way to a one-way coupling. Finally, a term-by-term energy budget analysis is performed to identify the key contributors to the transient growth mechanism.

Spectral gap characteristics in a daytime valley boundary layer

A correct estimation of turbulent variances and covariances in the atmospheric boundary layer relies on the determination of turbulent perturbations of wind speed components and scalar quantities, which requires the presence of a so‐called spectral gap. The goal of this work is to determine the range of gap scales necessary to define turbulent perturbations in a daytime valley boundary layer. To accomplish this, we analyze data from a large number of propeller‐vane and sonic anemometers using the fast Fourier transformation and the multiresolution flux decomposition. Daytime gap scales are found to range from 17 to 29 min and show large spatial variability across the valley floor and the adjacent slopes. Synoptically driven conditions that favour the occurrence of mesoscale phenomena, such as rotors and mountain waves, shift daytime gap scales toward longer periods. The low‐frequency end of the gap is also affected by the presence of slope winds that are characterized by a periodicity ranging from 80 to 200 min. Finally, we present a conceptual model of the daytime valley spectral gap which summarizes the findings of this study.

Numerical investigation of the boundary layer separation in chemical oxygen iodine laser

Large eddy simulation is carried out to model the flow process in a supersonic chemical oxygen iodine laser. Unlike the common approaches relying on the tensor representation theory only, the model in the present work is an explicit anisotropy-resolving algebraic Subgrid-scale scalar flux formulation. With an accuracy in capturing the unsteady flow behaviours in the laser. Boundary layer separation initiated by the adverse pressure gradient is identified using Large Eddy Simulation. To quantify the influences of flow boundary layer on the laser performance, the fluid computations coupled with a physical optics loaded cavity model is developed. It has been found that boundary layer separation has a profound effect on the laser outputs due to the introduced shock waves. The F factor of the output beam decreases to 10% of the original one when the boundary transit into turbulence for the setup depicted in the paper. Because the pressure is always greater on the downstream of the boundary layer, there will always be a tendency of boundary separation in the laser. The results inspire designs of the laser to apply positive/passive control methods avoiding the boundary layer perturbation.

Large-eddy simulation of flow over a cylinder with from to : a skin-friction perspective

We present wall-resolved large-eddy simulations (LES) of flow over a smooth-wall circular cylinder up to$Re_{D}=8.5\times 10^{5}$, where$Re_{D}$is Reynolds number based on the cylinder diameter$D$and the free-stream speed$U_{\infty }$. The stretched-vortex subgrid-scale (SGS) model is used in the entire simulation domain. For the sub-critical regime, six cases are implemented with$3.9\times 10^{3}\leqslant Re_{D}\leqslant 10^{5}$. Results are compared with experimental data for both the wall-pressure-coefficient distribution on the cylinder surface, which dominates the drag coefficient, and the skin-friction coefficient, which clearly correlates with the separation behaviour. In the super-critical regime, LES for three values of$Re_{D}$are carried out at different resolutions. The drag-crisis phenomenon is well captured. For lower resolution, numerical discretization fluctuations are sufficient to stimulate transition, while for higher resolution, an applied boundary-layer perturbation is found to be necessary to stimulate transition. Large-eddy simulation results at$Re_{D}=8.5\times 10^{5}$, with a mesh of$8192\times 1024\times 256$, agree well with the classic experimental measurements of Achenbach (J. Fluid Mech., vol. 34, 1968, pp. 625–639) especially for the skin-friction coefficient, where a spike is produced by the laminar–turbulent transition on the top of a prior separation bubble. We document the properties of the attached-flow boundary layer on the cylinder surface as these vary with$Re_{D}$. Within the separated portion of the flow, mean-flow separation–reattachment bubbles are observed at some values of$Re_{D}$, with separation characteristics that are consistent with experimental observations. Time sequences of instantaneous surface portraits of vector skin-friction trajectory fields indicate that the unsteady counterpart of a mean-flow separation–reattachment bubble corresponds to the formation of local flow-reattachment cells, visible as coherent bundles of diverging surface streamlines.

Excitation of controllable perturbations in the three-dimensional boundary layer using plasma actuators

Two versions of the structure of a multi-discharge plasma actuator intended to excite boundary layer perturbations in the neighborhood of the leading swept-wing edge are suggested. The actuator must prevent from appearance and development of the crossflow instability modes leading to laminarturbulent transition under the normal conditions. In the case of flow past a swept wing, excitation of controllable perturbations by the plasma actuator is simulated numerically in the steady-state approximation under the typical conditions of cruising flight of a subsonic aircraft. The local body force and thermal impact on the boundary layer flow which is periodic along the leading wing edge is considered. The calculations are carried out for the physical impact parameters realizable in the near-surface dielectric barrier discharge.

A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method

In this paper, a simple numerical method is proposed for solving singularly perturbed boundary layers problems exhibiting twin boundary layers. The method avoids the choice of fitted meshes. Firstly the original problem is transformed into a new boundary value problem whose solution does not change rapidly by a proper variable transformation; then the transformed problem is solved by using the reproducing kernel method. Two numerical examples are given to show the effectiveness of the present method.

Flow-induced noise generated by sub-boundary layer steps

The sound generated by a turbulent boundary layer with a smaller two-dimensional step was investigated and related to the perturbed flow field via a new scaling law. Experimental results were obtained using two types of sub-boundary layer steps (rectangular and triangular). Flow visualisation revealed an upstream separation zone and a downstream reattachment point. The sub-boundary layer steps, in general, resulted in a rapid thickening of the shear flow near the wall. The integral boundary layer results show the effect of the steps on the boundary layer can be likened to a disturbance followed by a boundary layer re-establishment region. The noise data revealed the nature of the noise created by the steps. The steps can be considered as acoustically compact (height much less than acoustic wavelength) and radiate noise in both streamwise and cross stream directions, suggesting the existence of compact superimposed dipole sources. The shape of the step has a large effect on the noise level, suggesting the front surface of the step has a dominant role in noise production. A new scaling law based on the perturbed boundary layer height was able to successfully collapse the noise data.

Nonlinear Response of a Compressible Boundary Layer to Free-stream Vortical Disturbances

The nonlinear response of a compressible boundary layer to unsteady free-stream vortical fluctuations of the convected-gust type is investigated. The amplitude of the disturbances is strong enough for nonlinear interactions to be induced within the boundary layer. Attention is focused on the induced low-frequency streamwise-stretched components of the boundary-layer disturbances, known as streaks or Klebanoff modes, which may become unstable and break down to fully developed turbulence. The streaks are described using the mathematical framework of the so-called boundary-region equations, i.e. the asymptotic limit of the Navier-Stokes equations for low-frequency disturbance, developed by Leib et al.1 and extended by Ricco & Wu 2 and Ricco et al.3 to linear perturbations in compressible boundary layers, and nonlinear disturbances in incompressible boundary layers, respectively. In the present work, compressibility is taken into account through aerodynamic heating effects due to the mean-flow velocity being comparable with the speed of sound. Both velocity and thermal (temperature) streaks are generated as well as are a new mean flow and fluctuations of higher frequencies. Nonlinearity attenuates the fluctuations of the streamwise velocity and a similar stabilizing effect is observed on the temperature.This represents the preliminary study which is necessary to carry out the secondary instability analysis on the new unsteady compressible three-dimensional flow generated by the nonlinear interactions.

Effect of Freestream Turbulence on Roughness-induced Crossflow Instability

The effect of freestream turbulence on generation of crossflow disturbances over swept wings is investigated through direct nu- merical simulations. The set up follows the experiments performed by Downs et al. (2012). In these experiments the authors use ASU(67)-0315 wing geometry which promotes growth of crossflow disturbances. Distributed roughness elements are locally placed near the leading edge with a given spanwise wavenumber to excite the corresponding stationary crossflow vortices. In present study, we partially reproduce the isotropic homogenous freestream turbulence through direct numerical simulations using freestream spectrum data from the experiments. The generated freestream fields are then applied as the inflow boundary condition for direct numerical simulation of the wing. The distributed roughness elements are modelled through wing surface deformation and placed near the leading edge to trigger the stationary crossflow disturbances. The effects of the generated freestream turbulence on the initial amplitudes and growth of the boundary layer perturbations are then studied.

Parametric perturbative study of the supercritical cross-flow boundary layer

A linear analysis of the transient evolution of small perturbations in the supercritical FSC cross-flow boundary layer is presented. We used the classical method based on the temporal evolution of individual three-dimensional travelling waves subject to near-optimal initial conditions and considered an extended portion of the parameter space. Our parametrization included the wave-number, the wave-angle, the cross-flow angle, the Hartree parameter and the Reynolds number. Special focus was given to the role played by the waveangle in inducing very steep initial transient growths in waves that proved to be stable in the long term.We found that the angular distribution of the asymptotically unstable waves and of the waves that show a transient growth depends greatly on the value of the cross flow angle and wave-angle as well as on the sign of the Hartree parameter, but depend much less on the Reynolds number. In the case of the decelerated boundary layer, at sufficiently short wavelengths, transient growths become much more rapid than the initial growth of the unstable waves. In all cases of transient growth, pressure perturbations at the wall are not synchronous with the kinetic energy of the perturbation.We present a comparison with the sub-critical results obtained by Breuer and Kuraishi (1994) (Re=500, sweep angle of π/4) for the same full range of the obliquity angle here considered (π radiants).

Active control of a turbulent boundary layer based on local surface perturbation

AbstractActive control of a turbulent boundary layer has been experimentally investigated with a view to reducing the skin-friction drag and gaining some insight into the mechanism that leads to drag reduction. A spanwise-aligned array of piezo-ceramic actuators was employed to generate a transverse travelling wave along the wall surface, with a specified phase shift between adjacent actuators. Local skin-friction drag exhibits a strong dependence on control parameters, including the wavelength, amplitude and frequency of the oscillation. A maximum drag reduction of 50 % has been achieved at 17 wall units downstream of the actuators. The near-wall flow structure under control, measured using smoke–wire flow visualization, hot-wire and particle image velocimetry techniques, is compared with that without control. The data have been carefully analysed using techniques such as streak detection, power spectra and conditional averaging based on the variable-interval time-average detection. All the results point to a pronounced change in the organization of the perturbed boundary layer. It is proposed that the actuation-induced wave generates a layer of highly regularized streamwise vortices, which acts as a barrier between the large-scale coherent structures and the wall, thus interfering with the turbulence production cycle and contributing partially to the drag reduction. Associated with the generation of regularized vortices is a significant increase, in the near-wall region, of the mean energy dissipation rate, as inferred from a substantial decrease in the Taylor microscale. This increase also contributes to the drag reduction. The scaling of the drag reduction is also examined empirically, providing valuable insight into the active control of drag reduction.

Floquet analysis of fundamental, subharmonic and detuned secondary instabilities of Görtler vortices

Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the Gortler instability up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental, subharmonic and detuned secondary instabilities. With the Gortler-vortices-distorted base flow, two classes of secondary disturbances, i.e. odd modes and even modes, are identified according to the eigenfunctions of the disturbances. These modes may result in different patterns in the late stages of the transition process. Li and Malik [1] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes I & II and odd modes I & II. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplification. The detuned modes are confirmed to be less amplified than the fundamental (for the odd mode I) and subharmonic modes (for even modes I & II and the odd mode II).

Formation of a three-dimensional plasma boundary after decay of the plasma response to resonant magnetic perturbation fields

First time experimental evidence is presented for a direct link between the decay of a n = 3 plasma response and the formation of a three-dimensional (3D) plasma boundary. We inspect a lower single-null L-mode plasma which first reacts at sufficiently high rotation with an ideal resonant screening response to an external toroidal mode number n = 3 resonant magnetic perturbation field. Decay of this response due to reduced bulk plasma rotation changes the plasma state considerably. Signatures such as density pump out and a spin up of the edge rotation—which are usually connected to formation of a stochastic boundary—are detected. Coincident, striation of the divertor single ionized carbon emission and a 3D emission structure in double ionized carbon at the separatrix is seen. The striated C II pattern follows in this stage the perturbed magnetic footprint modelled without a plasma response (vacuum approach). This provides for the first time substantial experimental evidence, that a 3D plasma boundary with direct impact on the divertor particle flux pattern is formed as soon as the internal plasma response decays. The resulting divertor structure follows the vacuum modelled magnetic field topology. However, the inward extension of the perturbed boundary layer can still not directly be determined from these measurements.