Perturbations In Boundary Layer Research Articles

A Combined Scheme based on the Multiscale Stochastic Perturbed Parameterization Tendencies and Perturbed Boundary Layer Parameterization for a Global Ensemble Prediction System

Abstract Stochastic representations of model uncertainties are of great importance for the performance of ensemble prediction systems (EPSs). The stochastically perturbed parameterization tendencies (SPPT) scheme with a single-scale random pattern has been used in the operational global EPS of China Meteorological Administration (CMA-GEPS) since 2018. To deal with deficiencies in this operational single-scale SPPT scheme, a combined scheme based on the multiscale SPPT (mSPPT) scheme and the stochastically perturbed parameterization for the planetary boundary layer (SPP-PBL) scheme is developed. In the combined scheme, the mSPPT component aims to expand model uncertainties characterized by SPPT at mesoscale, synoptic scale, and planetary scale. The SPP-PBL component with six vital parameters is used to capture uncertainties in PBL processes, which is underrepresented by SPPT for the tapering treatment within PBL. Comparisons between the operational SPPT scheme and the mSPPT scheme reveal that the mSPPT scheme can generate more improvements in both ensemble reliability and forecast skills mainly in tropics. Besides, additional benefits from SPP-PBL on top of mSPPT are shown to be primarily distributed in tropics at the lower layers below 850 hPa and surface. Furthermore, the combined scheme of mSPPT and SPP-PBL is suggested to yield better spread–error relationships and forecast skills than the operational SPPT scheme in terms of objective verification scores for standard upper-air variables and surface parameters. A case study for the extreme precipitation event on 20 July 2021 in Henan Province of China also demonstrates the better ability of the combined scheme in forecasting the precipitation intensity and location. Significance Statement A comprehensive and reasonable representation of model uncertainties helps to improve the performance of ensemble prediction systems (EPSs). Despite the popular usage in simulating model uncertainties, the stochastically perturbed parameterization tendencies (SPPT) scheme possesses several shortcomings. To overcome this, a combined scheme based on the multiscale SPPT (mSPPT) scheme and the stochastically perturbed parameterization for the planetary boundary layer (SPP-PBL) scheme is proposed. Based on the global EPS of China Meteorological Administration (CMA-GEPS), additional benefits from the independent usage of mSPPT and SPP-PBL are disclosed. And the combined scheme can inherit the merits of mSPPT and SPP-PBL and generate more improvements on ensemble performance than the original single-scale SPPT scheme. This research provides a guideline for future upgradation of CMA-GEPS.

Application of High-Speed Self-Aligned Focusing Schlieren System for Supersonic Flow Velocimetry

A self-aligned focusing schlieren (SAFS) system combines the field of view of a conventional schlieren system with the defocus blur of a focusing schlieren system away from the object plane. It can be assembled in a compact form, measuring 1.2 m (4 ft) in length in the described case. The depth of field is sufficiently shallow to distinguish specific spanwise features in a supersonic flow field within a 76.2 mm (3 in) wide test section. As a result, the boundary-layer perturbations on windows and window-material defects and surface imperfections are blurred. Analytical forms are derived for depth of field and vignetting of the SAFS system. A laser spark velocity measurement in Mach 2 flow is performed by tracking the blast wave of a laser spark using 500 kHz SAFS imaging with a 200 ns optical pulse width. The flow Mach number and stagnation temperature are measured by comparing the blast-wave dynamics to an analytical solution. Additionally, schlieren image velocimetry is performed by analyzing natural flow perturbations in 500 kHz SAFS images using a self-correlation method. Comparing the spectra of gas density perturbations from the core flow and a near-wall region reveals a significant difference, with high-frequency prevalence at the boundary-layer location.

Effect of Single Particle High-Speed Impingement on the Electrochemical Step Characteristics of a Stainless-Steel Surface.

In the process of particle erosion and electrochemical corrosion interaction, the electrolyte flow state change, product film destruction, and matrix structure change caused by particle impact affect the electrochemical corrosion process. Such transient, complex physical and electrochemical changes are difficult to capture because of the short duration of action and the small collision area. The peak, step time, and recovery time in this transient step cycle can indirectly reflect the smoothness and reaction rate of the electrochemical reaction system, and thus characterize the resistance to scouring corrosion coupling damage of metals in liquid-solid two-phase flow. In this study, in order to obtain the electrochemical response at the moment of particle impact, electrochemical monitoring experiments using a specially designed miniature three-electrode system were used to test step-critical values, including step potential, current, and resistance, among others. Meanwhile, an electrochemical step model under particle impact considering boundary layer perturbation was developed. The experimental results reflect the effect law of particle impact velocity and particle size on the peak step and recovery period. Meanwhile, the effect of particle impingement on the electrochemical step of stainless steel in different electrolyte solutions was obtained by comparing the step curves in distilled water and Cl-containing water. The connection between the parameters in the electrochemical step model and in the particle impact, as well as the effect of the variation of these parameters on the surface repassivation process are discussed in this paper. By fitting and modeling the test curves, a new mathematical model of electrochemical step-decay under single-particle impact was obtained, which can be used to characterize the change pattern of electrochemical parameters on the metal surface before and after the impingement.

Control of linear instabilities in two-dimensional airfoil boundary layers

The present study deals with the control of linear, modal and non-modal growth of perturbations in a trapezoidal wing boundary layer. The asymmetric NACA 2515 airfoil is chosen for the analysis. The boundary layer velocity profiles, at different locations on the airfoil, are obtained using the Falkner–Skan equations. The non-modal linear stability theory is used to obtain the amplification of the initial perturbations, for which the state-space approach is adopted. The control is brought about using a Linear Quadratic Regulator (LQR) controller by the means of addition of fluid momentum in the wall-normal direction from the wing surface. Maximum transient energy growth is calculated across a range of wavenumber pairs, and control is applied to the pair with the highest energy growth. In this numerical analysis, we show that the transient growth is higher towards the trailing edge because of the adverse pressure gradient of the flow. Upon control actuation, the reduction in the transient energy growth of perturbations is achieved up to a maximum of 54.6%.

Impact of compliant coating on Mack-mode evolution in hypersonic boundary layers

This paper focuses on the linear evolution of Mack instability modes in a hypersonic boundary layer over a flat plate that is partially coated by a compliant section. The compliant section is a thin, flexible membrane covering on a porous wall consisting of micro holes. The instability pressure could induce a vibration of the membrane, leading to a feedback to the boundary-layer fluids through the transverse velocity fluctuation. Such a process is formulated by an admittance boundary condition for the boundary-layer perturbation, which is dependent on the thickness and tension of the membrane, the properties of the porous wall, and the frequency of the Mack-mode perturbation. Using this admittance condition, the impact of the compliant coating on the Mack growth rate is studied systematically by solving the compressible Orr–Sommerfeld equations. It is found that the compliant coating could suppress the Mack instability with a frequency band in the neighbourhood of the most unstable frequency, and the stabilising frequency band widens as the membrane thickness and tension decrease, indicating a more favourable effect of a softer membrane. For a Mack mode with a specified dimensional frequency – since its dimensionless frequency, normalised by the local boundary-layer thickness and oncoming velocity, increases as it propagates downstream – the second-mode frequency band usually appears in downstream locations, and so does the stabilising effect of the membrane. Thus it is favourable to apply a compliant panel at a downstream region. In this situation, the solid–compliant junction could produce an additional scattering effect on the evolution of the Mack mode due to the sudden change of its boundary condition. The scattering effect is quantified by a transmission coefficient defined by the equivalent amplitude of the compliant-wall perturbation to the solid-wall perturbation, which can be obtained by the harmonic linearised Navier–Stokes (HLNS) approach. If the admittance is weak, then the transmission coefficient can also be predicted by an analytical solution based on the residue theorem. It is found that most of the second modes are suppressed by the scattering effect as long as the argument of the admittance is in the interval $[150^\circ, 210^\circ ]$ , agreeing with most of the physical situation. The analytical predictions agree well with the HLNS calculations when the modulus of the admittance is less than $O(0.1)$ .

Asymptotic Multiscale Solutions to Navier–Stokes Equations with Fast Oscillating Perturbations in Boundary Layers

Asymptotic Multiscale Solutions to Navier–Stokes Equations with Fast Oscillating Perturbations in Boundary Layers

Evolution of localized boundary-layer perturbations under conditions of the laminar-turbulent transition (review)

Evolution of localized boundary-layer perturbations under conditions of the laminar-turbulent transition (review)

Entrainment and growth of vortical disturbances in the channel-entrance region

The entrainment of free-stream unsteady three-dimensional vortical disturbances in the entry region of a channel is studied via matched asymptotic expansions and by numerical means. The interest is in flows at Reynolds numbers where experimental studies have documented the occurrence of intense transient growth, despite the flow being stable according to classical stability analysis. The analytical description of the vortical perturbations at the channel mouth reveals how the oncoming disturbances penetrate into the wall-attached shear layers and amplify downstream. The effects of the channel confinement, the streamwise pressure gradient and the viscous/inviscid interplay between the oncoming disturbances and the boundary-layer perturbations are discussed. The composite perturbation velocity profiles are employed as initial conditions for the unsteady boundary-region perturbation equations. At a short distance from the channel mouth, the disturbance flow is mostly confined within the shear layers and assumes the form of streamwise-elongated streaks, while farther downstream the viscous disturbances permeate the whole channel although the base flow is still mostly inviscid in the core. Symmetrical disturbances exhibit a more significant growth than anti-symmetrical disturbances, the latter maintaining a nearly constant amplitude for several channel heights downstream before growing transiently, a unique feature not reported in open boundary layers. The disturbances are more intense as the frequency decreases or the bulk Reynolds number increases. We compute the spanwise wavelengths that cause the most intense downstream growth and the threshold wall-normal wavelengths below which the perturbations are damped through viscous dissipation.

A Physically Based Stochastic Boundary Layer Perturbation Scheme. Part II: Perturbation Growth within a Superensemble Framework

AbstractConvection-permitting forecasts have improved the forecasts of flooding from intense rainfall. However, probabilistic forecasts, generally based upon ensemble methods, are essential to quantify forecast uncertainty. This leads to a need to understand how different aspects of the model system affect forecast behavior. We compare the uncertainty due to initial and boundary condition (IBC) perturbations and boundary layer turbulence using a superensemble (SE) created to determine the influence of 12 IBC perturbations versus 12 stochastic boundary layer (SBL) perturbations constructed using a physically based SBL scheme. We consider two mesoscale extreme precipitation events. For each, we run a 144-member SE. The SEs are analyzed to consider the growth of differences between the simulations, and the spatial structure and scales of those differences. The SBL perturbations rapidly spin up, typically within 12 h of precipitation commencing. The SBL perturbations eventually produce spread that is not statistically different from the spread produced by the IBC perturbations, though in one case there is initially increased spread from the IBC perturbations. Spatially, the growth from IBC occurs on larger scales than that produced by the SBL perturbations (typically by an order of magnitude). However, analysis across multiple scales shows that the SBL scheme produces a random relocation of precipitation up to the scale at which the ensemble members agree with each other. This implies that statistical postprocessing can be used instead of running larger ensembles. Use of these statistical postprocessing techniques could lead to more reliable probabilistic forecasts of convective events and their associated hazards.

A Physically Based Stochastic Boundary Layer Perturbation Scheme. Part I: Formulation and Evaluation in a Convection-Permitting Model

AbstractWe present a simple, physically consistent stochastic boundary layer scheme implemented in the Met Office’s Unified Model. It is expressed as temporally correlated multiplicative Poisson noise with a distribution that depends on physical scales. The distribution can be highly skewed at convection-permitting scales (horizontal grid lengths around 1 km) when temporal correlation is far more important than spatial. The scheme is evaluated using small ensemble forecasts of two case studies of severe convective storms over the United Kingdom. Perturbations are temporally correlated over an eddy-turnover time scale, and may be similar in magnitude to or larger than the mean boundary layer forcing. However, their mean is zero and hence they, in practice, they have very little impact on the energetics of the forecast, so overall domain-averaged precipitation, for example, is essentially unchanged. Differences between ensemble members grow; after around 12 h they appear to be roughly saturated; this represents the time scale to achieve a balance between addition of new perturbations, perturbation growth, and dissipation, not just saturation of initial perturbations. The scheme takes into account the area chosen to average over, and results are insensitive to this area at least where this remains within an order of magnitude of the grid scale.

Hypersonic boundary layer receptivity on flat plate with blunt leading edge due to acoustic disturbance

In the process of hypersonic boundary layer transition, the leading edge receptivity due to free-stream acoustic disturbance provides unstable perturbations in boundary layer with initial amplitudes, which is one of hot issues in the study about transition mechanism. The receptivity of leading edge is influenced by many factors, involving geometry parameters, disturbance types, etc., among which the bluntness plays a key role for generating disturbances. In order to reveal the mechanism of bluntness influence on the boundary layer transition, investigations into the acoustic receptivity on flat plates with sharp and blunt leading edge are carried out. The flow conditions are as follows: Mach number 6, Reynolds number 1e7/m, adiabatic wall. By introducing two-dimensional plane fast and slow acoustic waves into the free-stream, the whole receptivity process of free-stream disturbances passing through shock wave into boundary layer is simulated with high-order accuracy DNS method. With sharp leading edge as a reference, the generation mechanism of the perturbations near blunt leading edge and its influence on the boundary layer downstream are analyzed. Some conclusions are obtained: for acoustic disturbances in hypersonic free-streams, the receptivity mechanism of blunt leading edge is different from that of sharp leading edge; both the fast and the slow mode can be produced respectively near the sharp leading edge by the fast and the slow acoustic wave, while only fast mode appears near the blunt leading edge; the receptivity of blunt leading edge due to the fast acoustic is stronger than that due to slow acoustic, and is also stronger than that of the sharp leading edge in a certain region of boundary layer downstream.

The structure of perturbations in boundary layer created by a pulsed electric arc in the transversal magnetic field

The paper presents results of experimental study of surface MHD arc actuator as vortex generator in boundary layer. The study was held at flow velocities 20 to 50 m/s. The pulsed arc discharge was organized in external magnetic field. The amplitude of current was varied in the range from 8A to 160A, while pulse duration was from 40 μs up to 380 μs. The flow velocity was measured by PIV method. It was found that the increase of pulse duration leads to increase circulation vortex. The destruction of induced vortex was observed at 40 mm downstream from spark gap.

Ionization and dissociation effects on boundary-layer stability

Abstract

Low frequency instability and oscillating boundary layer in hybrid rocket combustion

The resonance of thermal lags of solid fuel with heat transfer oscillations in a boundary layer flow is the primary cause of low-frequency instability initiation in hybrid rocket combustion. A detailed study of two cases was conducted experimentally to investigate how the boundary layer is disturbed and leads to low-frequency instability (LFI); combustion with swirl injection and combustion with the frequency jump. The fluctuating boundary layer was successfully captured by visualizing images and proper orthogonal decomposition analysis was performed. The results show that swirl injection with an appropriate intensity substantially reduces the amplitudes of high frequency p’, and no boundary layer perturbation is found in the spectral analysis of mode 2, and Rayleigh index amplifications disappear. While the frequency jump occurs, the coupling status between p’ and q’ became weakly positive and the driving force disturbing the upstream flow was not made. As a result, oscillatory heat transfer was difficult to occur. Therefore, the appearance of boundary layer perturbation is the necessary precondition for the initiation of the low-frequency instability. And the resonance with the thermal lag characteristic leads to the occurrence of LFI.

The Impact of Warm and Moist Airmass Perturbations on Arctic Mixed-Phase Stratocumulus

AbstractThe Arctic is known to be particularly sensitive to climate change. This Arctic amplification has partially been attributed to poleward atmospheric heat transport in the form of airmass intrusions. Locally, such airmass intrusions can introduce moisture and temperature perturbations. The effect of airmass perturbations on boundary layer and cloud changes and their impact on the surface radiative balance has received increased attention, especially over sea ice with regard to sea ice melt. Utilizing cloud-resolving model simulations, this study addresses the impact of airmass perturbations occurring at different altitudes on stratocumulus clouds for open-ocean conditions. It is shown that warm and moist airmass perturbations substantially affect the boundary layer and cloud properties, even for the relatively moist environmental conditions over the open ocean. The cloud response is driven by temperature inversion adjustments and strongly depends on the perturbation height. Boundary layer perturbations weaken and raise the inversion, which destabilizes the lower troposphere and involves a transition from stratocumulus to cumulus clouds. In contrast, perturbations occurring in the lower free troposphere lead to a lowering but strengthening of the temperature inversion, with no impact on cloud fraction. In simulations where free-tropospheric specific humidity is further increased, multilayer mixed-phase clouds form. Regarding energy balance changes, substantial surface longwave cooling arises out of the stratocumulus break-up simulated for boundary layer perturbations. Meanwhile, the net surface longwave warming increases resulting from thicker clouds for airmass perturbations occurring in the lower free troposphere.

Trace pollutant fluctuations observed in Calicut city, India, during the annular solar eclipse on 26 December 2019

Atmospheric boundary layer perturbations were monitored during an annular solar eclipse event on December 26, 2019 to understand its impact on the meteorological parameters (temperature, relative humidity, wind speed, and wind direction) and trace gas concentrations (O3, NO, NO2, NH3, CO, and HONO) at Calicut (11.24° N, 75.78° E), a tropical city along the coastal belt of Arabian Sea in the southwest coast of Indian Subcontinent. The solar eclipse started at 8:05 IST (5.5 h ahead of UTC), reached to a maximum coverage of 93.28% at 09:27 IST and ends at 11:07 IST. Eclipse day data were compared with the nearby days' records from this site. The rapid fall in the irradiance caused cooling of the surface air by ~0.7 °C and weakened the wind speed, whereas the relative humidity, as expected, was increased by 5.1%. A gradual decrease in the surface O3 along with the reduction in solar irradiance was observed during the eclipse, due to the decreased efficiency in the photochemical formation of ozone. There was a decrease in mixing ratios of NO2 during the eclipse period, which was a result of the fall in ozone concentrations. No significant variation was observed in HONO levels, whereas variations in concentrations of NO and NH3 have followed the night time chemistry. The NO3 radical mixing ratios were below the detection limit during the eclipse event.

Boundary layer collapses described by the two-dimensional intermediate long-wave equation

We study the nonlinear dynamics of localized perturbations of a confined generic boundary-layer shear flow in the framework of the essentially two-dimensional generalization of the intermediate long-wave (2d-ILW) equation. The 2d-ILW equation was originally derived to describe nonlinear evolution of boundary layer perturbations in a fluid confined between two parallel planes. The distance between the planes is characterized by a dimensionless parameter D. In the limits of large and small D, the 2d-ILW equation respectively tends to the 2d Benjamin-Ono and 2d Zakharov-Kuznetsov equations. We show that localized initial perturbations of any given shape collapse, i.e., blow up in a finite time and form a point singularity, if the Hamiltonian is negative, which occurs if the perturbation amplitude exceeds a certain threshold specific for each particular shape of the initial perturbation. For axisymmetric Gaussian and Lorentzian initial perturbations of amplitude a and width σ, we derive explicit nonlinear neutral stability curves that separate the domains of perturbation collapse and decay on the plane (a, σ) for various values of D. The amplitude threshold a increases as D and σ decrease and tends to infinity at D → 0. The 2d-ILW equation also admits steady axisymmetric solitary wave solutions whose Hamiltonian is always negative; they collapse for all D except D = 0. But the equation itself has not been proved for small D. Direct numerical simulations of the 2d-ILW equation with Gaussian and Lorentzian initial conditions show that initial perturbations with an amplitude exceeding the found threshold collapse in a self-similar manner, while perturbations with a below-threshold amplitude decay.

On the algebraic perturbations in atmospheric boundary layer

A simple model for the development of submesoscale perturbations in the atmospheric boundary layer (ABL) is proposed. The growth of perturbations is associated with the shear algebraic instability of the wind velocity profile in the atmospheric boundary layer (ABL). For the scales of optimal perturbations (streaks) in the lower part of the ABL, estimates of their sizes were obtained about 100-200 m vertically and 300-600 m horizontally. Similar scales are noted for experimental data on the structure of the wind field in the lower part of the ABL, obtained in 2017, 2018 in the summer at the Tsimlyansk Scientific Station at the acoustic sounding of the atmosphere by the Doppler three-component minisodar of high resolution.

Turbulent boundary layer perturbation by two wall-mounted cylindrical roughness elements arranged in tandem: Effects of spacing and height ratio

The perturbation of a turbulent boundary layer by two cylindrical roughness elements in close proximity was experimentally investigated in a water channel using planar particle image velocimetry. The two cylinders were arranged in tandem with center-to-center streamwise spacings of 2d, 4d, and 6d, where d is the diameter of the cylinders. The downstream cylinder had a fixed height 0.2δ, where δ is the incoming boundary layer thickness; the height of the upstream cylinder was varied to achieve upstream to downstream cylinder height ratios of 1, 0.75, and 0.5. The flow measurements were made at Reδ = 56 800 and included measurements over an isolated cylinder as a baseline case. The results highlight the effects of sheltering by an upstream cylinder on the wake of the downstream cylinder. Flow features in the wake, including the downwash, upwash, recirculation zone, velocity deficit, Reynolds shear stress, and turbulent kinetic energy (TKE), are dependent on the degree of sheltering, which is reliant on both the streamwise spacing and height ratio. Overall, sheltering results in a reduction in the downwash and size of the recirculation zone past the downstream cylinder. The magnitude and spatial distribution of the Reynolds shear stress and TKE varied significantly from those past the isolated cylinder. Depending on the streamwise spacing and height ratio, the presence of an upstream cylinder has the potential to enhance or reduce the Reynolds shear stress past the downstream cylinder. For example, the maximum Reynolds shear stress in the near wake was approximately doubled for a spacing of 2d and a height ratio of 0.5 and nearly halved for a spacing of 2d and a height ratio of 1 (relative to that past the isolated cylinder). The variations in these flow features across the 9 considered arrangements suggest changes to the wake and its vortical structures due to the presence of an upstream cylinder. The results highlight the potential of flow control through a pair of roughness elements in close proximity to achieve desired outcomes such as reduced or redistributed Reynolds shear stress and TKE, relative to the isolated cylinder.

Compressible unsteady Görtler vortices subject to free-stream vortical disturbances

The perturbations triggered by free-stream vortical disturbances in compressible boundary layers developing over concave walls are studied numerically and through asymptotic methods. We employ an asymptotic framework based on the limit of high Görtler number, the scaled parameter defining the centrifugal effects; we use an eigenvalue formulation where the free-stream forcing is neglected; and we solve the receptivity problem by integrating the compressible boundary-region equations complemented by appropriate initial and boundary conditions that synthesize the influence of the free-stream vortical flow. Near the leading edge, the boundary-layer perturbations develop as thermal Klebanoff modes and, when centrifugal effects become influential, these modes turn into thermal Görtler vortices, i.e. streamwise rolls characterized by intense velocity and temperature perturbations. The high-Görtler-number asymptotic analysis reveals the condition for which the Görtler vortices start to grow. The Mach number is destabilizing when the spanwise diffusion is negligible and stabilizing when the boundary-layer thickness is comparable with the spanwise wavelength of the vortices. When the Görtler number is large, the theoretical analysis also shows that the vortices move towards the wall as the Mach number increases. These results are confirmed by the receptivity analysis, which additionally clarifies that the temperature perturbations respond to this reversed behaviour further downstream than the velocity perturbations. A matched-asymptotic composite profile, found by combining the inviscid core solution and the near-wall viscous solution, agrees well with the receptivity profile sufficiently downstream and at high Görtler number. The Görtler vortices tend to move towards the boundary-layer core when the flow is more stable, i.e. as the frequency or the Mach number increase, or when the curvature decreases. As a consequence, a region of unperturbed flow is generated near the wall. We also find that the streamwise length scale of the boundary-layer perturbations is always smaller than the free-stream streamwise wavelength. During the initial development of the vortices, only the receptivity calculations are accurate. At streamwise locations where the free-stream disturbances have fully decayed, the growth rate and wavelength are computed with sufficient accuracy by the eigenvalue analysis, although the correct amplitude and evolution of the Görtler vortices can only be determined by the receptivity calculations. It is further proved that the eigenvalue predictions of the growth rate and wavenumber worsen as the Mach number increases as these quantities show a dependence on the wall-normal direction. We conclude by qualitatively comparing our results with the direct numerical simulations available in the literature.