Inhomogeneous Boundary Layer Research Articles

Experimental Study of the Wave Train Development in a Longitudinal Trace in the Fat Plate Boundary Layer at Mach 2.5

The paper discusses experimental results on the wave train development in a longitudinal trace in the flat plate boundary layer at Mach 2.5. An analysis of the spatiotemporal distributions and frequency-wave spectra of pulsations, as well as their wave characteristics in the linear and weakly nonlinear phase of the wave train development in a homogeneous and inhomogeneous boundary layer at a fixed power of the controlled disturbances source has been carried out. During the analysis of the results, no subharmonic resonance was observed. Expansion into the wave spectrum of a stationary inhomogeneity and experimental data on wave characteristics and disturbance spectra made it possible to propose options for wave interaction for oblique breakdown.

Improvement of the parabolized stability equation to predict the linear evolution of disturbances in three-dimensional boundary layers based on ray tracing theory

A new method to predict the linear evolution of disturbances in three-dimensional inhomogeneous boundary layers is proposed, named RTPSE, in which the line-marching parabolized stability equation (PSE) is improved by applying ray tracing (RT) theory. Results show that RTPSE can accurately predict the spanwise wave number and amplitude ratio for both stationary and traveling crossflow waves, while the traditional PSE could not.

Assessing State-of-the-Art Capabilities for Probing the Atmospheric Boundary Layer: The XPIA Field Campaign

Abstract To assess current capabilities for measuring flow within the atmospheric boundary layer, including within wind farms, the U.S. Department of Energy sponsored the eXperimental Planetary boundary layer Instrumentation Assessment (XPIA) campaign at the Boulder Atmospheric Observatory (BAO) in spring 2015. Herein, we summarize the XPIA field experiment, highlight novel measurement approaches, and quantify uncertainties associated with these measurement methods. Line-of-sight velocities measured by scanning lidars and radars exhibit close agreement with tower measurements, despite differences in measurement volumes. Virtual towers of wind measurements, from multiple lidars or radars, also agree well with tower and profiling lidar measurements. Estimates of winds over volumes from scanning lidars and radars are in close agreement, enabling the assessment of spatial variability. Strengths of the radar systems used here include high scan rates, large domain coverage, and availability during most precipitation events, but they struggle at times to provide data during periods with limited atmospheric scatterers. In contrast, for the deployment geometry tested here, the lidars have slower scan rates and less range but provide more data during nonprecipitating atmospheric conditions. Microwave radiometers provide temperature profiles with approximately the same uncertainty as radio acoustic sounding systems (RASS). Using a motion platform, we assess motion-compensation algorithms for lidars to be mounted on offshore platforms. Finally, we highlight cases for validation of mesoscale or large-eddy simulations, providing information on accessing the archived dataset. We conclude that modern remote sensing systems provide a generational improvement in observational capabilities, enabling the resolution of finescale processes critical to understanding inhomogeneous boundary layer flows.

Transverse, propagating velocity perturbations in solar coronal loops

As waves and oscillations carry both energy and information, they have enormous potential as a plasma heating mechanism and, through seismology, to provide estimates of local plasma properties which are hard to obtain from direct measurements. Being sufficiently near to allow high-resolution observations, the atmosphere of the Sun forms a natural plasma laboratory. Recent observations have revealed that an abundance of waves and oscillations is present in the solar atmosphere, leading to a renewed interest in wave heating mechanisms.This short review paper gives an overview of recently observed transverse, propagating velocity perturbations in coronal loops. These ubiquitous perturbations are observed to undergo strong damping as they propagate. Using 3D numerical simulations of footpoint-driven transverse waves propagating in a coronal plasma with a cylindrical density structure, in combination with analytical modelling, it is demonstrated that the observed velocity perturbations can be understood in terms of coupling of different wave modes in the inhomogeneous boundaries of the loops. Mode coupling in the inhomogeneous boundary layers of the loops leads to the coupling of the transversal (kink) mode to the azimuthal (Alfvén) mode, observed as the decay of the transverse kink oscillations. Both the numerical and analytical results show the spatial profile of the damped wave has a Gaussian shape to begin with, before switching to exponential decay at large heights. In addition, recent analysis of CoMP (Coronal Multi-channel Polarimeter) Doppler shift observations of large, off-limb, trans-equatorial loops shows that Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. This excess high-frequency FFT power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvénic) turbulence.

Model for charged dust expansion across a magnetic field

Plasma fluctuations arise in the boundary region between charged dust clouds and background plasmas. A self-consistent computational model is developed to study expansion of a charged dust cloud across a magnetic field, creation of the inhomogeneous boundary layer and associated processes. The charging of the dust particulates produces a boundary layer and associated ambipolar electric field. This ambipolar field provides a source for low frequency dust acoustic waves in unmagnetized plasmas. A background magnetic field if sufficiently strong, may impact the dust acoustic wave evolution and dust density structures due to E×B and diamagnetic current generation. The dust acoustic density fluctuation generation across a strong magnetic field (ωpe/Ωce≪1) may be suppressed as compared to an unmagnetized dusty plasma, which will be discussed. Fluctuations generated at longer timescales propagating along the dust boundary layer will also be investigated in the lower hybrid and dust lower hybrid frequency range. Applications to space and laboratory plasmas are discussed.

Spatially resolved skin friction velocity measurements using Irwin sensors: A calibration and accuracy analysis

This study investigates the accuracy of spatially resolved skin friction velocity uτ measurements using a large number of Irwin sensors (Irwin, 1981). A fast and simple procedure to calibrate the sensors against a two-component hot-film anemometer is introduced which leads to a universal calibration function that can then be used for all sensors. Insignificantly lower accuracies are obtained using the universal calibration function instead of individual calibration functions for each sensor. The overall accuracy of the skin friction velocity measurements averages about ±5% for uτ>0.13ms−1 and decreases strongly to ±20% at lower uτ. The main sources of errors are as follows: (i) deviations from flush mounting of the sensors with the wall surface, (ii) inhomogeneous boundary layers produced in wind tunnels, (iii) pressure transducer inaccuracies, (iv) Irwin sensor geometry variations and (v) Irwin sensor calibration errors. An excellent linear relationship between uτ measured with the Irwin sensors and the free stream velocity as well as the good agreement of Irwin sensor with independent hot-film measurements validate the reliability of the measurement setup. An exemplary measurement of the skin friction velocity distribution around a single wall-mounted rectangular block is presented, discussed and compared to literature and can serve as a test case for simulations.

High-frequency electrostatic lower-hybrid (LH) waves in magnetic flux tubes

We study lower-hybrid (LH) instabilities and waves supported by magnetic flux tubes over supergranule in the high-frequency electrostatic mode (ω≳Ωi, where ω and Ωi are the wave frequency and ion cyclotron frequency, respectively). A slab model is used in the derivation of dispersion relations in the inhomogeneous boundary layer of current-circulating regions, where both density and temperature gradients exist. In the model, the electrons are treated as magnetized fluid, whereas the ions are described by means of the collision-free Boltzmann–Vlasov kinetic theory. It is shown that LH waves propagate in the boundary layer at the bottom end of the flux tube. The maximum growth rate is ∼\\!0.6ωLH (where ωLH is the LH frequency) in the absence of the temperature gradient. If ions are cold, the LH instability gives rise to propagating waves when the electric field produced by the thermoelectric effect is in the same direction as that of the density gradient, and the temperature gradient does not influence the instabilities very much; otherwise, the temperature gradient can produce propagating waves even when the electric field is in the opposite direction from the density gradient. The present work provides a clue to a mechanism to explain non-thermal ion accelerations via a LH-soliton heating process.

Resonant surface waves and instabilities in finite β plasmas

Magnetohydrodynamic surface waves are studied at an interface of finite thickness separating two homogeneous arbitrary finite β plasmas which are in parallel motion with respect to each other and are permeated by parallel magnetic fields. It is assumed that the density decreases and the magnetic field strength increases across the interface. The model is representative of the mantle-like boundary layer separating the fast flowing magnetosheath from the tail region of the magnetosphere. All existing wave modes are classified, their main properties are investigated, and analytical expressions for critical velocities are obtained. The resonant flow instability (RFI) and Kelvin–Helmholtz instability are studied when the finite thickness of the inhomogeneous boundary layer is taken into account. The theory of negative energy waves is applied to predict the behavior and interactions of the surface modes in such plasmas. Growth rates of RFIs are examined under various conditions. The dependence of critical velocities on the density ratio is studied under the assumption of a nonuniform magnetic field resulting in different plasma β on both sides of the inhomogeneous layer. Possible observational signatures of the RFI are also discussed.

Application of a Perturbation Recycling Method in the Large-Eddy Simulation of a Mesoscale Convective Internal Boundary Layer

An arrangement of boundary conditions is described and demonstrated that facilitates the large-eddy simulation (LES) of inhomogeneous boundary layers such as internal boundary layers. In addition to the domain where the internal boundary layer develops, the method requires a section of domain over the upwind surface that is of the order of 10 boundary layer thicknesses and thus similar in size to that needed for the LES of the upwind boundary layer. In addition to periodic lateral, closed upstream, and open downstream boundary conditions, a simple and efficient perturbation recycling technique, which follows from one of Lund, Wu, and Squires, is used to generate a steady supply of fully developed turbulence from the inflow boundary. The arrangement is used to simulate a convective internal boundary layer during a cold-air outbreak over water. Results show the method consistently produces a solution that is homogeneous over the upwind surface and inhomogeneous over the downwind surface, and that the statistics are stationary after spinup. The sensitivity to the placement of the outflow boundary is tested, and examples of instantaneous and mean fields generated by the simulations are shown.

The influence of resonant MHD wave coupling in the boundary layer on the reflection and transmission process

When a wave is incident on an inhomogeneous boundary layer separating two plasmas in relative motion, it is often argued that the resonant absorption rate can become when there is a sufficiently large velocity shear, thus giving back to the wave. However such treatment fails to distinguish the two exchange processes that are operative: extraction of wave by dissipative processes around the resonance point and exchange between the wave and the flow of the medium. By aid of the proper wave definitions recently discussed by Walker ([CITE]), rather than by the conventional concept of negative energy waves we reveal the important dependence of the resonant amplification process on the precise structure of the boundary layer profiles. We conclude that stratification in boundary layers is very important not only because the resulting wave coupling can cause resonant instabilities for velocity shears below the Kelvin-Helmholtz threshold, but also because the coupling can stabilize the Kelvin-Helmholtz instability above this threshold.

A critique of one- and two-dimensional models of boundary layer clouds with a binned representations of drop microphysics

A variety of models of boundary layer turbulence are increasingly being coupled to binned representation of cloud-drop spectra for the purpose of studying cloudy boundary layers and aerosol-cloud-drop interactions. A critique of one dimensional models shows that extant methods of coupling bin-microphysical models to the turbulence model omit important terms involving covariances of perturbation quantities. Errors incurred from the omission of these terms are significant: cloud-drop activation is not properly represented, and the initial stages of precipitation growth may be retarded in horizontally inhomogeneous boundary layers. If the promise of one-dimensional models is ever to be realized, some means of accurately representing these terms must be developed. Because large-scale models often have grid-spacings much larger than typical cloud-eddy-scale circulations, attempts to couple them to more detailed microphysical representations will also suffer from the problems discussed in the context of one-dimensional models. This should provide added motivation for improving the representation of microphysical processes on the sub-grid scale. An analysis of two-dimensional eddy-resolving models closed on the basis of energy inertial range arguments illustrates that the lack of an energy cascade in two dimensions results in increasingly vigorous circulations as the model's grid-mesh is refined. Two-dimensional model simulations can display significant variability to vanishingly small differences in the initial conditions, and drizzle rates vary by as much as 30% when total water concentrations are increased by only 1%. Such sensitivities make it difficult to constrain the models given the degree of uncertainty that characterizes measurements of state variables in clouds. Despite some inconsistencies in the formulation of their closure terms, two-dimensional models are at least able to qualitatively represent the interaction of the large-eddies and microphysical processes in boundary layer flows. For this reason they appear to be useful, not as surrogates for reality, but rather as a means for further refining hypotheses about the physical system thereby increasing the chances that such hypotheses can be tested observationally.

Local similarity relationships in a horizontally inhomogeneous boundary layer

Local similarity theory, an analogy to the Monin-Obukhov similarity theory, is successfully applied to airborne observations in a coastal area of South Australia. The boundary layer over this highly non-uniform surface is characterized by extensive variations in its thermal stratification and turbulence characteristics. However, the behaviour of some statistical parameters of second- and higher moments seems to be determined mainly by local forcing, while horizontal advection plays a less important role. For these parameters, local scaling is effective. It is shown that the dimensionless variances of vertical velocity and potential temperature are functions of z/λ only, where λ is the local Monin-Obukhov length and z is the height above ground. The dimensionless variance of horizontal velocity components is found to depend on h/λ, where h is the height of the oundary layer. Similarity relationships for some triple correlations are also discussed. The empirically determined local similarity relationships are found to agree with those obtained from surface-layer similarity. Finally, to illustrate the complexity of the local forcing, distributions of vertical energy and momentum fluxes, from which the local scaling parameters are derived, are shown.

A numerical simulation of particle deposition in turbulent boundary layers

A Lagrangian random-walk approach to modeling particle deposition in turbulent duct flows is presented. The inhomogeneous boundary layer turbulence is simulated by a discrete eddy field, characterized by a random normal velocity (drawn from a Gaussian probability distribution) and a random time scale (drawn from an exponential probability distribution). A mean streamwise velocity profile is superposed upon the turbulence field using the law-of-the-wall relations. The turbulent r.m.s. velocity and time scale profiles are obtained from experimental data. The particle equations of motion include Stokes' drag and shear-induced (Saffman) lift. The equations are numerically solved for particle relaxation times ( τ + ) ranging from 0.3 to 1000 and particle-fluid density ratios of 500—5000. Approximately 500—10,000 particle trajectories are computed for each case, simulating particle deposition in pipe flow with a sticky wall. Deposition velocity predictions compare favorably with measurements, showing that inertial impaction is dominant at lower values. A predicted decrease in deposition velocity occurs for large particle. ( τ − > 30 ) due to reduction in particle fluctuating velocity. Shear-induced lift increases particle deposition rate, most significantly for 1 < τ + < 10 . Particle concentration profiles reveal that smaller particles (τ + < 10) tend to accumulate in the near-wall region due to the sudden damping of fluid turbulence. Predicted particle r.m.s. velocity profiles compare favorably with measurements, showing a decrease in magnitude with increasing inertia.

A climatological model of dispersion in an inhomogeneous boundary layer

A non-Gaussian long term model (KAPPAG-LT) for atmospheric dispersion simulations is presented. The model is based on a two-dimensional analytic solution of the advection-diffusion equation for a shear flow. The vertical inhomogeneity of the atmospheric boundary layer is accounted for by power laws for wind velocity and eddy diffusivity profiles. The performance of the KAPPAG-LT model in estimating annual ground level mean concentrations is compared to that of the EPA Regulatory model ISCLT for the cases of an elevated point source and an area source. A preliminary evaluation against SO 2 data from a heavily industrialized area is presented.

The Boundary-Layer Growth Equation with Reynolds Averaging

Abstract A local interfacial boundary condition between a turbulent and non-turbulent layer is constructed in a manner that allows local entrainment. The Reynolds average of this equation produces a mean boundary-layer growth rate that contains additional terms not heretofore included in boundary-layer growth models. One of these terms represents the net effect of fluctuating horizontal entrainment and can be absorbed into the usual net entrainment term. The other two terms may become important in horizontally inhomogeneous boundary layers: one represents mean horizontal entrainment across an interface which slopes in the mean, and the other is a divergence of a small-scale horizontal flux of boundary-layer height which presumably acts to smooth variations in the mean boundary-layer height.

Hydrodynamic theory of surface-wave fluctuations in inhomogeneous plasma

This paper investigates the fluctuation spectrum of the surface waves in a semi-infinite plasma, and in a plasma cylinder, with an inhomogeneous boundary layer. It is shown that the correlations of the surface waves are dependent on temperature and density distributions in the boundary layer. The correlation function is determined by temperature values in the points of transition layer, where the longitudinal dielectric permeability becomes equal to zero. Dependence of the obtained correlation function on co-ordinates, in the electrostatic limit, is characterized by the complex correlation length, which is fully determined by the inhomogenity of the plasma density near the boundary.

Similarity theory and resistance laws for the planetary boundary layer

Methods are developed for the determination of parameters of the atmospheric planetary boundary layer, within the framework of similarity theory based on the external parameters — wind velocity at the upper boundary of the layer, its thickness, air temperature difference between the upper and the lower boundaries, roughness of the underlying surface, and buoyancy forces. The form of the resistance laws is discussed. Determination of the thickness of the stationary and horizontally homogeneous (Ekman) boundary layer is analyzed and generalizations of the latter are suggested for non-stationary and inhomogeneous boundary layers.

Transport and free carrier electromagnetic phenomena in semiconductor boundary layers

Standard semiconductor surface transport theory is rewritten in a classical Green function formulation physically equivalent to the path variable method. This makes it possible to account for surface boundary conditions, while improving upon the relaxation time solution of the Boltzmann equation itself. The extension to ac fields is trivial. The complex conductivity is written (in the relaxation time approximation) as a function of frequency, position in the inhomogeneous boundary layer, surface potential, polish parameter and external magnetic field. The way to study long wave electromagnetic properties of carriers in boundary layers is indicated and illustrated with applications to the theory of reflectivity as affected by boundary layers.