Turbulent Boundary Layer Research Articles

The roles of geometry and viscosity in the mobilization of coarse sediment by finer sediment

In rivers, the addition of finer sediment to a coarser riverbed is known to increase the mobility of the coarser fraction. Two mechanisms have been suggested for this: a geometric mechanism whereby smaller sizes smooth the bed, increasing near-bed velocity and thus mobility of the larger sizes, and a viscous mechanism whereby a transitionally smooth turbulent boundary layer forms, rendering the coarser grains more mobile. Here, we report on experiments using two sediment mixtures to better understand these proposed mechanisms. In Mixture 1, we used 0.5 and 5 mm grains, and in Mixture 2, we used 2 and 20 mm grains. If the entrainment of coarse gravel by finer sediment is a purely geometric effect, then the addition of finer material should produce the same effect on the mobility of the coarser material for both mixtures because they have the same size ratio. We show that addition of finer material has a different effect on the two mixtures. We observed an increase in the mobility of the coarse fraction for both mixtures, but the increase in coarse fraction mobility for Mixture 1 was almost twice that for Mixture 2. Our experiments show that in addition to the geometric effect, enhancement of coarse gravel transport by finer sediment is also driven by a viscous effect.

Potential of Wake Scaling Techniques for Vertical-Axis Wind Turbine Wake Prediction

Analytical wake models are widely used to predict wind turbine wakes. While these models are well-established for horizontal-axis wind turbines (HAWTs), the analytical wake models for vertical-axis wind turbines (VAWTs) remain under-explored in the wind energy community. In this study, the accuracy of two wake scaling techniques is evaluated to predict the change in the normalized maximum wake velocity deficit behind VAWTs by re-scaling the maximum wake velocity deficit behind an actuator disk with the same thrust coefficient. The wake scaling is defined in terms of equivalent diameter, considering the geometrical properties of the wake-generating object. Two different equivalent diameters are compared, namely the momentum diameter and hydraulic diameter. Different approaches are used to calculate the change in the normalized wake velocity deficit behind a disk with the same thrust coefficient as the VAWT. The streamwise distance is scaled with the equivalent diameter to predict the normalized maximum wake velocity deficit behind the desired VAWT. The performance of the proposed framework is assessed using large-eddy simulation data of VAWTs operating in a turbulent boundary layer with varying operating conditions and aspect ratios. For all of the cases, the momentum diameter scaling provides reasonable predictions of the VAWT normalized maximum wake velocity deficit.

Biological and dust aerosols as sources of ice-nucleating particles in the eastern Mediterranean: source apportionment, atmospheric processing and parameterization

Abstract. Aerosol–cloud interactions in mixed-phase clouds (MPCs) are one of the most uncertain drivers of the hydrological cycle and climate change. A synergy of in situ, remote-sensing and modelling experiments were used to determine the source of ice-nucleating particles (INPs) for MPCs at Mount Helmos in the eastern Mediterranean. The influences of boundary layer turbulence, vertical aerosol distributions and meteorological conditions were also examined. When the observation site is in the free troposphere (FT), approximately 1 in ×106 aerosol particles serve as INPs around −25 °C. The INP abundance spans 3 orders of magnitude and increases in the following order: marine aerosols; continental aerosols; and, finally, dust plumes. Biological particles are important INPs observed in continental and marine aerosols, whereas they play a secondary, although important, role during Saharan dust events. Air masses in the planetary boundary layer (PBL) show both enriched INP concentrations and a higher proportion of INPs to total aerosol particles, compared with cases in the FT. The presence of precipitation/clouds enriches INPs in the FT but decreases INPs in the PBL. Additionally, new INP parameterizations are developed that incorporate the ratio of fluorescent-to-nonfluorescent or coarse-to-fine particles and predict >90 % of the observed INPs within an uncertainty range of a factor of 10; these new parameterizations exhibit better performance than current widely used parameterizations and allow ice formation in models to respond to variations in dust and biological particles. The improved parameterizations can help MPC formation simulations in regions with various INP sources or different regions with prevailing INP sources.

Rapid Downwelling of Tracer Particles Across the Boundary Layer and Into the Pycnocline at Submesoscale Ocean Fronts

AbstractA neutrally buoyant float deployed in an atmospherically driven turbulent ocean boundary layer on the dense side of a submesoscale front was repeatedly carried across the boundary layer by the turbulence and then trapped beneath the slumping front. Lagrangian particles in a large‐eddy simulation of a similar baroclinically unstable front forced by surface cooling move along convergent surface filaments toward filament junctions. They are also caught by convective plumes that downwell them at speeds similar to those of the float. Subsequently, some are trapped in the pycnocline by frontal slumping due to ageostrophic secondary frontal circulations. In both observations and simulations, boundary layer turbulence and frontal circulations work together to trap and subduct particles from the mixed layer. The small‐scale boundary layer motions move them vertically within the boundary layer and larger, submesoscale frontal circulations move them laterally out of the boundary layer and under the slumping fronts.

A theoretical study of a radiofrequency wave propagation through a realistic turbulent marine atmospheric boundary layer based on large eddy simulation

This study aims at modeling and investigating the impact of realistic turbulence inhomogeneity on radiowave propagation by utilizing large eddy simulations (LES). An up-to-date version of the X-LES method for generating realistic turbulent phase screens is first introduced. It combines atmospheric simulations with the classical Tatarski statistical modeling. This method naturally incorporates vertical turbulence inhomogeneity into phase screens at scales resolved by LES. It is then extended to sub-grid scales by weighting statistically generated phase variations with the vertical profile of the turbulent structure constant extracted from atmospheric data. This method is applied to replicate turbulence of a classical tropical marine atmospheric boundary layer. The impact of the generated medium on the propagation of a 10 GHz spherical wave emanating from a Gaussian aperture is analyzed through a statistical study of log-amplitude profiles performed for three different source altitudes. Results first show that contrary to a classical homogeneous turbulence modeling, log-amplitude profiles resulting from the propagation into inhomogeneous turbulence exhibit a statistical heterogeneity strongly dependent of source altitude. Furthermore, classical stochastic phase screen generation from a homogeneous Von-Kàrmàn Kolmogorov spectrum seems to give a statistically significant underestimation of the actual impact of turbulence compared to the X-LES method.

Effects of Mach number on space-time characteristics of wall pressure fluctuations beneath turbulent boundary layers

Wall pressure fluctuations beneath turbulent boundary layers are a fundamental source of aerodynamic noise by exciting the wall structure, with their space-time characteristics serving as the basic ingredient for predicting the wall structural response. To this end, direct numerical simulations of fully developed compressible turbulent boundary layers at Mach numbers of 0.5, 1.2, and 2.0 are conducted to investigate wall pressure fluctuations comprehensively. The effects of Mach number on the single-point statistics of wall pressure fluctuations, such as the root mean square, skewness and flatness factors, probability density function, and frequency spectrum, are assessed to be very weak. Regarding the space-time characteristics, the convection velocity Uc determined by the space-time correlation of wall pressure fluctuations increases slightly with the Mach number, which only reflects the convective behavior of turbulent vortices. On the wavenumber–frequency spectrum, characteristic peaks of both the acoustic wave and convective vortices are identified. At Mach 0.5, the peaks of the fast (Uc+c) and slow (Uc−c) acoustic waves are unattached to others with c denoting acoustic speed, while only the peak of the fast acoustic wave is distinguishable from the convective peak at Mach 1.2 and 2.0. Due to the aerodynamic heating at supersonic conditions, the thermal effect on acoustic speed should be taken into account in determining the acoustic wavenumber. By introducing a convective Prandtl–Glauert parameter, a refined relation is proposed to provide a more accurate depiction of the acoustic domain in the wavenumber–frequency spectrum.

Study on secondary motions in supersonic boundary layers of a bent pipe

The present study employed direct numerical simulation to investigate the supersonic flow of Mach 3 in a bent pipe with a curvature of 0.0825, elucidating the dynamic mechanism of secondary motions within the turbulent boundary layer. The findings indicate that the compressible flow, affected by the wall curvature, is differentiated into several motion patterns as the bending angle increases: a portion of the outer fluid close to the wall, driven by the circumferential pressure gradient, moves inward through the lateral wall, causing an increase in the mass rate toward the lateral boundary layer and promoting the circumferential transport of energy and vorticity; other outer fluids at the start of the bent section, due to the centrifugal force, approach the wall to form a thinner boundary layer downstream; meanwhile, the fluid near the inner wall experiences the expansion, followed by the flow separation and reattachment at a bending angle of 14.6° and 22.0°, respectively, which induce a shear layer that develops from the inner end point toward the mainstream center, gradually reshaping the high-speed flow area within the pipe cross section into a U-shape, and enhancing the vorticity and temperature field of the inner region. Additionally, this study reveals a remarkable phenomenon that the separated flow in a localized inner region forms a rotating field, inducing vortices distinct from the mainstream Dean vortices in the low-speed flow region enclosed by the shear layer.

Evolution of Turbulent Boundary Conditions on the Surface of Large Barchan Dunes: Anomalies in Aerodynamic Roughness and Shear Velocity, Aeolian Threshold, and the Role of Dune Skewness

AbstractWe recorded aerodynamic roughness and shear velocity along transects on and around mature crescent‐shaped barchan dunes of and height above the horizontal rock‐covered Qatar desert by fitting to the log‐law time‐averaged vertical velocity profiles acquired from triads of ultrasonic anemometers penetrating the inner turbulent boundary layer. Shear velocity first decreased, then recovered as air climbed on the dune, with a local maximum ahead of the crest as predicted by the Jackson and Hunt (1975, https://doi.org/10.1002/qj.49710143015) theory. Unlike flows over gentler bedforms without a slope discontinuity, an anomalous peak of shear velocity also arose on the dune centerline at the brink, which the theory attributed to skewness in the dune transect profile. The onset of aeolian transport produced a log‐law passing through the Bagnold (1941, https://doi.org/10.1007/978‐94‐009‐5682‐7) focal point. It was bracketed by noticeable hysteretic peaks in the correlation between wind speed and entrained sand flux. The dunes' rocky surroundings and topography produced an aerodynamic roughness at odds with the Nikuradse (1933, https://ntrs.nasa.gov/citations/19930093938) data for fully developed turbulent boundary layers. Large‐eddy numerical simulations illustrated the sensitivity of shear velocity to wide changes in aerodynamic roughness from desert floor to dune surface.

An improved immersed boundary method for turbulent flow simulations on Cartesian grids: extension of a global geometric approach for thin boundary layers and strong flow incidence

This paper presents further improvements to the immersed boundary method introduced in [1]. The proposed developments take place during the pre- and post-processing stages of the simulation workflow and aim to further increase the accuracy of the approach for steady-state simulations of high Reynolds number turbulent flows around aerodynamic geometries facing strong incidence. To this end, the location of the forcing points is further optimized prior to simulation, with an adaptive and local modeling height that accounts for the evolution of the turbulent boundary layer thickness, especially at the leading edge. In addition, the direct extrapolation of the pressure solution at the wall is replaced by first- and second-order reconstructions using the normal pressure gradients interpolated at a new set of image points. This second approach is used only in post-processing, after the simulation, and prevents the degradation of the wall pressure in the presence of strong curvatures or thin boundary layers. These developments have been validated by simulating subsonic turbulent flows around the NACA0012 profile, 2D multi-element airfoil (2DMEA), and HL-CRM half-plane at significant angles of attack. Smooth and accurate skin pressure and friction coefficients are observed, in excellent agreement with body fitted wall-resolved solutions, even for coarser Cartesian meshes. Better drag and lift coefficients calculated by direct near-field integrations are obtained, along with accurate predictions of the near-wall flow physics throughout the turbulent boundary layer.

The Wave-Coherent Stress and Turbulent Structure over Swell Waves

Abstract The generation of ocean surface waves by wind has been studied for a century, giving rise to wave forecasting and other crucial applications. However, the reacting force of swell waves on the turbulence in the marine atmospheric boundary layer (ABL) remains unknown partly due to the unclear magnitude and profile of wave-coherent (WC) stress. In this study, the intersection frequency between the energy-containing range and inertial subrange range in the turbulent spectra is identified based on the attached eddy model (AEM), as the intersection modulated by swell wave could help to comprehend the physical process between the ocean surface wave and the marine ABL. Using observations from a fixed platform located in the South China Sea, this study shows that the intersection when the WC stress accounts for a lower proportion of the total wind stress (<10%) follows U/(2πz) given by AEM, where U is the wind speed and z is the height. While the intersection depends on the drag coefficient of WC stress for the case, WC stress accounts for a large part of the total wind stress (>10%). Considering the unclear magnitude and profile of WC stress, this study derives a new function to depict the WC stress. Significance Statement Turbulence located in the energy-containing range of the spectra is the primary source of momentum, heat, and water vapor fluxes between the ocean and marine atmospheric boundary layer (ABL). Thus, a better understanding of the turbulent structure within the wave boundary layer can help us accurately parameterize those fluxes. In addition to absorbing energy from the marine ABL, waves, especially swell waves, influence the turbulent structure. However, until now, the turbulent structure is unclear due to the unclear wave-coherent stress size and profile. In this study, a function that can depict the wave-coherent stress is proposed. We found that the wave-coherent stress can modulate the intersection between the energy-containing range and the inertial subrange range in the turbulent spectra.

Surface Currents and Relative-Wind Stress in Coupled Ocean–Atmosphere Simulations of the Northern California Current System

Abstract The dependence of surface-current damping on the definition of surface current for the relative wind is examined in coupled ocean–atmosphere numerical simulations of the northern California Current System (nCCS) during March–October 2009. The model response is analyzed for wind stress computed from relative wind for six different choices of effective model surface velocity. Simulations without surface-current coupling are also considered. As a function of the geographically varying uppermost grid-level depth, the model uppermost grid-level velocity is found to have a wind-drift component with a log-layer structure. Mean geostrophic wind work is concentrated in the shelf and slope regions during March–May (MAM) and in the deep offshore region in June–September (JJAS). The surface-current damping effect on ocean kinetic energy depends more strongly on the parameterization of atmospheric planetary boundary layer (PBL) turbulence than on the surface-current coupling formulation: weaker PBL mixing gives stronger surface-current damping. The damping effect is stronger in the less energetic offshore region than in the more energetic region closer to the coast. During MAM, the changes in kinetic energy and geostrophic wind work in the shelf and slope regions are spatially correlated, while during JJAS, the changes in geostrophic wind work are strongly modulated by SST–stress coupling. The wind-drift-corrected surface-current formulations result in large changes in the effective wind work based on the product of stress and relative-wind surface current but result in only small changes in the kinetic energy of the circulation. Significance Statement Ocean currents and atmospheric winds are coupled by the exchange of momentum across the air–sea interface, the strength of which depends on the relative wind, the difference between the surface wind and surface current. The purpose of this work was to examine the dependence of a coupled ocean–atmosphere model of the northern California Current System (nCCS) on the representations of the relative-wind surface current and turbulent mixing in the lower atmosphere. The model surface current was found to have a shallow wind-drift response. The model ocean circulation was driven primarily by near-coast winds during the spring and by offshore winds during the summer. The ocean response depended more strongly on the atmospheric turbulent mixing than on the surface current representation.

Hypersonic Stability and Breakdown Measurements on the AFRL/AFOSR BOLT II Flight Geometry

The Air Force Research Laboratory/Air Force Office of Scientific Research (AFRL/AFOSR) introduced the Boundary Layer Turbulence (BOLT II) flight experiment to further the understanding and modeling of a hypersonic turbulent boundary layer on a geometry that features concave surfaces with swept leading edges. In support of the flight experiment, this paper identifies and documents the transition instabilities and quantifies the breakdown to turbulence on a 25%-scale BOLT II model in hypersonic flow. Experiments were conducted in the conventional Actively Controlled Expansion wind tunnel facility and the Mach 6 Quiet Tunnel located at the Texas A&M University National Aerothermochemistry and Hypersonics Laboratory. Global surface heating was viewed using infrared thermography with on-surface measurements made using high-frequency Kulite and PCB Piezotronics surface pressure transducers. Modal growth was observed among the sensors both upstream and downstream of the model. Off-surface measurements were made in the mixed-mode region utilizing constant-temperature hot-film anemometry in the Mach 6 Quiet Tunnel. Comparisons were made to the Direct Numerical Simulation (DNS) results from the University of Minnesota. Amplified content was observed between f=53 and 75 kHz in the root-mean-square voltage fluctuations of the hot-film measurements.

Improved Wall Function Method for Hypersonic Reacting Turbulent Boundary Layers

The chemical reaction and cold wall effects in hypersonic reacting turbulent boundary layers (HRTBLs) cause the failure of the existing wall function method. Therefore, this paper proposes an improved wall function method to simulate skin friction cf and wall heat flux qw in HRTBLs accurately and efficiently. Firstly, the temperature–velocity relation is extended to a generalized enthalpy–velocity relation to comprehensively involve the chemical reaction and cold wall effects. Then, a new unified velocity law of the wall for the inner layer of HRTBLs is theoretically derived. Finally, an improved wall function method is designed with the new laws of the wall. Numerical experiments of typical HRTBLs show that, compared with the existing wall function method, the improved wall function method can significantly reduce the errors of cf and qw from 8.0% and 10.2% to 0.4% and 0.5%, respectively, when the near-wall grids are relaxed to the viscous sublayer, while from 11.0% and 15.3% to 1.2% and 5.8%, respectively, when the near-wall grids are further relaxed to the logarithmic layer, bringing 2.7 and 15 times enhancement of the simulation efficiency. Moreover, by introducing the reference point, the improved wall function method removes the boundary layer edge quantities while ensuring accurate results.

Publisher's Note: “Scaling of self-similar turbulent boundary layers under adverse pressure gradient” [Phys. Fluids 36, 085204 (2024)]

Publisher's Note: “Scaling of self-similar turbulent boundary layers under adverse pressure gradient” [Phys. Fluids <b>36</b>, 085204 (2024)]

Direct numerical simulation of skin friction drag reduction on supersonic turbulent boundary layers with micro-blowing

The flow control mechanism and skin friction drag reduction characteristics of micro-blowing on a Ma2.25 supersonic turbulent boundary layers are investigated through direct numerical simulations, and the effects of blowing intensity and micro-hole arrangement on turbulent structure and skin friction drag in the local control region and downstream region are considered. The results show that the skin friction drag decreases remarkably in the control region under the influence of micro-blowing, and a certain drag reduction can still be maintained in the downstream region. The drag reduction performance in the control region is jointly determined by blowing intensity and micro-hole arrangement. The drag reduction performance of the staggered arrangement is 5.7% and 11.1% higher than that of the inline arrangement at blowing intensities of 0.2% and 0.5%, respectively. However, it is found that the drag reduction in the downstream region is only determined by the blowing intensity and almost independent of the micro-hole arrangement. The effect of micro-blowing on turbulent structures is quantitatively characterized by energy spectrum analysis, and it shows that the streamwise scales of the near-wall streaks are significantly reduced under the influence of micro-blowing. In addition, the compressibility of fluids and the local reverse transfer in the strong expansion region are significantly improved under the influence of micro-blowing. These effects should be considered when performing Large Eddy Simulation modeling of supersonic turbulent boundary layers with micro-blowing.

Effect of three-dimensionality of turbulence on the along-wind loads of square cross-sectional structures

The existing theories for along-wind loads on slender structures, based on the “strip assumption” overlook the three-dimensionality of turbulence. However, numerous experimental phenomena contradicting the “strip assumption” highlight the need to consider the effects of three-dimensional turbulence (3D effect). This study develops an analysis model that considers the three-dimensionality of turbulence and derives a function containing the section-shape-dependent characteristic parameters to represent the 3D effect. A method for identifying the parameters through a wind tunnel test is proposed to solve this function. The parameters for the square cross section are then identified in two different turbulence fields, revealing that the identification parameters of both cases are nearly identical. This similarity indicates that the parameters are independent of the turbulence validating the proposed theories. Finally, the 3D effect on square cross-sectional structures with different aspect ratios under various turbulence integral scales is analyzed. The results showed that as the ratio of the turbulence integral scale to the windward width of the structures increases, the 3D effect reduces, but the rate of reduction slows down. In addition, increasing the aspect ratios of structures further mitigates the 3D effect, enhancing the accuracy of the “strip assumption.” These results can be a reference for evaluating the accuracy of the “strip assumption” theory for square cross-sectional high-rise buildings in atmospheric boundary layer turbulence. The proposed method can be applied to investigate the 3D effect on along-wind loads of slender structures with various cross-sectional shapes.

The K‐Profile Parameterization Augmented by Deep Neural Networks (KPP_DNN) in the General Ocean Turbulence Model (GOTM)

AbstractThis study utilizes Deep Neural Networks (DNN) to improve the K‐Profile Parameterization (KPP) for the vertical mixing effects in the ocean's surface boundary layer turbulence. The deep neural networks were trained using 11‐year turbulence‐resolving solutions, obtained by running a large eddy simulation model for Ocean Station Papa, to predict the turbulence velocity scale coefficient and unresolved shear coefficient in the KPP. The DNN‐augmented KPP schemes (KPP_DNN) have been implemented in the General Ocean Turbulence Model (GOTM). The KPP_DNN is stable for long‐term integration and more efficient than existing variants of KPP schemes with wave effects. Three different KPP_DNN schemes, each differing in their input and output variables, have been developed and trained. The performance of models utilizing the KPP_DNN schemes is compared to those employing traditional deterministic first‐order and second‐moment closure turbulent mixing parameterizations. Solution comparisons indicate that the simulated mixed layer becomes cooler and deeper when wave effects are included in parameterizations, aligning closer with observations. In the KPP framework, the velocity scale of unresolved shear, which is used to calculate ocean surface boundary layer depth, has a greater impact on the simulated mixed layer than the magnitude of diffusivity does. In the KPP_DNN, unresolved shear depends not only on wave forcing, but also on the mixed layer depth and buoyancy forcing.

Precursor boundary layer conditions for shallow and deep convection: inferences from CAIPEEX field measurements over the Indian Peninsula

The diurnal cycle of environmental conditions for shallow and deep convection regimes within the Indian monsoon environment is investigated using comprehensive observations from the surface, boundary layer, and cloud layers. For shallow convection (SC) and deep convection (DC) in the afternoon hours, thermodynamics, moisture convergence, and several other environmental variables provide information on the factors that control the vertical extent of convection in both regimes. The SC regime is characterized by high sensible heat flux, leading to stronger boundary layer turbulence, a higher mixed layer, and increased dry air entrainment from the free troposphere. Evaluation of several pre-conditioning parameters with T-test statistics suggests that stronger mid-level meridional wind shear and lack of mid-level moistening are detrimental to the growth of clouds in the SC regime. Conversely, the DC regime is driven by low surface fluxes and low surface-level buoyancy, with higher boundary layer and mid-layer moisture and more mid-layer instability, supporting larger Convective Available Potential Energy (CAPE). Morning precursor conditions for the preference of SC versus DC regime in the afternoon reveal that total column water vapor, relative humidity and CAPE are significantly higher on DC days. Large-scale moisture transport in the early morning within and above the boundary layer, driven by stronger westerly winds, is a key factor for the development of DC later in the day. This investigation enhances our understanding of boundary layer controls on shallow and deep convection within the Indian Monsoon environment.

Development of the BOLT-2 Roughness Experiment for Flight

A sounding rocket research flight called BOLT-2, which stands for Boundary Layer Turbulence 2, was initiated with the goal of studying hypersonic boundary-layer transition and turbulence. The BOLT-2 research vehicle is based on a three-dimensional geometry with concave surfaces and swept leading edges that provides two separate and distinct, also redundant, flowpaths for conducting measurements. One side of BOLT-2 is dedicated to smooth surface transition and turbulence, to better study the natural instability processes, whereas the other has been assigned to study forced transition and turbulence using discrete roughness trips. The present paper is intended to document the primary drivers and decisions made that lead up to finalizing the roughness-side experiment for the BOLT-2 flight.

Numerical Investigation of Aero-Optical Distortions from High-Speed Turbulent Boundary Layers

Wall-modeled large-eddy simulations of turbulent boundary-layer flows over a flat plate at Mach 3.5, 7.87, and 13.64 were carried out, and the aero-optical distortions resulting from density fluctuations were investigated. The conditions for the Mach 3.5 case match those of a direct numerical simulation in the literature. The Mach 7.87 conditions are representative of the Hypersonic Wind Tunnel at Sandia National Laboratories, and the Mach 13.64 conditions match those of the Arnold Engineering Development Complex Hypervelocity Tunnel 9. The wall-modeled large-eddy simulations were validated using available experimental and DNS reference data. The normalized root-mean-square optical path difference for all three cases is in good agreement with respective data obtained from reference direct numerical simulations and experiments (within 1.53% for M∞=3.5, 1.25% for M∞=7.87, and 12% for M∞=13.64, compared to numerical data). Above M∞=5.0, the normalized path difference obtained from the simulations is above the value predicted by a semi-analytical relationship by Notre Dame University. With increasing Mach number, the bulk contribution to the total optical distortion shifts toward the boundary-layer edge. In addition, a proper orthogonal decomposition reveals that the nature of the dominant density fluctuations, which are located near the boundary-layer edge, changes from three-dimensional to two-dimensional. Understanding how the coherent structures contribute to the optical path difference may pave a way toward devising active flow control strategies geared toward a reduction of the optical path difference.