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At least 433 records · Page 24

A buoyancy–shear–drag–scalar-based turbulence model for power-law acceleration-driven Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A previously developed phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing based on a general buoyancy–shear–drag model [O. Schilling, “A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing,” Physica D 402, 132238 (2020)] is extended to include active or passive scalar mixing and power-law acceleration-driven Rayleigh–Taylor mixing. The buoyancy–shear–drag equations are coupled to a scalar variance equation that is used to define the molecular mixing parameter θ m , and when the scalar is active, modifies the Rayleigh–Taylor and Kelvin–Helmholtz mixing layer growth parameters to depend on the asymptotic value of this parameter, θ mol . Here, the scalar variance equation is closed by algebraically or differentially modeling the scalar variance dissipation rate. Nonlinear analytical solutions of the model are obtained in the total and separate bubble and spike mixing layer width formulations with the algebraic scalar variance dissipation rate for each instability, which are then used to calibrate the mechanical and scalar equation coefficients to predict specific values of physical observables and molecular mixing parameters. Surrogate mechanical and scalar turbulent fields can be constructed by multiplying a presumed self-similar spatial profile by appropriate functions of the width and its time derivative, and of the scalar obtained by solving the ordinary differential model equations. The explicit modeling and solution of turbulent transport equations are not required. The bubble and spike mixing layer width and scalar variance equations are then solved numerically for constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing, confirming that the prescribed level of molecular mixing is correctly predicted and illustrating the spatiotemporal evolution of the scalar fields.

Buoyancy–drag↗

A two-equation turbulence model for compressible reacting flows

A two-equation turbulence model (k-epsilon) has been modified to model compressible reacting flows. A compressibility correction model based on modeling the dilatational terms in the Reynolds stress equations has been used. Computations are carried out using the Navier-Stokes solver SPARK which includes a finite rate chemistry model for hydrogen-air combustion. Initially, planar compressible mixing layers are simulated. Comparisons of the predictions with available experimental data and the predictions of a compressible Reynolds stress closure indicate that the model is well suited for the study of such flows. The decrease in the growth rate of the mixing layer with increasing convective Mach number is well predicted. The model is then tested on a three-dimensional supersonic flow problem where solid boundaries are present. An axisymmetric nonreacting mixing layer flow involving dissimilar gases is evaluated next using the model and the predictions are compared with available experimental data. Finally, two reacting turbulent flow configurations have been studied and comparison of predictions and experimental data has been done. The comparisons indicate that the model predicts the overall features of the test cases very well.

Narayan, J. R.↗

High resolution transmission electron microscopy of two stony meteorites - Murchison and Kenna

Matrix material from the Murchison C2(M) carbonaceous chondrite and less than micrometer-size pyroxene inclusions in an olivine from the Kenna ureilite have been characterized using high resolution transmission electron microscopy. A diversity of textures and mineral associations, including serpentine-type and brucite-type mixed-layering, occur in the Murchison matrix. Such mixed layer structures are new types of layer silicate. Their presence in the matrix may prove to be genetically significant. The Kenna inclusions, formed at the olivine grain margins, are of two types: (1) a disordered orthopyroxene-clinopyroxene which may have inverted from protopyroxene and (2) a pigeonite with narrow anti-phase domains (80 A to 250 A) and boundaries parallel to (100).

Mackinnon, I. D. R.↗

Influence of penetrating solar radiation on the heat budget of the equatorial Pacific Ocean

Recent satellite observations of ocean transparency, coupled with climatological surface heat fluxes and ocean density profiles, are used here to show that solar radiation in visible frequencies, usually assumed to be absorbed at the sea surface, in fact penetrates to a significant degree to below the upper mixed layer of the ocean which interacts actively with the atmosphere. The net effect is a reduction of the heat input into the upper layer; for a 20 m-thick mixed layer this is equivalent to an annual reduction in temperature of about 5-10 K. The results provide a natural explanation for the discrepancy between the SSTs predicted by models and those observed.

Lewis, Marlon R.↗

Exploring the Inner Edge of the Habitable Zone with Fully Coupled Oceans

The role of rotation in planetary atmospheres plays an important role in regulating atmospheric and oceanic heat flow, cloud formation and precipitation. Using the Goddard Institute for Space Studies (GISS) three dimension General Circulation Model (3D-GCM) we demonstrate how varying rotation rate and increasing the incident solar flux on a planet are related to each other and may allow the inner edge of the habitable zone to be much closer than many previous habitable zone studies have indicated. This is shown in particular for fully coupled ocean runs -- some of the first that have been utilized in this context. Results with a 100m mixed layer depth and our fully coupled ocean runs are compared with those of Yang et al. 2014, which demonstrates consistency across models. However, there are clear differences for rotations rates of 1-16x present earth day lengths between the mixed layer and fully couple ocean models, which points to the necessity of using fully coupled oceans whenever possible. The latter was recently demonstrated quite clearly by Hu & Yang 2014 in their aquaworld study with a fully coupled ocean when compared with similar mixed layer ocean studies and by Cullum et al. 2014. Atmospheric constituent amounts were also varied alongside adjustments to cloud parameterizations (results not shown here). While the latter have an effect on what a planet's global mean temperature is once the oceans reach equilibrium they do not qualitatively change the overall relationship between the globally averaged surface temperature and incident solar flux for rotation rates ranging from 1 to 256 times the present Earth day length. At the same time this study demonstrates that given the lack of knowledge about the atmospheric constituents and clouds on exoplanets there is still a large uncertainty as to where a planet will sit in a given star's habitable zone.

solar flux↗

Turbulence modeling for high speed compressible flows

The following grant objectives were delineated in the proposal to NASA: to offer course work in computational fluid dynamics (CFD) and related areas to enable mechanical engineering students at North Carolina A&T State University (N.C. A&TSU) to pursue M.S. studies in CFD, and to enable students and faculty to engage in research in high speed compressible flows. Since no CFD-related activity existed at N.C. A&TSU before the start of the NASA grant period, training of students in the CFD area and initiation of research in high speed compressible flows were proposed as the key aspects of the project. To that end, graduate level courses in CFD, boundary layer theory, and fluid dynamics were offered. This effort included initiating a CFD course for graduate students. Also, research work was performed on studying compressibility effects in high speed flows. Specifically, a modified compressible dissipation model, which included a fourth order turbulent Mach number term, was incorporated into the SPARK code and verified for the air-air mixing layer case. The results obtained for this case were compared with a wide variety of experimental data to discern the trends in the mixing layer growth rates with varying convective Mach numbers. Comparison of the predictions of the study with the results of several analytical models was also carried out. The details of the research study are described in the publication entitled 'Compressibility Effects in Modeling Turbulent High Speed Mixing Layers,' which is attached to this report.

Chandra, Suresh↗

Airborne Lidar Measurements of Ozone and Aerosol Profiles Over Major US Metropolitan Areas

During field missions in 2021 and 2023, the airborne NASA Langley Research Center High Spectral Resolution Lidar 2 (HSRL 2) measured the temporal and spatial evolution of ozone and aerosol distributions impacting urban air quality over the four most populated cities in the United States. HSRL-2 measurements in 2021 were acquired over the Houston metropolitan region, including Galveston Bay and the Houston Ship Channel, as part of the NASA Tracking Aerosol Convection Experiment – Air Quality (TRACER-AQ) mission conducted in collaboration with the Department of Energy. HSRL-2 measurements were acquired over Los Angeles, Chicago, and New York City in 2023 as part of the NASA Synergistic TEMPO Air Quality Science (STAQS) mission conducted in collaboration with the NOAA Atmospheric Emissions and Reactions Observed from Megacities to Marine Areas (AEROMMA) mission. HSRL 2 provided nadir vertical profiles of ozone, aerosol backscatter, extinction, and depolarization as the aircraft flew lawnmower type patterns at 9 km for several hours over these urban areas. HSRL-2 measured profiles of aerosol extinction and aerosol optical depth (AOD) via the HSRL technique at 355 and 532 nm and profiles of aerosol backscatter and depolarization at 355, 532, and 1064 nm. Mixed Layer Heights (MLH) were derived by locating sharp vertical gradients in the profiles of aerosol backscatter. The flights were comprised of up to three repeating lawnmower patterns over each city showing the evolution of the ozone and aerosol distributions from the morning through the afternoon. The HSRL-2 measurements reveal ozone enhancements near the surface as well as in the free troposphere above the mixed layer. Some lidar measurements over Chicago and New York City show the daytime boundary layer growing into elevated layers of biomass burning aerosol. These layers complicate efforts to use column-integrated satellite measurements to infer surface air quality. As expected, mixed layer height (MLH) typically increased significantly during the day; however, during some flights, particularly over the Houston area, MLH also showed large spatial variability associated with changes in surface cover and/or small scale circulations. Often HSRL-2 measurements of AOD also showed large spatial and temporal variability throughout the day over these cities. We discuss how the ozone and aerosol profiles are averaged over different vertical and horizontal scales near the surface for use in assessments of regional air quality models and near-surface ozone retrievals from NASA’s recently launched Tropospheric Emissions: Monitoring Pollution (TEMPO) satellite.

Lidar↗

HSRL-2 Observations over the Houston, TX Region during TRACER-AQ

During field missions in 2021 and 2023, the airborne NASA Langley Research Center High Spectral Resolution Lidar 2 (HSRL 2) measured the temporal and spatial evolution of ozone and aerosol distributions impacting urban air quality over the four most populated cities in the United States. HSRL-2 measurements in 2021 were acquired over the Houston metropolitan region, including Galveston Bay and the Houston Ship Channel, as part of the NASA Tracking Aerosol Convection Experiment – Air Quality (TRACER-AQ) mission conducted in collaboration with the Department of Energy. HSRL-2 measurements were acquired over Los Angeles, Chicago, and New York City in 2023 as part of the NASA Synergistic TEMPO Air Quality Science (STAQS) mission conducted in collaboration with the NOAA Atmospheric Emissions and Reactions Observed from Megacities to Marine Areas (AEROMMA) mission. HSRL 2 provided nadir vertical profiles of ozone, aerosol backscatter, extinction, and depolarization as the aircraft flew lawnmower type patterns at 9 km for several hours over these urban areas. HSRL-2 measured profiles of aerosol extinction and aerosol optical depth (AOD) via the HSRL technique at 355 and 532 nm and profiles of aerosol backscatter and depolarization at 355, 532, and 1064 nm. Mixed Layer Heights (MLH) were derived by locating sharp vertical gradients in the profiles of aerosol backscatter. The flights were comprised of up to three repeating lawnmower patterns over each city showing the evolution of the ozone and aerosol distributions from the morning through the afternoon. The HSRL-2 measurements reveal ozone enhancements near the surface as well as in the free troposphere above the mixed layer. Some lidar measurements over Chicago and New York City show the daytime boundary layer growing into elevated layers of biomass burning aerosol. These layers complicate efforts to use column-integrated satellite measurements to infer surface air quality. As expected, mixed layer height (MLH) typically increased significantly during the day; however, during some flights, particularly over the Houston area, MLH also showed large spatial variability associated with changes in surface cover and/or small scale circulations. Often HSRL-2 measurements of AOD also showed large spatial and temporal variability throughout the day over these cities. We discuss how the ozone and aerosol profiles are averaged over different vertical and horizontal scales near the surface for use in assessments of regional air quality models and near-surface ozone retrievals from NASA’s recently launched Tropospheric Emissions: Monitoring Pollution (TEMPO) satellite.

Lidar↗

Assessment of the literature about Be-W mixed material layer formation in the fusion reactor environment

All plasma facing surfaces in a fusion reactor, whether initially pure or an alloy, will rapidly evolve into a mixed material due to plasma-induced erosion, migration and redeposition. Beryllium (Be) erosion from the main chamber, and its transport and deposition on to a tungsten (W) divertor results in the growth of mixed Be-W layers, which can evolve to form beryllides. These Be-W mixed materials exhibit generally less desirable properties than pure tungsten or pure beryllium, such as lower melting points. In order to better understand the parameter space for growth of these alloys, this paper reviews the literature on Be-W mixed material formation experiments—in magnetically confined fusion reactors, in linear plasma test stands, and during thin-film deposition—and on computational modeling of Be-W interactions, as well as briefly assesses the Be-W growth kinetics. We conclude that the following kinetic steps drive the material mixing: adsorption of the implanted/deposited ion on the metal surface; diffusion of the implanted/deposited ion from surface into the bulk, which is accelerated by defects; and loss of deposited material through erosion. Adsorption dominates (or prevents) material mixing in thin-film deposition experiments, whereas diffusion drives material mixing in plasma exposures due to the energetic ion implantation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Assessment of the literature about Be-W mixed material layer formation in the fusion reactor environment

Abstract All plasma facing surfaces in a fusion reactor, whether initially pure or an alloy, will rapidly evolve into a mixed material due to plasma-induced erosion, migration and redeposition. Beryllium (Be) erosion from the main chamber, and its transport and deposition on to a tungsten (W) divertor results in the growth of mixed Be-W layers, which can evolve to form beryllides. These Be-W mixed materials exhibit generally less desirable properties than pure tungsten or pure beryllium, such as lower melting points. In order to better understand the parameter space for growth of these alloys, this paper reviews the literature on Be-W mixed material formation experiments—in magnetically confined fusion reactors, in linear plasma test stands, and during thin-film deposition—and on computational modeling of Be-W interactions, as well as briefly assesses the Be-W growth kinetics. We conclude that the following kinetic steps drive the material mixing: adsorption of the implanted/deposited ion on the metal surface; diffusion of the implanted/deposited ion from surface into the bulk, which is accelerated by defects; and loss of deposited material through erosion. Adsorption dominates (or prevents) material mixing in thin-film deposition experiments, whereas diffusion drives material mixing in plasma exposures due to the energetic ion implantation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Update on Area Production in Mixing of Supercritical Fluids

The focus of this research is on supercritical C7H16/N2 and O2/H2 mixing layers undergoing transitions to turbulence. The C7H16/N2 system serves as a simplified model of hydrocarbon/air systems in gas-turbine and diesel engines; the O2/H2 system is representative of liquid rocket engines. One goal of this research is to identify ways of controlling area production to increase disintegration of fluids and enhance combustion in such engines. As used in this research, "area production" signifies the fractional rate of change of surface area oriented perpendicular to the mass-fraction gradient of a mixing layer. In the study, a database of transitional states obtained from direct numerical simulations of the aforementioned mixing layers was analyzed to investigate global layer characteristics, phenomena in regions of high density-gradient magnitude (HDGM), irreversible entropy production and its relationship to the HDGM regions, and mechanisms leading to area production.

Okongo, Nora↗

The influence of the shock-to-reshock time on the Richtmyer–Meshkov instability in reshock

Experiments on the Richtmyer–Meshkov instability (RMI) in a dual driver vertical shock tube (DDVST) are described. An initially planar, stably stratified membraneless interface is formed by flowing air from above and sulfur hexafluoride from below the interface location using the method of Jones & Jacobs ( Phys. Fluids , vol. 9, issue 1997, 1997, pp. 3078–3085). A random three-dimensional, multi-modal initial perturbation is imposed by vertically oscillating the gas column to produce Faraday waves. The DDVST design generates two shock waves, one originating above and one below the interface, with these shocks having independently controllable strengths and interface arrival times. The shock waves have nominal strengths of $M_L=1.17$ and $M_H=1.18$ for the shock wave originating in the light and heavy gas, respectively, with these strengths chosen to result in arrested bulk interface motion following reshock. The influence of the length of the shock-to-reshock time, as well as the order of shock arrival, on the post-reshock RMI is examined. The mixing layer width grows according to $h\propto t^\theta$ , where $\theta _H=0.36\pm 0.018$ (95 %) and $\theta _L=0.38\pm 0.02$ (95 %) for heavy and light shock first experiments, respectively, indicating no strong dependence on the order of shock wave arrival. Volume integrated specific turbulent kinetic energy (TKE) in the mixing layer versus time is found to decay according to $E_{tot}/\bar {\rho }\propto t^p$ with $p_H=-0.823\pm 0.06$ (95 %) and $p_L=-1.061\pm 0.032$ (95 %) for heavy and light shock first experiments, respectively. Notably, the 95 % confidence intervals do not overlap. Analysis on the influence of the shock-to-reshock time on turbulent length scales, transition criteria, spectra and mixing layer anisotropy are also presented.

Ferguson, Kevin (ORCID:0000000166537482)↗

Limitations in Representation of Physical Processes Prevents Successful Simulation of PM2.5 During KORUS-AQ

High levels of fine particulate matter (PM2.5) pollution in East Asia often exceed local air quality standards. Observations from the Korea United States-Air Quality (KORUS-AQ) field campaign in May and June 2016 showed that development of extreme pollution (haze) occurred through a combination of long-range transport and favorable meteorological conditions that enhanced local production of PM2.5. Atmospheric models often have difficulty simulating PM2.5 chemical composition during haze, which is of concern for the development of successful control measures. We use observations from KORUS-AQ to examine the ability of the GEOS-Chem chemical transport model to simulate PM2.5 composition throughout the campaign and identify the mechanisms driving the pollution event. At the surface, the model underestimates sulfate by -64% but overestimates nitrate by +36%. The largest underestimate in sulfate occurs during the pollution event, where models typically struggle to generate elevated sulfate concentrations due to missing heterogeneous chemistry in aerosol liquid water in the polluted boundary layer. Hourly surface observations show that the model nitrate bias is driven by an overestimation of the nighttime peak. In the model, nitrate formation is limited by the supply of nitric acid, which is biased by +100% against aircraft observations. We hypothesize that this is due to a large missing sink, which we implement here as a factor of five increase in dry deposition. We show that the resulting increased deposition velocity is consistent with observations of total nitrate as a function of photochemical age. The model does not account for factors such as the urban heat island effect or the heterogeneity of the built-up urban landscape resulting in insufficient model turbulence and surface area over the study area that likely results in insufficient dry deposition. Other species such as NH3 could be similarly affected but were not measured during the campaign. Nighttime production of nitrate is driven by NO2 hydrolysis in the model, while observations show that unexpectedly elevated nighttime ozone (not present in the model) should result in N2O5 hydrolysis as the primary pathway. The model is unable to represent nighttime ozone due to an overly rapid collapse of the afternoon mixed layer and excessive titration by NO. We attribute this to missing nighttime heating driving deeper nocturnal mixing that would be expected to occur in a city like Seoul. This urban heating is not considered in air quality models run at large enough scales to treat both local chemistry and long-range transport. Key model failures in simulating nitrate, mainly overestimated daytime nitric acid, incorrect representation of nighttime chemistry, and an overly shallow and insufficiently turbulent nighttime mixed layer, exacerbate the model’s inability to simulate the buildup of PM2.5 during haze pollution. To address the underestimate in sulfate most evident during the haze event, heterogeneous aerosol uptake of SO2 is added to the model which previously only considered aqueous production of sulfate from SO2 in cloud water. Implementing a simple parameterization of this chemistry improves the model abundance of sulfate but degrades the SO2 simulation implying that emissions are underestimated. We find that improving model simulations of sulfate has direct relevance to determining local vs. transboundary contributions to PM2.5. During the haze pollution event, the inclusion of heterogeneous aerosol uptake of SO2 decreases the fraction of PM2.5 attributable to long-range transport from 66% to 54%. Locally-produced sulfate increased from 1% to 25% of locally-produced PM2.5, implying that local emissions controls would have a larger effect than previously thought. However, this additional uptake of SO2 is coupled to the model nitrate prediction which affects the aerosol liquid water abundance and chemistry driving sulfate-nitrate-ammonium partitioning. An additional simulation of the haze pollution with heterogeneous uptake of SO2 to aerosol and simple improvements to the model nitrate simulation results in 30% less sulfate due to 40% less nitrate and aerosol water, and results in an underestimate of sulfate during the haze event. Future studies need to better consider the impact of model physical processes such as dry deposition and nighttime boundary layer mixing on the simulation of nitrate and the effect of improved nitrate simulations on the overall simulation of secondary inorganic aerosol (sulfate+nitrate+ammonium) in East Asia. Foreign emissions are rapidly changing, increasing the need to understand the impact of local emissions on PM2.5 in South Korea to ensure continued air quality improvements.

Katherine R. Travis↗

Estimating the Distribution of Colored Dissolved Organic Matter During the Southern Ocean Gas Exchange Experiment Using Four-Dimensional Variational Data Assimilation

We diagnosed the effect of various physical processes on the distribution of mixed-layer colored dissolved organic matter (CDOM) and a sulfur hexauoride (SF6) tracer during the Southern Ocean Gas Exchange Experiment (SO GasEx). The biochemical upper ocean state estimate uses in situ and satellite biochemical and physical data in the study region, including CDOM (absorption coefcient and spectral slope), SF6, hydrography, and sea level anomaly. Modules for photobleaching of CDOM and surface transport of SF6 were coupled with an ocean circulation model for this purpose. The observed spatial and temporal variations in CDOM were captured by the state estimate without including any new biological source term for CDOM, assuming it to be negligible over the 26 days of the state estimate. Thermocline entrainment and photobleaching acted to diminish the mixed-layer CDOM with time scales of 18 and 16 days, respectively. Lateral advection of CDOM played a dominant role and increased the mixed-layer CDOM with a time scale of 12 days, whereas lateral diffusion of CDOM was negligible. A Lagrangian view on the CDOM variability was demonstrated by using the SF6 as a weighting function to integrate the CDOM elds. This and similar data assimilation methods can be used to provide reasonable estimates of optical properties, and other physical parameters over the short-term duration of a research cruise, and help in the tracking of tracer releases in large-scale oceanographic experiments, and in oceanographic process studies.

Del Castillo, C. E.↗

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

reynolds averaging↗

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSGLRR full second-moment Reynolds stress models are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST) two-equation models.

computational fluid dynamics↗

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

Full seven-equation Reynolds stress turbulence models are promising tools for today’s aerospace technology challenges. This paper examines two such models for computing challenging turbulent flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and were evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results computed using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

reynolds averaging↗

Towards enhancing and delaying disturbances in free shear flows

The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modeling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial value problem. The results show that there is a continuous as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behavior of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.

Criminale, W. O.↗