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Supersonic shear imaging (SSI) is a new ultrasound-based technique for real-time visualization of soft tissue viscoelastic properties. Using ultrasonic focused beams, it is possible to remotely generate mechanical vibration sources radiating low-frequency, shear waves inside tissues. Relying on this concept, SSI proposes to create such a source and make it move at a supersonic speed. In analogy with the "sonic boom" created by a supersonic aircraft, the resulting shear waves will interfere constructively along a Mach cone, creating two intense plane shear waves. These waves propagate through the medium and are progressively distorted by tissue heterogeneities. An ultrafast scanner prototype is able to both generate this supersonic source and image (5000 frames/s) the propagation of the resulting shear waves. Using inversion algorithms, the shear elasticity of medium can be mapped quantitatively from this propagation movie. The SSI enables tissue elasticity mapping in less than 20 ms, even in strongly viscous medium like breast. Modalities such as shear compounding are implementable by tilting shear waves in different directions and improving the elasticity estimation. Results validating SSI in heterogeneous phantoms are presented. The first in vivo investigations made on healthy volunteers emphasize the potential clinical applicability of SSI for breast cancer detection.

Compressible turbulence shapes the structure of the interstellar medium of our Galaxy and likely plays an important role also during structure formation in the early Universe. The density probability distribution function (PDF) and the power spectrum of such compressible, supersonic turbulence are the key ingredients for theories of star formation. However, both the PDF and the spectrum are still a matter of debate, because theoretical predictions are limited and simulations of supersonic turbulence require enormous resolutions to capture the inertial-range scaling. To advance our limited knowledge of compressible turbulence, we here present and analyse the world's largest simulations of supersonic turbulence. We compare hydrodynamic models with numerical resolutions of 2563–40963 mesh points and with two distinct driving mechanisms, solenoidal (divergence-free) driving and compressive (curl-free) driving. We find convergence of the density PDF, with compressive driving exhibiting a much wider and more intermittent density distribution than solenoidal driving by fitting to a recent theoretical model for intermittent density PDFs. Analysing the power spectrum of the turbulence, we find a pure velocity scaling close to Burgers turbulence with P(v) ∝ k−2 for both driving modes in our hydrodynamical simulations with Mach number |$\mathcal{M}=17$|⁠. The spectrum of the density-weighted velocity ρ1/3v, however, does not provide the previously suggested universal scaling for supersonic turbulence. We find that the power spectrum P(ρ1/3v) scales with wavenumber as k−1.74 for solenoidal driving, close to incompressible Kolmogorov turbulence (k−5/3), but is significantly steeper with k−2.10 for compressive driving. We show that this is consistent with a recent theoretical model for compressible turbulence that predicts P(ρ1/3v) ∝ k−19/9 in the presence of a strong |$\nabla \cdot {\boldsymbol {v}}$| component as is produced by compressive driving and remains remarkably constant throughout the supersonic turbulent cascade.

Copper clusters ranging in size from 1 to 29 atoms have been prepared in a supersonic beam by laser vaporization of a rotating copper target rod within the throat of a pulsed supersonic nozzle using helium for the carrier gas. The clusters were cooled extensively in the supersonic expansion [T(translational) 1 to 4 K, T(rotational)=4 K, T(vibrational)=20 to 70 K]. These clusters were detected in the supersonic beam by laser photoionization with time-of-flight mass analysis. Using a number of fixed frequency outputs of an exciplex laser, the threshold behavior of the photoionization cross section was monitored as a function of cluster size. The 7.9 eV photon energy of the F2 excimer laser was found to be above the ionization potential of all clusters, and the photoion mass spectrum thus produced showed the copper cluster concentration in the beam to follow a monotonically decreasing function of cluster size. The 6.4 eV ArF exciplex laser photon energy was found to be above the photoionization threshold of clusters with three or more atoms in the case of odd-numbered clusters, but only for clusters with eight or more atoms for even-numbered clusters. Extending out to clusters as large as 29 atoms, laser photoionization at 6.4 eV produced a time-of-flight mass distribution with a pronounced even/odd alternation in cluster photoion intensity. This alternation in ionization threshold behavior was attributed to an even/odd alternation in the electronic structure of the copper clusters with the highest occupied molecular orbital (HOMO) of the even clusters being considerably more strongly bonding than it is in the clusters with an odd number of copper atoms. The 4.98 eV photon energy of the KrF exciplex laser was found to lie below the ionization threshold of all clusters in the 1 to 29 atom range. An extensive survey of the ultraviolet absorption spectrum of the copper dimer was also performed with this supersonic beam source. Resonance two-photon ionization (R2PI) with mass selective detection allowed the detection of five new electronic band systems in the region between 2690 and 3200 Å, for each of the three naturally occurring isotopic forms of Cu2. In the process of scanning the R2PI spectrum of these new electronic states, the ionization potential of the copper dimer was determined to be 7.894±0.015 eV.

It is argued that because of the lack of intrinsic length and time scales in the core part of the jet flow, the radiated noise spectrum of a high-speed jet should exhibit similarity. A careful analysis of all the axisymmetric supersonic jet noise spectra in the data-bank of the Jet Noise Laboratory of the NASA Langley Research Center has been carried out. Two similarity spectra, one for the noise from the large turbulence structures/instability waves of the jet flow, the other for the noise from the fine-scale turbulence, are identified. The two similarity spectra appear to be universal spectra for axisymmetric jets. They fit all the measured data including those from subsonic jets. Experimental evidence are presented showing that regardless of whether a jet is supersonic or subsonic the noise characteristics and generation mechanisms are the same. There is large turbulence structures/instability waves noise from subsonic jets. This noise component can be seen prominently inside the cone of silence of the fine-scale turbulence noise near the jet axis. For imperfectly expanded supersonic jets, a shock cell structure is formed inside the jet plume. Measured spectra are provided to demonstrate that the presence of a shock cell structure has little effect on the radiated turbulent mixing noise. The shape of the noise spectrum as well as the noise intensity remain practically the same as those of a fully expanded jet. However, for jets undergoing strong screeching, there is broadband noise amplification for both turbulent mixing noise components. It is discovered through a pilot study of the noise spectrum of rectangular and elliptic supersonic jets that the turbulent mixing noise of these jets is also made up of the same two noise components found in axisymmetric jets. The spectrum of each individual noise component also fits the corresponding similarity spectrum of axisymmetric jets.

Understanding the formation of stars in galaxies is central to much of modern astrophysics. However, a quantitative prediction of the star formation rate and the initial distribution of stellar masses remains elusive. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift (known as ambipolar diffusion in astrophysics). Recently, however, both observational and numerical work has begun to suggest that supersonic turbulent flows rather than static magnetic fields control star formation. To some extent, this represents a return to ideas popular before the importance of magnetic fields to the interstellar gas was fully appreciated. This review gives a historical overview of the successes and problems of both the classical dynamical theory and the standard theory of magnetostatic support, from both observational and theoretical perspectives. The outline of a new theory relying on control by driven supersonic turbulence is then presented. Numerical models demonstrate that, although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic-scale star formation. It suggests that individual star-forming cores are likely not quasistatic objects, but dynamically collapsing. Accretion onto these objects varies depending on the properties of the surrounding turbulent flow; numerical models agree with observations showing decreasing rates. The initial mass distribution of stars may also be determined by the turbulent flow. Molecular clouds appear to be transient objects forming and dissolving in the larger-scale turbulent flow, or else quickly collapsing into regions of violent star formation. Global star formation in galaxies appears to be controlled by the same balance between gravity and turbulence as small-scale star formation, although modulated by cooling and differential rotation. The dominant driving mechanism in star-forming regions of galaxies appears to be supernovae, while elsewhere coupling of rotation to the gas through magnetic fields or gravity may be important.

Large-eddy simulation of an underexpanded sonic jet injection into supersonic crossflows is performed to obtain insights into key physics of the jet mixing. A high-order compact differencing scheme with a recently developed localized artificial diffusivity scheme for discontinuity-capturing is used. Progressive mesh refinement study is conducted to quantify the broadband range of scales of turbulence that are resolved in the simulations. The simulations aim to reproduce the flow conditions reported in the experiments of Santiago and Dutton [Santiago, J. G., and Dutton, J. C., Velocity Measurements of a Jet Injected into a Supersonic Crossflow, Journal of Propulsion and Power, Vol.132,1997, pp. 264―273] and elucidate the physics of the jet mixing. A detailed comparison with these data is shown. Statistics obtained by the large-eddy simulation with turbulent crossflow show good agreement with the experiment, and a series of mesh refinement studies shows reasonable grid convergence in the predicted mean and turbulent flow quantities. The present large-eddy simulation reproduces the large-scale dynamics of the flow and jet fluid entrainment into the boundary-layer separation regions upstream and downstream of the jet injection reported in previous experiments, but the richness of data provided by the large-eddy simulation allows a much deeper exploration of the flow physics. Key physics of the jet mixing in supersonic crossflows are highlighted by exploring the underlying unsteady phenomena. The effect of the approaching turbulent boundary layer on the jet mixing is investigated by comparing the results of jet injection into supersonic crossflows with turbulent and laminar crossflows.

Introduction S OME qualifications to the pretentious nature of the title of this Paper are in order. Research in this context is applied, i.e., it is directed toward the design and development of devices. The devices are air breathing propulsion systems, wherein supersonic combustion is inherent or it provides an adjunct benefit. Principal applications of the former are manned hypersonic aircraft, transatmospheric accelerators, and missiles. Typical examples of the latter are external burning systems that sustain thrust or reduce drag when used in tandem with primary accelerator engines. This Paper is not at all representative of the complete body of the research on supersonic combustion. Instead, what is presented is primarily based on material with which the writer has had either direct involvement or a first-hand knowledge. It does not do justice to the exemplary works of many other investigators. Hopefully, this is somewhat rectified by the extensive list of references. The reader is encouraged to consult these manuscripts to obtain a more balanced perspective. This applied research must be viewed from the perspective of the engineer who is charged with expediting development and is in the need of design tools. Exact physics have frequently been abandoned to produce functional models. Much of the experimental verification upon which the models are based has been obtained in facilities which have known imperfections with respect to duplication of flight conditions. Moreover, compromises have been made in the analysis and interpretation of the experimental data, in part due to imperfect or incomplete diagnostic instrumentation, and in part due to a limited understanding of the underlying physics. An example that embodies all of these deficiencies would be a design model that is based on the use of integral techniques to describe combustion in supersonic flow from experiments conducted in an arc-heated tunnel.

A solution describing the spatial evolution of small-amplitude instability waves and their associated sound field of axisymmetric supersonic jets is found using the method of matched asymptotic expansions (see Part 1, Tam & Burton 1984). The inherent axisymmetry of the problem allows the instability waves to be decomposed into azimuthal wave modes. In addition, it is found that because of the cylindrical geometry of the problem the gauge functions of the inner expansion, unlike the case of two-dimensional mixing layers, are no longer just powers of ε. Instead they contain logarithmic terms. To test the validity of the theory, numerical results of the solution are compared with the experimental measurements of Troutt (1978) and Troutt & McLaughlin (1982). Two series of comparisons at Strouhal numbers 0.2 and 0.4 for a Mach-number 2.1 cold supersonic jet are made. The data compared include hot-wire measurements of the axial distribution of root-mean-squared jet centreline mass-velocity fluctuations and radial and axial distributions of near-field pressure-level contours measured by microphones. The former is used to test the accuracy of the inner (or instability-wave) solution. The latter is used to verify the correctness of the outer solution. Very favourable overall agreements between the calculated results and the experimental measurements are found. These very favourable agreements strongly suggest that the method of solution developed in Part 1 paper is indeed valid. Furthermore, they also offer concrete support to the proposition made previously by a number of investigators that instability waves are important noise sources in supersonic jets.

Recent interest in supersonic combustion (scramjets) and noise reduction for the high speed civil transport (HSCT) plane prompted renewed research in supersonic mixing processes and means to control them. The scramjet propulsion concept requires rapid mixing between fuel and air in order to minimize the size of the combustor and affect the performance of the entire vehicle system. Also, accelerated mixing of exhaust plumes with coflowing air has been shown to lead to jet noise reduction. Other examples of technological applications requiring control of mixing in compressible flows include thrust augmenting ejectors, thrust vector control, metal deposition, and gas dynamic lasers. The technological challenge of mixing enhancement in compressible flows stems from the inherently low growth rates of supersonic shear layers. Many mixing augmentation methods employed efficiently in sub­ sonic flows failed to work at elevated Mach numbers, and some were inefficient because they were utilized outside their effective range. Never-

We have studied the relaxation of conformers and the formation/relaxation of isomeric, weakly bonded dimers in pulsed supersonic expansions of seeded inert gases (He, Ne, Ar, Kr). The relaxation was determined from the intensity of a rotational transition for the higher energy species as a function of carrier gas composition, using the Balle/Flygare Fourier transform microwave spectrometer. Of thirteen molecules with rotational conformers which we examined, those with barriers to internal rotation greater than 400 cm−1 did not relax significantly in any of the carriers. The higher energy forms of ethyl formate, ethanol, and isopropanol, with smaller barriers, were not relaxed by He; those of ethanol and isopropanol were somewhat relaxed by Ne; and all were completely relaxed by as little as 5 to 20 mole percent of Ar or Kr in He or Ne. The relaxation in He or Ne is first order in the concentration of added Ne, Ar, or Kr as well as in the concentration of the high energy conformer. The pseudo first-order rate constants (larger in Ne than in He) increase sharply with Z of the rare gas, roughly in a 0:1:2:4 progression for He, Ne, Ar, and Kr, suggesting that the relaxation involves relatively long-range polarization effects. Similar behavior was found in the formation/relaxation of the weakly bonded dimer pairs: linear OCO–HCN, T-shaped HCN–CO2; linear FH–NNO and bent NNO–HF; and bent HF–DF and DF–HF. The case of the HCN/CO2 dimers is particularly striking. The T-shaped dimer was found first, using Ar as the carrier gas. Five years later the linear form was found with first run neon as carrier, but it could not be detected at all with Ar as the carrier. These results show that in favorable cases high energy species can be studied in supersonic expansions by freezing out a ‘‘high-temperature’’ concentration with a nonrelaxing carrier gas.

Molecular clouds have broad linewidths suggesting turbulent supersonic motions in the clouds. These motions are usually invoked to explain why molecular clouds take much longer than a free-fall time to form stars. It has classically been thought that supersonic hydrodynamical turbulence would dissipate its energy quickly, but that the introduction of strong magnetic fields could maintain these motions. In a previous paper it has been shown, however, that isothermal, compressible, MHD and hydrodynamical turbulence decay at virtually the same rate, requiring that constant driving occur to maintain the observed turbulence. In this paper direct numerical computations of uniformly driven turbulence with the ZEUS astrophysical MHD code are used to derive the absolute value of energy dissipation as a function of the driving wavelength and amplitude. The ratio of the formal decay time of turbulence E_{kin}/\\dot{E}_{kin} to the free-fall time of the gas can then be derived as a function of the ratio of driving wavelength to Jeans wavelength and rms Mach number, and shown to be most likely far less than unity, again showing that turbulence in molecular clouds must be constantly and strongly driven. (abridged)

A spatially developing supersonic adiabatic flat plate boundary layer flow (at M∞=2.25 and Reθ≈4000) is analyzed by means of direct numerical simulation. The numerical algorithm is based on a mixed weighted essentially nonoscillatory compact-difference method for the three-dimensional Navier–Stokes equations. The main objectives are to assess the validity of Morkovin’s hypothesis and Reynolds analogies, and to analyze the controlling mechanisms for turbulence production, dissipation, and transport. The results show that the essential dynamics of the investigated turbulent supersonic boundary layer flow closely resembles the incompressible pattern. The Van Driest transformed mean velocity obeys the incompressible law-of-the-wall, and the mean static temperature field exhibits a quadratic dependency upon the mean velocity, as predicted by the Crocco–Busemann relation. The total temperature has been found not to be precisely uniform, and total temperature fluctuations are found to be non-negligible. Consistently, the turbulent Prandtl number is not unity, and it varies between 0.7 and 0.8 in the outer part of the boundary layer. Nonetheless, a modified strong Reynolds analogy is still verified. In agreement with the low Mach number results, the streamwise velocity component and the temperature are only weakly anti-correlated. The turbulent kinetic energy budget also shows similarities with the incompressible case provided all terms of the equation are properly scaled; indeed, the leading compressibility contributions are negligible throughout the boundary layer.

We compute 3D models of supersonic, sub-Alfv\'enic, and super-Alfv\'enic decaying turbulence, with an isothermal equation of state appropriate for star-forming interstellar clouds of molecular gas. We find that in 3D the kinetic energy decays as ${t}^{\ensuremath{-}\ensuremath{\eta}}$, with $0.85<\ensuremath{\eta}<1.2$. In 1D magnetized turbulence actually decays faster than unmagnetized turbulence. We compared different algorithms, and performed resolution studies reaching ${256}^{3}$ zones or ${70}^{3}$ particles. External driving must produce the observed long lifetimes and supersonic motions in molecular clouds, as undriven turbulence decays too fast.

Abstract We study the organization of turbulence in supersonic boundary layers through large-scale direct numerical simulations (DNS) at ${M}_{\infty } = 2$ , and momentum-thickness Reynolds number up to ${\mathit{Re}}_{{\delta }_{2} } \approx 3900$ (corresponding to ${\mathit{Re}}_{\tau } \approx 1120$ ) which significantly extend the current envelope of DNS in the supersonic regime. The numerical strategy relies on high-order, non-dissipative discretization of the convective terms in the Navier–Stokes equations, and it implements a recycling/rescaling strategy to stimulate the inflow turbulence. Comparison of the velocity statistics up to fourth order shows nearly exact agreement with reference incompressible data, provided the momentum-thickness Reynolds number is matched, and provided the mean velocity and the velocity fluctuations are scaled to incorporate the effects of mean density variation, as postulated by Morkovin’s hypothesis. As also found in the incompressible regime, we observe quite a different behaviour of the second-order flow statistics at sufficiently large Reynolds number, most of which show the onset of a range with logarithmic variation, typical of ‘attached’ variables, whereas the wall-normal velocity exhibits a plateau away from the wall, which is typical of ‘detached’ variables. The modifications of the structure of the flow field that underlie this change of behaviour are highlighted through visualizations of the velocity and temperature fields, which substantiate the formation of large jet-like and wake-like motions in the outer part of the boundary layer. It is found that the typical size of the attached eddies roughly scales with the local mean velocity gradient, rather than being proportional to the wall distance, as happens for the wall-detached variables. The interactions of the large eddies in the outer layer with the near-wall region are quantified through a two-point amplitude modulation covariance, which characterizes the modulating action of energetic outer-layer eddies.

A theory is proposed to describe the generation of sound by turbulence at high Mach numbers. The problem is formulated most conveniently in terms of the fluctuating pressure, and a convected wave equation (2.8) is derived to describe the generation and propagation of the pressure fluctuations. The supersonic turbulent shear zone is examined in detail. It is found that, at supersonic speeds, sound is radiated as eddy Mach waves, and as the Mach number increase, this mechanism of generation becomes increasingly dominant. Attention is concentrated on the properties of the pressure fluctuations just outside the shear zone where the interactions among the weak shock waves have had little effect. An asymptotic solution for large M is derived by a Green's function technique, and it is found that radiation with given frequency n and weve-number K can be associated with a coresponding critical layer within the shear zone. It is found that $(\overline {p - p_0})^2 $ increases approximately as $\rm {M}^{\frac {3} {2}}$ for M [Gt ] 1 contrasting with the M 8 variation found by Lightill for M [Lt ] 1. The acoustic efficiency thus varies as $\rm {M}^-{\frac {3} {2}}$ for M [Gt ] 1, and as M 5 for M [Lt ] 1, indicating a maximum acoustic efficiency for Mach numbers near one. The directional distribution of the radiation is discussed and the direction of maximum intensity is shown to move towards the perpendicular to the shear zone as M increases. The predictions of the theory are supported qualitatively by the few available experimental observations.

A review of various analytical methods and experimental results of supersonic and hypersonic panel flutter is presented. The analytical methods are categorized into two main methods. The first category is the classical methods, which include Galerkin in conjunction with numerical integration, harmonic balance and perturbation methods. The second category is the finite element methods in either the frequency domain (eigensolution) or the time domain (numerical integration). A review of the experimental literature is given. The effects of different parameters on the flutter behavior are described. The parameters considered include inplane forces, thermal loading, flow direction, and initial curvature. Active control of composite panels at supersonic speeds and elevated temperatures is also considered. This review article cites 84 references.

Two-stream supersonic turbulent mixing layers with a free-stream Mach number of 2.3 on the high-velocity side are experimentally investigated. A large-scale vortical structure, which has been believed to dominate the development of incompressible mixing layers, is also observed in the present supersonic layers. The spreading rate of the layer is correlated with a velocity ratio of the free streams and a Mach number based on the velocity difference across the layer.

A detailed experimental study of supersonic, Mach 2, flow over a three-dimensional cavity was conducted using shadowgraph visualization, unsteady surface pressure measurements, and particle image velocimetry. Large-scale structures in the cavity shear layer and visible disturbances inside the cavity were clearly observed. A large recirculation zone and high-speed reverse flow was revealed in the cavity. In addition, supersonic microjets were used at the leading edge to suppress flow unsteadiness within the cavity. With a minimal mass flux (blowing coefficient B c = 0.0015), the activation of microjets led to reductions of up to 20 dB in the amplitudes of cavity tones and of more than 9 dB in the overall sound pressure levels. The microjet injection also modified the cavity mixing layer and resulted in a significant reduction in the flow unsteadiness inside the cavity as revealed by the shadowgraphs and the velocity-field measurements.

Although a great deal of attention has been given to the role of water vapor from supersonic transport (SST) exhaust in the stratosphere, oxides of nitrogen from SST exhaust pose a much greater threat to the ozone shield than does an increase in water. The projected increase in stratospheric oxides of nitrogen could reduce the ozone shield by about a factor of 2, thus permitting the harsh radiation below 300 nanometers to permeate the lower atmosphere.