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At least 253 records · Page 14
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NASA NTRS1992

Buckling behavior of long symmetrically laminated plates subjected to combined loads

A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loadings is presented. The loading conditions considered are axial tension and compression, transverse tension and compression, and shear. Results obtained using a special purpose analysis, well suited for parametric studies are presented for clamped and simply supported plates. Moreover, results are presented for some common laminate constructions, and generic buckling design charts are presented for a wide range of parameters. The generic design charts are presented in terms of useful nondimensional parameters, and dependence of the nondimensional parameters on laminate fiber orientation, stacking sequence, and material properties is discussed. An important finding of the study is that the effects of anisotropy are much more pronounced in shear-loaded plates than in compression loaded plates. In addition, the effects of anisotropy on plates subjected to combined loadings are generally manifested as a phase shift of self-similar buckling interaction curves. A practical application of this phase shift is the buckling resistance of long plates can be improved by applying a shear loading with a specific orientation. In all cases considered, it is found that the buckling coefficients of infinitely long plates are independent of the bending stiffness ratio (D sub 11/D sub 22) sup 1/4.

Nemeth, Michael P.↗
NASA NTRS1994

Magnetically driven jets and winds: Exact solutions

We present a general class of self-similar solutions of the full set of MHD equations that include matter flow, electromagnetic fields, pressure, and gravity. The solutions represent axisymmetric, time-independent, nonrelativistic, ideal, magnetohydrodynamic, collimated outflows (jet and winds) from magnetized accretion disks around compact objects. The magnetic field extracts angular momentum from the disk, accelerates the outflows perpedicular to the disk, and provides collimation at large distances. The terminal outflow velocities are of the order of or greater than the rotational velocity of the disk at the base of the flow. When a nonzero electric current flows along the jet, the outflow radius oscillates with axial distance, whereas when the total electric current is zero (with the return current flowing across the jet's cross section), the outflow radius increase to a maximum and then decreases. The method can also be applied to relativistic outflows.

Contopoulos, J.↗
NASA NTRS1994

Nonlinear instability of accelerating shock waves with application to supernovae

We consider the stability of a planar accelerating shock front in an exponential atmosphere, a situation that can be described by a self-similar solution. A previous linear instability analysis showed that there are three regimes, depending on the wavelength of the perturbation along the direction of the shock front: at long wavelengths the shock is unstable, at intermediate wavelengths it is overstable, and at short wavelenghts it is stable, where the characteristic length is set by the initial density scale height. We have carried out numerical simulations of such an accelerating shock front and have confirmed the results of the semianalytic linear analysis in the linear regime. In the nonlinear regime, the evolution again depends on the three wavelength domains. At long wavelengths, the instability continuously grows but the flow remains smooth, and at short wavelengths, the flow is stable. The intermediate wavelength, overstable regime shows more complex evolution. The growing linear oscillations saturate soon after entering the nonlinear regime and the oscillations continue with the same approximate period. The shock front develops moving points of intersection, which generate weak shock fronts and density and pressure structure in the immediate postshock flow. The density fluctuations, with a contrast of a factor of 2-3, become frozen into the downstream flow. The growth of the instability is slow, so substantial initial perturbations are needed; thesemay be present in Type II supernovae with red supergiant progenitor stars which have outer convective regions. The clumping in the outer supernova atmosphere may affect spectral line formation and may play a role in the formation of fast knots.

Luo, Ding↗
NASA NTRS1995

Is walking a random walk? Evidence for long-range correlations in stride interval of human gait

Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.

Hausdorff, Jeffrey M.↗
NASA NTRS1995

The distance to the heliospheric VLF emission region

Two major episodes of heliospheric VLF emissions near 3 kHz have been observed by the Voyager spacecraft in 1983/84 and 1992/3. This higher-frequency component is apparently triggered by solar wind transients with sufficiently large spatial extents and energies to continue to propagate as shocks in the heliosheath. Entrainment of previously unshocked material and changed flow conditions in the heliosheath both tend to slow the shock propagation. The shock evolution is not self-similar. Rather, it is intermediate to two blast-wave similarity solutions in the moving solar wind frame. In one solution the shock moves as time to the 2/3 power and in the other as time to the 4/5 power. Using these models, the shock/Forbush decrease observed at Voyager 2 in September, 1991 and the turn-on of the 1992 emission is consistent with an emission region distance of approximately 130 AU (assuming no additional slowing of the shock in the heliosheath). If the termination shock was at approximately 70 AU when the transient shock collided with it, the true distance to the source region was probably closer to approximately 115 AU.

Mcnutt, R. L., Jr.↗
NASA NTRS1995

Getting granite dikes out of the source region

Whether a dike can propagate far from a magma reservoir depends upon the competition between the rate at which propagation widens the dike and the rate at which freezing constricts the aperture available for magma flow. Various formulations are developed for a viscous fluid at temperature T(sub m) intruding a growing crack in an elastic solid. The initial solid temperature equals T(sub m) at the source and decreases linearly with distance from the source. If T(sub m) is the unique freezing temperature of the fluid, dike growth is initially self-similar and an essentially exact solution is obtained; if T(sub m) is above the solidus temperature, the solution is approximate but is designed to overestimate the distance the dike may propagate. The ability of a dike to survive thermally depends primarily upon a single parameter that is a measure of the ratio of the dike frozen margin thickness to elastic thickness. Perhaps more intuitively, one may define a minimum distance from the essentially solid reservoir wall to the point at which the host rock temperature drops below the solidus, necessary for dikes to propagate far into subsolidus rock. It is concluded that for reasonable material properties and source conditions, most basalt dikes will have little difficulty leaving the source region, but most rhyolite dikes will be halted by freezing soon after the magma encounters rock at temperatures below the magma solidus. While these results can explain why granitic dikes are common near granitic plutons but rare elsewhere, the potentially large variation in magmatic systems makes it premature to rule out the possibility that most granites are transported through the crust in dikes. Nonetheless, these results highlight difficulties with such proposals and suggest that it may also be premature to rule out the possibility that most granite plutons ascend as more equidimensional bodies.

Rubin, Allan M.↗
NASA NTRS1995

Magnetohydrodynamic Riemann problem and the structure of the magnetic reconnection layer

We present a complete solution for a set of magnetohydrodynamic (MHD) Riemann problems in which the upstream and downstream states have the same total pressure, and in which the normal component of the magnetic field is very small. These solutions are pertinent to subfast flows in the earth's magnetic tail and near the magnetopause. In a coplanar situation a family of solutions exists that depend on two parameters as well as on dissapation mechanisms. In the parallel case the transverse magnetic field either does not change direction or changes the direction twice by involving two intermediate shocks. In the antiparallel case an intermediate shock is always required, except when the solution consists of two switch-off shocks. In a noncoplanar case the solution is not self-similar as a function of x/t, but continues to evolve. At early times the evolution is similar to the coplanar case. In general two time-dependent intermediate shocks are required to rotate the magnetic fields. The velocity shear has a strong effect on the Riemann solution. In some cases no Riemann solution can exist because of the cavitation caused by the slow refraction waves. The calculated magnetopause structure resembles the observed structure for northward interplanetary magnetic field (IMF). However, for southward IMF, the MHD result shows the existence of a depletion layer, which is not supported by observations. We also show that on the magnetosheath side, the Walen relation, which is exact for a rotational discontinuity, can also be well satisfied by a slow shock, an intermediate shock, or the head of a slow rarefaction wave.

Wu, C. C.↗
NASA NTRS1995

Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma

In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue -- a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index gamma and a dimensionless quantity kappa the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and gamma. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for gamma greater than 1 and all values of kappa, only oscillations are possible. For gamma less than 1, however, both oscillations and expansion are allowed. For gamma less than 1 and kappa below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For gamma less than 1 and kappa above critical, however, only expansion occurs. Thus by increasing kappa while keeping gamma fixed (less than 1), a phase transition occurs at kappa = kappa(sub critical) and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self-similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases critical conditions can occur for gamma greater than 1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of kappa and gamma, collapse may be averted.

Osherovich, V. A.↗
NASA NTRS1989

Cross correlation and length scales in turbulent flows near surfaces

Two kinds of length scales are used in turbulent flows; 'functional length scales' such as mixing length, dissipation length L(sub epsilon), etc., and 'flow-field length scales' derived from cross correlations of velocity, pressure, etc. in the flow. Some connection between these scales are derived here. We first consider the cross correlation R(sub vv)(y,y(sub 1)) of the normal components u at two heights y, y(sub 1) above a rigid surface, normalized by the velocity y(sub 1) (greater than y). For shear-free boundary layers it is found theoretically, and in field and numerical experiments that R(sub vv) approximately equals y/y(sub 1). For shear layers it is also found that R(sub vv) approximately equals f(y/y(sub 1)) less than or equal to y,y(sub 1). This function f differs slightly between low Reynolds number numerical simulations and field experiments. The lateral structure defined by R(sub vv)(y,r(sub 3); y(sub 1),0) is also self similar and shows that the eddies centered at about y(sub 1) appear to have constant lateral width a(sub 3) above and below y(sub 1), where a(sub 3, sup +) approximately equals 7+1/(1.4dU(sup +)/dy(sup +)), when normalized on u(sub *) and v, where U is the mean velocity. Results for L(sub epsilon, sup -1) from direct numerical simulation are found to compare well with the formula L(sub epsilon, sup -1) = A(sub B)/y + A(sub S)dU/dy/v, for unidirectional and reversing turbulent boundary layers and channel flow, except near where dU/dy approximately equals 0. The conclusion is that the large-scale eddy structure and length scales in these flows are determined by a combination of shear and blocking, and that the vertical component of turbulence has a self-similar structure in both kinds of boundary layer.

Hunt, J. C. R.↗
NASA NTRS1995

The 11 Micron Emissions of Carbon Stars

A new classification scheme of the IRAS LRS carbon stars is presented. It comprises the separation of 718 probable carbon stars into 12 distinct self-similar spectral groupings. Continuum temperatures are assigned and range from 470 to 5000 K. Three distinct dust species are identifiable: SiC, alpha:C-H, and MgS. In addition to the narrow 11 + micron emission feature that is commonly attributed to SiC, a broad 11 + micron emission feature, that is correlated with the 8.5 and 7.7 micron features, is found and attributed to alpha:C-H. SiC and alpha:C-H band strengths are found to correlate with the temperature progression among the Classes. We find a spectral sequence of Classes that reflects the carbon star evolutionary sequence of spectral types, or alternatively developmental sequences of grain condensation in carbon-rich circumstellar shells. If decreasing temperature corresponds to increasing evolution, then decreasing temperature corresponds to increasing C/O resulting in increasing amounts of carbon rich dust, namely alpha:C-H. If decreasing the temperature corresponds to a grain condensation sequence, then heterogeneous, or induced nucleation scenarios are supported. SiC grains precede alpha:C-H and form the nuclei for the condensation of the latter material. At still lower temperatures, MgS appears to be quite prevalent. No 11.3 micron PAH features are identified in any of the 718 carbon stars. However, one of the coldest objects, IRAS 15048-5702, and a few others, displays an 11.9 micron emission feature characteristic of laboratory samples of coronene. That feature corresponds to the C-H out of plane deformation mode of aromatic hydrocarbon. This band indicates the presence of unsaturated, sp(sup 3), hydrocarbon bonds that may subsequently evolve into saturated bonds, sp(sup 2), if, and when, the star enters the planetary nebulae phase of stellar evolution. The effusion of hydrogen from the hydrocarbon grain results in the evolution in wavelength of this 11.9 micron emission feature to the 11.3 micron feature.

Goebel, J. H.↗
NASA NTRS1995

The 11 Micron Emissions of Cabon Stars

A new classification scheme of the IRAS LRS carbon stars is presented. It comprises the separation of 718 probable carbon stars into 12 distinct self-similar spectral groupings. Continuum temperatures are assigned and range from 470 to 5000 K. Three distinct dust species are identifiable: SiC, alpha:C-H, and MgS. In addition to the narrow 11 + micron emission feature that is commonly attributed to SiC, a broad 11 + micron emission feature, that is correlated with the 8.5 and 7.7 micron features, is found and attributed to alpha:C-H. SiC and alpha:C-H band strengths are found to correlate with the temperature progression among the Classes. We find a spectral sequence of Classes that reflects the carbon star evolutionary sequence of spectral types, or alternatively developmental sequences of grain condensation in carbon-rich circumstellar shells. If decreasing temperature corresponds to increasing evolution, then decreasing temperature corresponds to increasing CIO resulting in increasing amounts of carbon rich dust, namely alpha:C-H. If decreasing the temperature corresponds to a grain condensation sequence, then heterogeneous, or induced nucleation scenarios are supported. SiC grains precede alpha:C-H and form the nuclei for the condensation of the latter material. At still lower temperatures, MgS appears to be quite prevalent. No 11.3 micron PAH features are identified in any of the 718 carbon stars. However, one of the coldest objects, IRAS 15048-5702, and a few others, displays an 11.9 micron emission feature characteristic of laboratory samples of coronene. That feature corresponds to the C-H out of plane deformation mode of aromatic hydrocarbon. This band indicates the presence of unsaturated, sp(sup 3), hydrocarbon bonds that may subsequently evolve into saturated bonds, sp(sup 2), if, and when, the star enters the planetary nebulae phase of stellar evolution. The effusion of hydrogen from the hydrocarbon grain results in the evolution in wavelength of this 11.9 micron emission feature to the 11.3 micron feature.

Goebel, J. H.↗
NASA NTRS1995

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(exp -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Tsai, John C.↗
NASA NTRS1995

The Distance to the Heliospheric VLF Emission Region

Two major episodes of heliospheric VLF emissions near 3 kHz have been observed by the Voyager spacecraft in 1983-1984 and 1992-1993. This higher-frequency component is apparently triggered by solar wind transients with sufficiently large spatial extents and energies to continue to propagate as shocks in the heliosheath. Entrainment of previously unshocked material and changed flow conditions in the heliosheath both tend to slow the shock propagation. The shock evolution is not self-similar. Rather, it is intermediate to two blast-wave similarity solutions in the moving solar wind frame. In one solution the shock moves as time to the 2/3 power and in the other as time to the 4/5 power. Using these models, the shock/Forbush decrease observed at Voyager 2 in September, 1991 and the turn-on of the 1992 emission is consistent with an emission region distance of approx. 130 AU (assuming no additional slowing of the shock in the heliosheath). If the termination shock was at approx. 70 AU when the transient shock collided with it, the true distance to the source region was probably closer to approx. 115 AU.

McNutt, R. L., Jr.↗
NASA NTRS1995

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(sup -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Tsai, John C.↗
NASA NTRS1983

Stability and Interaction of Coherent Structure in Supersonic Reactive Wakes

A theoretical formulation and analysis is presented for a study of the stability and interaction of coherent structure in reacting free shear layers. The physical problem under investigation is a premixed hydrogen-oxygen reacting shear layer in the wake of a thin flat plate. The coherent structure is modeled as a periodic disturbance and its stability is determined by the application of linearized hydrodynamic stability theory which results in a generalized eigenvalue problem for reactive flows. Detailed stability analysis of the reactive wake for neutral, symmetrical and antisymmetrical disturbance is presented. Reactive stability criteria is shown to be quite different from classical non-reactive stability. The interaction between the mean flow, coherent structure and fine-scale turbulence is theoretically formulated using the von-Kaman integral technique. Both time-averaging and conditional phase averaging are necessary to separate the three types of motion. The resulting integro-differential equations can then be solved subject to initial conditions with appropriate shape functions. In the laminar flow transition region of interest, the spatial interaction between the mean motion and coherent structure is calculated for both non-reactive and reactive conditions and compared with experimental data wherever available. The fine-scale turbulent motion determined by the application of integral analysis to the fluctuation equations. Since at present this turbulence model is still untested, turbulence is modeled in the interaction problem by a simple algebraic eddy viscosity model. The applicability of the integral turbulence model formulated here is studied parametrically by integrating these equations for the simple case of self-similar mean motion with assumed shape functions. The effect of the motion of the coherent structure is studied and very good agreement is obtained with previous experimental and theoretical works for non-reactive flow. For the reactive case, lack of experimental data made direct comparison difficult. It was determined that the growth rate of the disturbance amplitude is lower for reactive case. The results indicate that the reactive flow stability is in qualitative agreement with experimental observation.

Menon, Suresh↗
NASA NTRS1994

Sonic and Supersonic Jet Plumes

Study of sonic and supersonic jet plumes are relevant to understanding such phenomenon as jet-noise, plume signatures, and rocket base-heating and radiation. Jet plumes are simple to simulate and yet, have complex flow structures such as Mach disks, triple points, shear-layers, barrel shocks, shock- shear- layer interaction, etc. Experimental and computational simulation of sonic and supersonic jet plumes have been performed for under- and over-expanded, axisymmetric plume conditions. The computational simulation compare very well with the experimental observations of schlieren pictures. Experimental data such as temperature measurements with hot-wire probes are yet to be measured and will be compared with computed values. Extensive analysis of the computational simulations presents a clear picture of how the complex flow structure develops and the conditions under which self-similar flow structures evolve. From the computations, the plume structure can be further classified into many sub-groups. In the proposed paper, detail results from the experimental and computational simulations for single, axisymmetric, under- and over-expanded, sonic and supersonic plumes will be compared and the fluid dynamic aspects of flow structures will be discussed.

Venkatapathy, E.↗
NASA NTRS1994

Experimental and Computational Study of Sonic and Supersonic Jet Plumes

Study of sonic and supersonic jet plumes are relevant to understanding such phenomenon as jet-noise, plume signatures, and rocket base-heating and radiation. Jet plumes are simple to simulate and yet, have complex flow structures such as Mach disks, triple points, shear-layers, barrel shocks, shock-shear-layer interaction, etc. Experimental and computational simulation of sonic and supersonic jet plumes have been performed for under- and over-expanded, axisymmetric plume conditions. The computational simulation compare very well with the experimental observations of schlieren pictures. Experimental data such as temperature measurements with hot-wire probes are yet to be measured and will be compared with computed values. Extensive analysis of the computational simulations presents a clear picture of how the complex flow structure develops and the conditions under which self-similar flow structures evolve. From the computations, the plume structure can be further classified into many sub-groups. In the proposed paper, detail results from the experimental and computational simulations for single, axisymmetric, under- and over-expanded, sonic and supersonic plumes will be compared and the fluid dynamic aspects of flow structures will be discussed.

Venkatapathy, E.↗
NASA NTRS1995

Linear Stability Regime Analysis of the Compressible Reacting Mixing Layer

Previous investigations have shown that a compressible reacting mixing layer can develop two peaks in the mean density weighted vorticity profile. Linear stability analyses show that at these peaks two distinct 'outer' instability modes appear in addition to the more common central mode, which exists unaccompanied in incompressible nonreacting flows. The present study parametrically analyzes the effects of compressibility, heat release, stoichiometry, and density ratio on the amplification rate and obliquity of each stability mode. The mean profiles used in the spatial stability calculation are generated by self-similar solutions of the compressible boundary layer equations combined with the assumption of infinitely fast chemistry. It is shown that the influence of stoichiometry and density ratio on the peaks of the density weighted vorticity profile determines which modes will dominate. Of particular interest are the conditions where two modes are equally amplified, causing the mixing layer to develop into a 'colayer' structure.

Day, M. J.↗