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Goldstein, M. E.

Publications and source records attributed to Goldstein, M. E..

At least 37 records · Page 2
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NASA NTRS1991

Noise from turbulent shear flows

The generation of sound in turbulent shear flows with high Reynolds numbers is discussed. Solid surface effects, representation of incident turbulence, sound generation and the role of instability waves, sound generation by turbulence interacting with itself (the jet noise problem), compressible Rayleigh equations, sound generation from streamwise variations in mean flow, complex turbulent flows, and supersonic flows are among the topics discussed.

Goldstein, M. E.↗
NASA NTRS1990

The effect of small streamwise velocity distortion on the boundary layer flow over a thin flat plate with application to boundary layer stability theory

Researchers show how an initially linear spanwise disturbance in the free stream velocity field is amplified by leading edge bluntness effects and ultimately leads to a small amplitude but linear spanwise motion far downstream from the edge. This spanwise motion is imposed on the boundary layer flow and ultimately causes an order-one change in its profile shape. The modified profiles are highly unstable and can support Tollmein-Schlichting wave growth well upstream of the theoretical lower branch of the neutral stability curve for a Blasius boundary layer.

Goldstein, M. E.↗
NASA NTRS1990

Spatial evolution of nonlinear acoustic mode instabilities on hypersonic boundary layers

The effects are considered of strong critical layer nonlinearity on the spatial evolution of an initially linear acoustic mode instability wave on a hypersonic flat plate boundary layer. The analysis shows that nonlinearity, which is initially confined to a thin critical layer, first becomes important when the amplitude of the pressure fluctuations become O(1/M exp 4 in M exp 2), where M is the free stream Mach number. The flow outside the critical layer is still determined by linear dynamics and therefore takes the form of a linear instability wave, but with its amplitude completely determined by the flow within the critical layer. The latter flow is determined by a coupled set of nonlinear equations, which were solved numerically.

Goldstein, M. E.↗
NASA NTRS1990

On the instabilities of supersonic mixing layers - A high-Mach-number asymptotic theory

The stability of a family of tanh mixing layers is studied at large Mach numbers using perturbation methods. It is found that the eigenfunction develops a multilayered structure, and the eigenvalue is obtained by solving a simplified version of the Rayleigh equation (with homogeneous boundary conditions) in one of these layers which lies in either of the external streams. This analysis leads to a simple hypersonic similarity law which explains how spatial and temporal phase speeds and growth rates scale with Mach number and temperature ratio. Comparisons are made with numerical results, and it is found that this similarity law provides a good qualitative guide for the behavior of the instability at high Mach numbers. In addition to this asymptotic theory, some fully numerical results are also presented (with no limitation on the Mach number) in order to explain the origin of the hypersonic modes (through mode splitting) and to discuss the role of oblique modes over a very wide range of Mach number and temperature ratio.

Balsa, Thomas F.↗
NASA NTRS1990

Nonlinear spatial evolution of externally excited instability waves in free shear layers

The effects of critical-layer nonlinearity on spatially growing instability waves on shear layers between parallel streams are considered. In the two-dimensional incompressible case, the flow in the critical layer is governed by a nonequilibrium, nonlinear vorticity equation. The initial exponential growth of the instability wave is converted into algebraic growth during the streamwise 'aging' of the critical layer into a quasi-equilibrium state. This leads to a next stage of evolution where the instability-wave growth is affected by both mean-flow-divergence and nonlinear effects and is eventually converted to decay. A uniformly valid composite formula for the instability wave amplitude, accounting for both nonparallel and nonlinear effects, is given and compared to experimental results. The inviscid solutions to these equations always end in a singularity at finite downstream distance.

Hultgren, L. S.↗
NASA NTRS1989

Spatial evolution of nonlinear acoustic mode instabilities on hypersonic boundary layers

The effects are considered of strong critical layer nonlinearity on the spatial evolution of an initially linear acoustic mode instability wave on a hypersonic flat plate boundary layer. The analysis shows that nonlinearity, which is initially confined to a thin critical layer, first becomes important when the amplitude of the pressure fluctuations become 0(1/M exp 4 In M exp 2), where M is the free stream Mach number. The flow outside the critical layer is still determined by linear dynamics and therefore takes the form of a linear instability wave, but with its amplitude completely determined by the flow within the critical layer. The latter flow is determined by a coupled set of nonlinear equations, which were solved numerically.

Goldstein, M. E.↗
NASA NTRS1989

Nonlinear evolution of oblique waves on compressible shear layers

The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.

Goldstein, M. E.↗
NASA NTRS1989

Nonlinear evolution of interacting oblique waves on two-dimensional shear layers

The effects of critical layer nonlinearity are considered on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. The numerical solutions always end in a singularity at a finite downstream distance.

Goldstein, M. E.↗
NASA NTRS1989

Nonlinear evolution of interacting oblique waves on two-dimensional shear layers

The effects of critical layer nonlinearity are considered on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. The numerical solutions always end in a singularity at a finite downstream distance.

Goldstein, M. E.↗
NASA NTRS1989

Nonlinear interaction between the sinuous and varicose instability modes in a plane wake

The nonlinear interaction between sinuous and varicose instability modes in a plane wake is examined in the nonlinear-nonequilibrium critical layer regime. Equations governing the evolution of the instability wave amplitudes and critical layer vorticity distributions are derived. Numerical solutions for these equations are obtained for a number of wake defects and initial amplitude ratios. The results show that the primary effects of the nonlinear interaction are the suppression of the varicose mode and the downstream shift of the peak of the sinuous mode.

Leib, S. J.↗
NASA NTRS1989

Boundary-layer receptivity to long-wave free-stream disturbances

The present treatment of the early stages of boundary layer-transition phenomena, where the unsteady motion is of small amplitude and can be accordingly treated as a small perturbation of an appropriate mean flow, elaborates the Heinrich et al. (1988) discussion of the role played by this 'receptivity' stage: in which the unsteady flow exhibits the same harmonic time-dependence as the externally-imposed forcing. Freestream disturbance wavelengths are noted to often be much longer than the Tollmien-Schlichting wavelength. Attention is given to the variety of wavelength-reduction mechanisms able to couple the long-wavelength, freestream disturbances to the comparatively short Tollmien-Schlichting waves.

Goldstein, M. E.↗
NASA NTRS1988

Nonlinear spatial evolution of an externally excited instability wave in a free shear layer

This paper considers a disturbance evolving from a strictly linear finite-growth-rate instability wave, with nonlinear effects first becoming important in the critical layer. By incorporating viscous effects into the nonlinear critical-layer analysis of Goldstein and Leib (1988), it was possible to demonstrate how an initially linear instability wave evolves as it propagates downstream and how the viscous effects eventually become important, even when the viscosity is very small, due to continually decreasing scales generated by the nonlinear effects.

Goldstein, M. E.↗
NASA NTRS1988

Nonlinear roll-up of externally excited free shear layers

The effects of strong critical-layer nonlinearity on the spatially growing instabilities of a shear layer between two parallel streams are considered. A composite expansion technique is used to obtain a single formula that accounts for both shear-layer spreading and nonlinear critical-layer effects. Nonlinearity causes the instability to saturate well upstream of the linear neutral stability point. It also produces vorticity roll-up that cannot be predicted by linear theory.

Goldstein, M. E.↗
NASA NTRS1987

Roll-up of vorticity in adverse-pressure-gradient boundary layers

It is shown how the unsteady, nonlinear critical-layer equation determines the evolution of instability waves in a weak adverse-pressure-gradient boundary layer. Numerical solutions show that the nonlinearity halts the growth of these inviscidly unstable waves. The stabilizing effect of nonlinearity, in the present case, can be described as a consequence of either the increase (toward zero) of the phase jump across the critical layer or the roll-up of the critical-layer disturbance vorticity.

Goldstein, M. E.↗
NASA NTRS1987

Generation of Tollmien-Schlichting waves on interactive marginally separated flows

This paper is concerned with the interaction of very-long-wavelength free-stream disturbances with the small but abrupt changes in the mean flow that occur near the minimum-skin-friction point in an interactive marginally separated boundary layer. The source frequency is chosen so that the eigensolutions with that frequency have an 'interactive' structure in the region of marginal separation. The eigensolution wavelength scale must then differ from the lengthscale of the marginal separation, and a composite expansion technique has to be used to obtain the solution. The initial instability wave amplitude turns out to be exponentially small, but eventually dominates the original disturbance owing to its exponential growth. It then begins to decay but ultimately turns into a standard spatially growing Tollmien-Schlichting wave much further downstream.

Goldstein, M. E.↗
NASA NTRS1987

A note on the generation of Tollmien-Schlichting waves by sudden surface-curvature change

This note is primarily concerned with the generation of spatially growing Tollmien-Schlichting waves by the interaction of very long-wavelength free-stream disturbances with a discontinuity in the curvature of a bounding surface (whose slope may or may not be continuous). The theory is combined with a numerical solution of the local Orr-Sommerfeld equation, and the result is used to predict the Tollmien-Schlichting amplitude in a relevant experiment carried out by Leehey and Shapiro (1980). The calculated results are in satisfactory agreement with their observations.

Goldstein, M. E.↗
NASA NTRS1987

The generation of Tollmien-Schlichting waves by long wavelength free stream disturbances

The paper is primarily concerned with explaining how very long wavelength free stream disturbances are able to generate very short wavelength Tollmien-Schlichting waves in laminar boundary layers. Consideration is given to the case where the disturbances are of small amplitude and have harmonic time dependence and where the Mach number is effectively zero. It is shown that the free stream wavelength reduction occurs as a result of nonparallel flow effects which can arise from: (1) the slow viscous growth of the boundary layer, and (2) small but abrupt changes in surface geometry that produce only very weak static pressure variations. Analyses of these two mechanisms are carried out by linearizing the unsteady motion about an appropriate steady flow and asymptotically expanding the result in inverse powers of an appropriate Reynolds number. The analyses are compared with each other and with available experimental data, and they are used to explain the physics of the two mechanisms.

Goldstein, M. E.↗