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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

The nonlinear evolution of modes on unstable stratified shear layers

The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber, and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by an integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear.

Blackaby, Nicholas↗
NASA NTRS1991

Nonlinear evolution of subsonic and supersonic disturbances on a compressible free shear layer

The effects of a nonlinear-nonequilibrium-viscous critical layer on the spatial evolution of subsonic and supersonic instability modes on a compressible free shear layer is considered. It is shown that the instability wave amplitude is governed by an integrodifferential equation with cubic-type nonlinearity. Numerical and asymptotic solutions to this equation show that the amplitude either ends in a singularity at a finite downstream distance or reaches an equilibrium value, depending on the Prandtl number, viscosity law, viscous parameter and a real parameter which is determined by the linear inviscid stability theory. A necessary condition for the existence of the equilibrium solution is derived, and whether or not this condition is met is determined numerically for a wide range of physical parameters including both subsonic and supersonic disturbances. it is found that no equilibrium solution exists for the subsonic modes unless the temperature ratio of the low-to-high-speed streams exceeds a critical value, while equilibrium solutions for the most rapidly growing supersonic mode exist over most of the parameter range examined.

Leib, S. J.↗
NASA NTRS1965

Shear-wave detection

Angular accelerometers and transducers compared in detection of seismic waves and shear waves

TRANSDUCER↗
NASA NTRS1966

Acoustic Kjeldaas edge in potassium.

Kjeldaas absorption edge in cryogenic potassium for shear magnetoacoustic wave propagation in spherical metallic Fermi surface with spin density wave ground state

SHEAR DISTURBANCE↗
NASA NTRS1989

Measuring Laminar-Separation Bubbles On Airfoils

Nonintrusive multielement heat-transfer sensor overcomes limitations of previous methods. New technique determines simultaneously extent of laminar boundary layer and locations of laminar separation, transition in separated layer, and turbulent reattachment. In tests, only small amounts of heat introduced, and heated thin films caused little disturbance to shear layer or to each other. Promising tool for measurements of stability of laminar boundary layers, separated shear layers, and transitional separation bubbles. Simple and capable of providing comprehensive picture of state of shear flow along entire surface. Significant savings in tunnel (or flight) test time with corresponding savings in cost.

Stack, John P.↗
NASA NTRS1994

Numerical simulations of upstream blocking, columnar disturbances, and bores in stably stratified shear flows over an obstacle

A two-dimensional, nonhydrostatic, elastic numerical model has been used to study the generation of gravity waves for a stably stratified shear flow over an obstacle. When a low-level wind shear is included in the simulation, we find that the predictions for noticeable upstream effects based on Froude number for a uniform flow are no longer accurate. Upstream effects are encountered in the form of upstream propagating columnar disturbances and internal bores away from the obstacle. The limited parameter space studies conducted in this study suggest that the ratio of the shear depth to the obstacle heigh (d/H), the obstacle aspect ratio (H/L), and the Froude number (U/NH) are instrumental in determining the strength and the existence of these upstream disturbances. Thus, the present theoretical and empirical understanding of the importance of the Froude number for determining the nature of upstream effects should be modified substantially to include additional nondimensional parameters when shear is present.

Chen, Chaing↗
NASA NTRS1988

Proximal ecological effects of the 1980 eruptions of Mount St. Helens

The diversity of ecosystems and volcanic processes involved in the 1980 eruptions of Mount St. Helens, southwest Washington, provide an excellent setting for examining effects of volcanic events on ecosystems. These eruptions included a lateral blast, debris avalanche, mudflows, pyroclastic flows, and airfall tephra. Affected ecosystems within 30 km of the vent were lakes, streams, upland and riparian forest, and meadows. Ecological disturbances imposed by the Mount St. Helens events were predominantly physical, rather than climatic or chemical which are the dominant classes of disturbances considered in analysis of global catastrophes. Analysis of ecosystem response to disturbance should be based on consideration of composition and structure of the predisturbance system in terms that represent potential survivability of organisms, mechanisms in the primary disturbance, initial survivors, secondary disturbances arising from the primary disturbance and the biological responses to secondary disturbances, invasion of the site by new propagules, interactions among secondary disturbance processes and surviving and invading organisms. Predicting ecosystem response to disturbance is enchanced by considering the mechanisms of disturbance rather than type of disturbance. In the 1980 Mount St. Helens events, the disturbance types, involved primarily the mechanisms of sedimentation, heating, and shear stress. Each disturbance type involved one or more mechanisms. Ecosystem response varied greatly across the landscape. Analysis of ecosystem response to disturbance, regardless of type, should include detailed consideration of the properties of individual species, primary and secondary disturbance mechanisms, and their distributions across landscapes.

Swanson, F. J.↗
NASA NTRS1995

Large-Amplitude Long-Wave Instability of a Supersonic Shear Layer

For sufficiently high Mach numbers, small disturbances on a supersonic vortex sheet are known to grow in amplitude because of slow nonlinear wave steepening. Under the same external conditions, linear theory predicts slow growth of long-wave disturbances to a thin supersonic shear layer. An asymptotic formulation is given here which adds nonzero shear-layer thickness to the weakly nonlinear formulation for a vortex sheet. Spatial evolution is considered, for a spatially periodic disturbance having amplitude of the same order, in Reynolds number, as the shear-layer thickness. A quasi-equilibrium inviscid nonlinear critical layer is found, with effects of diffusion and slow growth appearing through nonsecularity condition. Other limiting cases are also considered, in an attempt to determine a relationship between the vortex-sheet limit and the long-wave limit for a thin shear layer; there appear to be three special limits, corresponding to disturbances of different amplitudes at different locations along the shear layer.

Messiter, A. F.↗
NASA NTRS2003

Optimal Disturbances in Boundary Layers Subject to Streamwise Pressure Gradient

Laminar-turbulent transition in shear flows is still an enigma in the area of fluid mechanics. The conventional explanation of the phenomenon is based on the instability of the shear flow with respect to infinitesimal disturbances. The conventional hydrodynamic stability theory deals with the analysis of normal modes that might be unstable. The latter circumstance is accompanied by an exponential growth of the disturbances that might lead to laminar-turbulent transition. Nevertheless, in many cases, the transition scenario bypasses the exponential growth stage associated with the normal modes. This type of transition is called bypass transition. An understanding of the phenomenon has eluded us to this day. One possibility is that bypass transition is associated with so-called algebraic (non-modal) growth of disturbances in shear flows. In the present work, an analysis of the optimal disturbances/streamwise vortices associated with the transient growth mechanism is performed for boundary layers in the presence of a streamwise pressure gradient. The theory will provide the optimal spacing of the control elements in the spanwise direction and their placement in the streamwise direction.

Tumin, Anatoli↗
NASA NTRS1999

Disturbance Dynamics in Transitional and Turbulent Flows

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. First the decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr-Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow. Second, homogeneous shear flow, where disturbances can be described by rapid distortion theory (RDT), is studied. The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined.

Grosch, Chester E.↗
NASA NTRS1989

Compressibility and shock wave interaction effects on free shear layers

Two compressible free shear layers with convective Mach numbers of .51 and .86 were studied as baseline configurations to investigate the effects of compressibility on the turbulence characteristics. These shear layers were then disturbed by the placement of an obstruction in the shear layer in an attempt to enhance the shear layer growth rate. These models produced a curved shock in the supersonic side of the shear layer. The results indicate a significant reduction in turbulence levels with increased compressibility. However, there are not any significant changes due to the bow shock interaction with the shear layer.

Samimy, M.↗
NASA NTRS1977

Effects of inviscid parallel shear flows on steady and unsteady aerodynamics and flutter

A general theory of planar disturbances in inviscid parallel shear flows, analogous to thin-wing theory in potential flows, has been developed. Integral relations between surface pressure and deformation are obtained which are similar to, and can be solved by the same numerical methods as, those of potential flow. Computed results are shown which illustrate the effects of a model turbulent boundary layer on various lifting and nonlifting surfaces, including an elastic panel in low supersonic flow and an airfoil control surface in subsonic flow.

Williams, M. H.↗