Stability theory for ordinary differential equations.
LaSalle stability theorems refined for ordinary differential equations, discussing classical Liapunov results on system stability
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LaSalle stability theorems refined for ordinary differential equations, discussing classical Liapunov results on system stability
Stability and asymptotic behavior of dynamical systems defined by autonomous functional or partial differential equation and conditions for applying Liapunov theorem
Proof of Hermite-Fujiwara theorem of dynamic system stability based on Liapunov-type methods
Extended dynamical system to describe operators in study of stability
Liapunov function for analyzing stability of nonlinear equilibrium solutions in hydrodynamics
Existence, uniqueness, and stability criteria for linear and nonlinear operational differential equations in Banach and Hilbert spaces
The linear stability of a fully three-dimensional boundary layer formed over a general aviation fuselage was investigated. The location of the onset of transition was estimated using the N-factor method. The results were compared with existing experimental data and indicate N-factors of approximately 8.5 on the side of the fuselage and 3.0 near the top. Considerable crossflow existed along the side of the body, which significantly affected the unstable modes present in the boundary layer. Fair agreement was found between the predicted frequency range of linear instability modes and available experimental data concerning the spectral content of the boundary layer.
Recent developments of the SALLY computer code for stability analysis of laminar flow control wings are summarized. Extensions of SALLY to study three dimensional compressible flows, nonparallel and nonlinear effects are discussed.
Analytical methods to determine capability of space vehicle guidance system, and Liapunov functions for stability of nonlinear systems
The method used by Drazin to investigate the stability of unbounded, viscous, homogeneous, parallel shear flow to small wavenumber disturbances is extended to study the effect of thermal stratification on the stability of unbounded jets and shear layers. By this method the stability characteristics of continuous profiles are inferred from the stability characteristics of discontinuous profiles. The characteristic value problem for discontinuous jet and shear layers is posed by the requirement that the solutions of the governing differential equation satisfy the matching conditions and boundedness conditions for layers that extend to infinity. The analysis leads to a characteristic determinant which is required to vanish for the characteristic values of the parameters: the Reynolds number, the wavenumber, and the wave speed. The stabilizing effect of the thermal stratification as parameterized by the Richardson number was found to be most stabilizing for small wavenumber (large-scale) disturbances.
Extending Liapunov second method by simultaneous use of several functions and of higher order derivatives in criteria for motion stability
The effects of normal mass injection and suction on boundary-layer stability and transition are studied on a flat plate. Titanium panels, in which 0.063 mm diameter holes were drilled on 0.635 mm centers, are inserted in the plate. Suction level and distribution are variable. Disturbances are introduced by means of a vibrating ribbon and measurements of both mean- and disturbance-flow velocities are made with a hot wire. Disturbance amplitudes are measured as a function of Reynolds number, frequency, and suction characteristics, and are compared with the previous results obtained over a Dynapore surface. Transition measurements under natural and forced conditions are also made. The stabilizing effects of suction are documented. It is also shown that very high local flow rates through the suction holes (which approach a hole Reynolds number of 300) do not destabilize the flow. On the other hand, weak blowing lowers the transition Reynolds number, but is found not to cause serious problems.
Past work on the influence of Mach number on the viscous and inviscid instability of flat-plate boundary layers is reviewed, and new spatial calculations are presented. These calculations support the previous view that viscosity is only stabilizing for both two- and three-dimensional first-mode waves above M1 = 3.0, and for second-mode waves at all Mach numbers. It is concluded that the calculations of Wazzan, Taghavi, and Keltner that show viscous instability at M1 = 6.0 for first-mode 50 deg waves, and at M1 = 3.0 for two-dimensional second-mode waves, are not correct.
A model for dendritic growth in a binary alloy melt, in the presence of a positive temperature gradient in the liquid, is presented. The model describes satisfactorily the transition from a dendritic interface to a planar interface at very low and very large growth rates. A dendrite tip stability parameter is derived, strictly from steady state considerations, without resorting to a perturbation analysis. The estimates of the parameter agree with those obtained by models based on perturbation analyses.
The morphological instability of a growing epitaxially strained dislocation-free solid film is analyzed. An evolution equation for the film surface is derived in the dilute limit of vacancies based on surface diffusion driven by a stress-dependent chemical potential. From the time-dependent linear stability problem the conditions for which a growing film is unstable are determined. It is found that the instability is driven by the lattice mismatch between the film and the substrate; however, low temperatures as well as elastically stiff substrates are stabilizing influences. The results also reveal that the critical film thickness for instability depends on the growth rate of the film itself. Detailed comparison with experimental observations indicates that the instability described exhibits many of the observed features of the onset of the 'island instability'.
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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.
Measurements of waves initiated by wind-tunnel sounds are obtained for both supersonic and hypersonic speed. Flat-plate experiments carried out at Mach numbers of 4.5, 3.7, and 2.4 under the condition of laminar tunnel-wall boundary layers whereby a low background fluctuation level prevailed are outlined, as well as flat-plate experiments with sound-induced waves at supersonic speeds. Experimental studies of 'natural' wave growth on sharp cones at zero angle of attack and Mach numbers near 8 are discussed. Attention is focused on experimental research needed on boundary-layer receptivity to eddy Mach-wave radiation, hypersonic speed, and the stability-transition relationship in zero-pressure-gradient layers.