Search NASA⌕ Search

SEARCH · Search NASA

Results for “ASYMPTOTIC SOLUTIONS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Pulse asymptotics of three-dimensional baroclinic waves

The asymptotic development at large time of waves arising from localized disturbances in a baroclinic flow is examined. Vertical structures unlike those associated with the more commonly examined temporal normal modes are found both for the pulse confined to a channel as previously examined, and for the unconfined pulse on an infinite beta-plane. These structures and their implied transports are compared to observations in the regions of storm tracks. It is also found that the meridional extent of the asymptotic solution becomes large compared to observed cyclone wavetrains, emphasizing the importance of flow inhomogeneity and sphericity effects in determining the latitudinal structure of eddies.

Farrell, B. F.↗
NASA NTRS1984

Tearing instability in an anisotropic neutral sheet

A study is made of the collisionless tearing-mode stability properties of a field-reversed plasma layer whose temperature distribution is anisotropic. The plasma is confined by its self magnetic field with no external field. A kinetic description is used for both ions and electrons. The effects of the axis-crossing and nonaxis-crossing orbits are discussed. It is found that the conventional technique of matching the inner and outer asymptotic solutions at the electron inner-region is inadequate for the anisotropic case. An intermediate region in which the axis-crossing ion orbits are important is identified. The eigenvalue equation is solved using both analytic approximations and numerical methods to obtain the eigenmode structure and the linear dispersion relation. Previously announced in STAR as N84-14920

Chen, J.↗
NASA NTRS1984

Numerical studies of motion of vortex filaments - Implementing the asymptotic analysis

A computational code is developed for the integro-differential equations governing the motion of the centerlines of vortex filaments submerged in a background potential flow. These equations, which are derived from the method of matched asymptotic analysis, include the effect of the decaying large-magnitude circumferential and axial velocity components in the vortical cores. Numerical examples are presented to assess the effect of a large axial velocity and that of nonsimilar initial profiles in the vortical cores. The initial configurations of the filaments are chosen so as to fulfill the basic assumption of the asymptotic analysis, which is that the effective vortical core size is much smaller than all the other length scales in the flowfield, e.g., the radius of curvature and the interfilament distance. The computations are continued until the basic assumption is no longer valid, that is when the merging or intersection of filaments has begun. A classification of the various types of local or global merging or intersection of filaments is made and demonstrated by numerical examples. It is then shown that the asymptotic solution not only provides the initial data but also can be used to formulate the appropriate boundary conditions for the numerical solution of a merged region.

Liu, C. H.↗
NASA NTRS1984

Numerical calculations of complex Mach reflection

Numerical simulations of the interaction of a planar blast wave with a compression ramp are presented. The split coefficient matrix (SCM) method in conjunction with boundary shock and floating discontinuity-fitting procedures was employed to obtain the time-asymptotic solutions of the two-dimensional, unsteady Euler equations. The solutions were computed for the complex Mach reflection (CMR) regime of the shock diffraction problem in an attempt to explore the basic physical process governing the evolution of an incipient second Mach stem and the associated topological changes. Numerical results were obtained for shock diffraction over a 40 degree ramp with varying incident shock Mach numbers. The validity of the present approach has been substantiated by experimental observations and earlier numerical calculations.

Yamamoto, O.↗
NASA NTRS1984

Higher-order parabolic approximations for sound propagation in stratified moving media

Asymptotic solutions of order k-n are developed for the equations governing the propagation of sound through a stratified moving medium. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial differential equations. These corrections account for the diffraction effects caused by variation of the field normal to the ray path and the interaction of these transverse variations with the variation of the field along the ray. The theory is illustrated by application to simple examples.

Mcaninch, G. L.↗
NASA NTRS1985

Modeling the effects of latitudinal gradients in stellar winds, with application to the solar wind

A steady, axisymmetric, quasi-radial, global model previously developed for stellar winds with embedded magnetic fields has been extended to include latitudinal gradient effects on the azimuthal velocity and magnetic field. The linear results at large radii are presented for large-amplitude latitudinal variations in the radial magnetic field, mass loss rate, and radial velocity of the wind. The magnetohydrodynamic (MHD) equations predict meridional flows that develop naturally from internal magnetic stresses. The flows open flux tubes in the star's equatorial plane, redistributing mass and magnetic flux as a function of stellar latitude. The plasma spins up to conserve angular momentum in fields and plasma. The results are generally applicable to stellar winds (including radiatively driven winds), provided that the internal structure is not dominated by rotation. The asymptotic solutions do not explicitly depend on the form of the energy equation, although the assumed O(1) state which drives these solutions depends on the deposition of energy and momentum throughout the wind.

Nerney, S.↗
NASA NTRS1985

Thermocapillary Flows and Their Stability: Effects of Surface Layers and Contamination

The objective is to study quantitatively thermocapillary flows in two-dimensional and axisymmetric geometries in order to learn the impact of such flows on float-zone refining configurations. The work begins with the analytical study of steady flows in slots and zones to obtain predictions of surface curvature, flow and heat transport. It then examines the instability of such flows. Three new instability mechanisms have been identified and the results show that thermocapillary flows of high Prandtl number fluid become convectively unstable while those of low Prandtl number fluid become hydrodynamically unstable. The work includes numerical simulations of steady, high Marangoni number flows in unit aspect ratio boxes and asymptotic solutions in large boxes. Furthermore, the effect of surface contamination on the steady thermocapillary flows was examined. This fundamental study focused on fluid dynamical systems used to understand events in the flow of melts in float-zone geometries both on Earth and in microgravity environments.

Davis, S. H.↗
NASA NTRS1986

Higher order parabolic approximations of the reduced wave equation

Asymptotic solutions of order k to the nth are developed for the reduced wave equation. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory, and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial differential equations. These corrections account for the diffraction effects caused by variation of the field normal to the ray path and the interaction of these transverse variations with the variation of the field along the ray. The theory is applied to the example of radiation from a piston, and it is demonstrated that the higher order approximations are more accurate for decreasing values of k.

Mcaninch, G. L.↗
NASA NTRS1986

The neutral curve for stationary disturbances in rotating-disk flow

The neutral curve for stationary vortex disturbances in rotating-disk flow is computed up to a Reynolds number of 10 to the 7th using the sixth-order system of linear stability equations which includes the effects of streamline curvature and Coriolis force. It is found that the neutral curve has two minima: one at R = 285.36 (upper branch) and the other at R = 440.88 (lower branch). At large Reynolds numbers, the upper branch tends to Stuart's asymptotic solution while the lower branch tends to a solution that is associated with the wave angle corresponding to the direction of zero mean wall shear.

Malik, M. R.↗
NASA NTRS1987

The acoustic radiation damping of the modes of a rectangular panel

The acoustic damping for single modes of a finite rectangular panel, simply supported in an infinite baffle, is theoretically determined from the ratio of the acoustic energy radiated per cycle to the vibratory energy of the panel. Asymptotic solutions for the low-frequency region are presented for a panel mode driven at an arbitrary frequency and for a panel mode vibrating at its natural frequency. Curves of acoustic damping for a panel mode vibrating at resonance, as a function of the panel thickness-to-length ratio, are presented for various panel aspect ratios. For panels vibrating below the critical frequency, the damping depends on the aspect ratio with square panels developing the smallest value. For panels vibrating above the critical frequency, the damping is nearly independent of the aspect ratio.

Wallace, C. E.↗
NASA NTRS1986

Viscous vortex flows

Several computational studies are currently being pursued that focus on various aspects of representing the entire lifetime of the viscous trailing vortex wakes generated by an aircraft. The formulation and subsequent near-wing development of the leading-edge vortices formed by a delta wing are being calculated at modest Reynolds numbers using a three-dimensional, time-dependent Navier-Stokes code. Another computational code was developed to focus on the roll-up, trajectory, and mutual interaction of trailing vortices further downstream from the wing using a two-dimensional, time-dependent, Navier-Stokes algorithm. To investigate the effect of a cross-wind ground shear flow on the drift and decay of the far-field trailing vortices, a code was developed that employs Euler equations along with matched asymptotic solutions for the decaying vortex filaments. And finally, to simulate the conditions far down stream after the onset of the Crow instability in the vortex wake, a full three-dimensional, time-dependent Navier-Stokes code was developed to study the behavior of interacting vortex rings.

Weston, R. P.↗
NASA NTRS1988

Acousto-ultrasonic input-output characterization of unidirectional fiber composite plate by SV waves

A unidirectional fiberglass epoxy compostie specimen is modelled as a homogeneous transversely isotropic continuum plate medium. Acousto-ultrasonic noncontact input-output characterization is studied theoretically with a transmitting and a receiving transducer located on the same face of the plate. The single reflection problem for an incident SV wave at a plane boundary in transversely isotropic medium is analyzed. An obliquely incident SV wave results in a reflected SV wave and a reflected P wave for an angle of incidence of the incident SV wave less than the critical angle. Otherwise, there exists only an SV wave in the medium as the reflected P wave degenerates into a surface wave travelling parallel to the plane boundary. The amplitude ratio of the reflected SV wave is -1 when the angle of incidence is greater than or = the critical angle. The directional dependence of the phase velocity of the SV wave propagating in the transversely isotropic medium has a significant effect on the delay time, as opposed to the directional independence of the phase velocity of a shear wave propagating in an isotropic medium. The displacements associated with the SV wave in the plate and which may be detected by the noncontact receiving transducer are approximated by an asymptotic solution for an infinite transversely isotropic medium subjected to a harmonic point load.

Liao, Peter↗
NASA NTRS1988

Acousto-ultrasonic input-output characterization of unidirectional fiber composite plate by P waves

The single reflection problem for an incident P wave at a stress free plane boundary in a semi-infinite transversely isotropic medium whose isotropic plane is parallel to the plane boundary is analyzed. It is found that an obliquely incident P wave results in a reflected P wave and a reflected SV wave. The delay time for propagation between the transmitting and the receiving transducers is computed as if the P waves were propagating in an infinite half space. The displacements associated with the P waves in the plate and which may be detected by a noncontact NDE receiving transducer are approximated by an asymptotic solution for an infinite transversely isotropic medium subjected to a harmonic point load.

Liao, Peter↗
NASA NTRS1988

Mode-medium instability in an unstable resonator

The mode-medium instability of an active medium in an unstable resonator is investigated. The asymptotic solution due to Horwitz (1973), valid for large Fresnel numbers in an empty cavity, is modified by introducing gain/phase sheets in front of the resonator mirrors. The effect of medium coupling to the mode in the cavity is obtained by introducing a general time-independent Green's function in the Fox-Li (1961) formulation. The time evolution is then obtained by repeated integration of the beam propagation in the cavity. The diffractive terms are shown to grow rapidly at the expense of the geometric term. This instability responsible for the deterioration of the beam quality is studied numerically for a CO2 lasing system as an example.

Sung, C. C.↗
NASA NTRS1988

Self-similar dynamics of polytropic gaseous spheres

The fundamental equations governing the self-similar dynamics of 'polytropic' gaseous spheres are derived, and the asymptotic solutions are given. The solutions divide into cases with and without 'critical points' in closed analogy with the solar wind solutions of Holzer and Axford (1970). Properties for solutions with critical points are discussed, and their behavior around the critical point is derived explicitly for n = 1. Numerical examples of self-similar solutions for n = 1 and n = 2 - gamma are presented, and the properties of the solutions are discussed.

Suto, Yasushi↗
NASA NTRS1989

Viscous flow in simple curved gaps. I - An asymptotic theory. II - Viscous stress and shape function

The present asymptotic theory for generalized incompressible two-dimensional steady flow in curved channels has been constructed in the limit when gas thickness approaches zero with its lateral dimensions fixed; successive asymptotic solution terms are analytically generated by quadratures. In the second part of this work, the curvature of the gap treated is arbitrary. It is established that each term in the series solution of velocity and pressure is the product of a scale factor and a universal shape functions. Various interaction modes between the volume rate-of-flow, curvature, and its variations, are identified and quantitatively characterized.

Fan, D.-N.↗
NASA NTRS1990

Asymptotic theory of steady axisymmetrical needlelike crystal growth

The present paper is concerned with the stationary needle crystal growth with arbitrary undercooling. Two classes of asymptotic solutions are discussed: (1) the regular-tip solutions, and (2) the smooth-root solutions. When the surface tension is nonzero, the regular-tip solutions may not have smooth roots. Among the regular-tip solutions, however, one can identify a 'principal regular-tip solution', which has the best behavior in the far field and is physically acceptable.

Xu, Jian-Jun↗
NASA NTRS1990

Analysis of delamination in fiber composite laminates out-of-plane under bending

Delamination in the form of cracking or separation between plies in an advanced fiber composite laminate is a problem of major concern. Both advanced analytical methods and advanced computational analyses are conducted to: (1) develop an asymptotic solution for a composite laminate subject to out-of-plane bending; (2) construct advanced singular finite elements in conjunction with the development of nonsingular elements for this bending problem; and (3) evaluate the delamination failure mechanics parameters and the subsequent modes of fracture. A parametric study was also conducted to evaluate the influences of various lamination parameters on the delaminated composites.

Wang, S. S.↗