Linearized theory of stagnation region skin friction and mass transfer at hypersonic speeds
Linearized theory of stagnation region skin friction and mass transfer at hypersonic speeds
Yoshikawa, K. K.↗
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A test of Lee's quasi-linear theory of ion acceleration by interplanetary traveling shocks
Lee's (1983) quasi-linear theory of ion acceleration is tested using ISEE-3 measurements of the November 12, 1978 quasi-parallel interplanetary shock. His theory accounts with varying degrees of precision for the energetic proton spatial profiles; the dependence of the spectral index of the power law proton velocity distribution upon the shock compression ratio; the power law dependence of the upstream proton scalelength upon energy; the absolute magnitude of the upstream proton scale length; the behavior of the energetic proton anisotropy upstream and downstream of the shock; the behavior of the alpha-particle proton ratio upstream; the equality of the spatial scale lengths at the shock of the upstream waves and of the protons that resonate with them; and the dependence of the integrated wave energy density upon the proton energy density at the shock. However, the trace magnetic field frequency spectra disagree with his theory in two ways. The part of the spectrum that can resonate with the observed protons via first-order cyclotron resonance is flat, whereas Lee's theory predicts an f exp - 7/4 frequency dependence for the November 12 shock. Higher frequency waves, which could not resonate with the observed upstream protons, increased in amplitude as the shock approached, suggesting that they too were generated by the shock.
Kennel, C. F.↗
Correlation, evaluation, and extension of linearized theories for tire motion and wheel shimmy
An evaluation is made of the existing theories of a linearized tire motion and wheel shimmy. It is demonstrated that most of the previously published theories represent varying degrees of approximation to a summary theory developed in this report which is a minor modification of the basic theory of Von Schlippe and Dietrich. In most cases where strong differences exist between the previously published theories and summary theory, the previously published theories are shown to possess certain deficiencies. A series of systematic approximations to the summary theory is developed for the treatment of problems too simple to merit the use of the complete summary theory, and procedures are discussed for applying the summary theory and its systematic approximations to the shimmy of more complex landing-gear structures than have previously been considered. Comparisons of the existing experimental data with the predictions of the summary theory and the systematic approximations provide a fair substantiation of the more detailed approximate theories.
Smiley, Robert F↗
Macroscopic quasi-linear theory of the two- stream instability.
Counterstreaming electron beams instability, considering hydrodynamics approximated by macroscopic quasi-linear theory
Voelk, H. J.↗
Linearized Theory of Wind-tunnel Jet-boundary Corrections and Ground Effect for VTOL-STOL Aircraft
A linearized theory is developed to obtain interference factors for wind tunnels and ground effect. The calculated results, presented in tabular form in NASA Technical Notes D-933, D-934, D-935, and D-936, indicate that the degree to which the wake is deflected downward has a primary effect on the magnitude of the interference. When the wake is undeflected the corrections are essentially the same as those of classical theory. When the wake is deflected severely downward, the corrections are primarily determined by the floor of the wind tunnel. Under these conditions, the corrections are, in general, much larger than those given by previously available results. Because of deformations at the lower boundary of the jet, the corrections for an open wind tunnel are uncertain. Testing at low speeds and high lift coefficients in open wind tunnels, therefore, is not recommended. Although the theory is developed expressly for single-element, vanishingly small models, methods, with sample calculations, are given for extending the results to multielement and finite span models. The theory is at least partially verified by available test data; however, complete verification would require a substantially more detailed experimental study.
V/STOL aircraft↗
A new approach to the linear theory of single-species tearing in two-dimensional quasi-neutral sheets
We have developed the linear theory of collisionless ion tearing in a two-dimensional magnetotail equilibrium for a single resonant species. We have solved the normal mode problem for tearing instability by an algorithm that employs particle-in-cell simulation to calculate the orbit integrals in the Maxwell-Vlasov eigenmode equation. The results of our single-species tearing analysis can be applied to ion tearing where electron effects are not included. We have calculated the tearing growth rate as a function of the magnetic field component B(sub n) normal to the current sheet for thick and thin current sheets, and we show that marginal stability occurs when the normal gyrofrequency Omega(sub n) is comparable to the Harris neutral sheet growth rate. A cross-tail B(sub y) component has little effect on the growth rate for B(sub y) approximately = B(sub n). Even in the limit B(sub y) much greater than B(sub n), the mode is strongly stabilized by B(sub n). We report than random pitch angle scattering can overcome the stabilizing effect of B(sub n) and drive the growth rate up toward the Harris neutral sheet (B(sub n) = 0) value when the pitch angle diffusion rate is comparable to Omega(sub n).
Brittnacher, M.↗
Mesoscale lake-effect snowstorms in the vicinity of Lake Michigan - Linear theory and numerical simulations
Mesoscale lake-effect snowstorms in the vicinity of Lake Michigan are studied by a linear steady-state analytic model and a nonlinear time-dependent numerical model with parameterized subgrid-scale physics. The solutions of the linear model show that the orientation of the mean wind field to the surface heating pattern is crucial to the shapes of the disturbances. The results indicate that the relative warmth of the lake surface can induce three updraft centers under a westerly wind, two updraft centers/bands under a northwesterly wind, and a convergence band under a northerly wind. Such convergences are caused by the interaction between the mean wind and the local circulations forced by the curved thermal contrasts. The numerical results from the nonlinear model not only produce convergence patterns very similar to those found in the linear theory and in other numerical studies, but also capture the transient property in some of the lake-induced disturbances. All of these results are qualitatively confirmed by satellite images.
Hsu, Hsiao-Ming↗
Linear theory of equatorial spread F
A fluid dispersion relation for the drift and interchange (Rayleigh-Taylor) modes in a collisional plasma forms the basis for a linear theory of equatorial spread F. The collisional-drift-mode growth rate will exceed the growth rate of the Rayleigh-Taylor mode at short perpendicular wavelengths and density-gradient scale lengths. The drift mode can grow on the top-side as well as the bottom-side density gradients. It is concluded that below the F peak where spread F predominates, both the drift and Rayleigh-Taylor modes contribute to the total spread F spectrum, with the Rayleigh-Taylor mode dominating at long and the drift mode at short perpendicular wavelengths above the ion Larmor radius.
Hudson, M. K.↗
Quasi-linear theory of forced magnetic reconnection for the transition from the linear to the Rutherford regime
Abstract Using the in-viscid two-field reduced magneto-hydrodynamic (MHD) model, a new analytical theory is developed to unify the Hahm–Kulsrud–Taylor (HKT) linear solution and the Rutherford quasi-linear regime. Adopting a quasi-linear approach, we obtain a closed system of equations for plasma response in the Taylor problem. An integral form of an analytical solution is obtained for the forced magnetic reconnection, uniformly valid throughout the entire regimes from the HKT linear solution to the Rutherford quasi-linear solution. In particular, the quasi-linear effect can be described by a single coefficient K s ∝ S 8 / 5 ψ c 2 , where S = τ R τ A and ψ c are the Lundquist number and amplitude of external magnetic perturbation, respectively. The HKT linear solution for the response can be recovered when the index K s → 0. On the other hand, the quasi-linear effect plays a key role in the island growth when K s ~ 1. Our new analytical solution has also been compared with reduced MHD simulations with agreement.
Physics↗
Resonance excitation of spiral density waves in a gaseous disk. I - A linear theory
The wave propagation in a gaseous disk which is self-gravitating and viscous is studied. Waves are generated by an external disturbance and are maintained in motion among forces due to rotation, self-gravity, and pressure. A linear theory is developed for the general case in which all factors are taken into account. The general solution can be applied to the photostellar disk of the solar nebula and the circumstellar disk of a binary in which the effects of self-gravity and pressure are equally important. The theory confirms in great detail that a long wave is excited at one of the Lindblad resonances gravitationally by the external periodic potential, propagates toward the corotation, is reflected before reaching there at the Q-barrier, and finally propagates in the reverse direction toward and past the Lindblad resonance as a short wave.
Yuan, Chi↗
Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations
Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.
Lisano, Michael E.↗
A Linear Theory for Inflatable Plates of Arbitrary Shape
A linear small-deflection theory is developed for the elastic behavior of inflatable plates of which Airmat is an example. Included in the theory are the effects of a small linear taper in the depth of the plate. Solutions are presented for some simple problems in the lateral deflection and vibration of constant-depth rectangular inflatable plates.
McComb, Harvey G., Jr.↗
When is quasi-linear theory exact
We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.
Jones, F. C.↗
A numerical method for the prediction of high-speed boundary-layer transition using linear theory
A method is described of estimating the location of transition in an arbitrary laminar boundary layer on the basis of linear stability theory. After an examination of experimental evidence for the relation between linear stability theory and transition, a discussion is given of the three essential elements of a transition calculation: (1) the interaction of the external disturbances with the boundary layer; (2) the growth of the disturbances in the boundary layer; and (3) a transition criterion. The computer program which carried out these three calculations is described. The program is first tested by calculating the effect of free-stream turbulence on the transition of the Blasius boundary layer, and is then applied to the problem of transition in a supersonic wind tunnel. The effects of unit Reynolds number and Mach number on the transition of an insulated flat-plate boundary layer are calculated on the basis of experimental data on the intensity and spectrum of free-stream disturbances. Reasonable agreement with experiment is obtained in the Mach number range from 2 to 4.5.
Mack, L. M.↗
Linear Theory of Electromagnetic Ion Beam Instabilities in the Earth’s Forshock: Peter Gary’s Contributions (1981–1991)
We discuss Peter Gary’s contributions to the understanding of the origin and properties of ultra-low frequency (ULF) waves in the Earth’s foreshock during the period when the International Sun Earth Explorer spacecraft (ISEE-1 and -2) provided unique data about the plasma and wave environment in this region. Peter’s work concerning the linear theory of electromagnetic ion beam instabilities is contained in five journal articles and then summarized in a review article, all of which are discussed here. Brief summaries of observations and theory prior to ISEE as well as to later work are also included.
79 ASTRONOMY AND ASTROPHYSICS↗
Linear Theory of Electromagnetic Ion Beam Instabilities in the Earth’s Forshock: Peter Gary’s Contributions (1981-1991)
We discuss Peter Gary’s contributions to the understanding of the origin and properties of ultra-low frequency (ULF) waves in the Earth’s foreshock during the period when the International Sun Earth Explorer spacecraft (ISEE-1 and -2) provided unique data about the plasma and wave environment in this region. Peter’s work concerning the linear theory of electromagnetic ion beam instabilities is contained in five journal articles and then summarized in a review article, all of which are discussed here. Brief summaries of observations and theory prior to ISEE as well as to later work are also included.
Dan Winske↗
Linearized theory of radiative heat transfer for ablating bodies at meteoric speeds.
Linearized radiative heat transfer theory for ablating bodies flying in earth atmosphere at meteoric speeds
Yoshikawa, K. K.↗
Artificial ion beam instabilities. I - Linear theory. II - Simulations
Some of the important plasma instabilities that result when an artificial ion beam is injected into the ionospheric F region are studied using linear Vlasov theory. The variation in wave spectra at the receiver as the receiver and plasma gun separate perpendicularly to the magnetic field is consistent with a beam density decrease at or near the receiver. At separation distances that are large fractions of the beam gyrodiameter, usually narrow-band waves near the background lower hybrid and H+ gyroharmonic frequencies are measured. These observations are consistent with waves expected to be generated by beam densities on the order of or less than a few percent of the background density. At smaller separation distances, broadband waves are usually observed with frequencies from zero up to and above the lower hybrid frequency. Electrostatic particle simulation studies of the plasma instabilities indicate that the broadband fluidlike lower hybrid instability is the most important for background particle heating. Perpendicular H+ heating is more efficient than perpendicular O+ or parallel electron heating for the drift velocity regime most relevant to past experiments.
Scales, W. A.↗