Engineering Papers⌕ Search

Engineering topics

Spiegel, E. A.

Publications and source records attributed to Spiegel, E. A..

16 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Stellar and Jovian vortices

The characteristics of 'Jovian' vortices (the large vortices observed in the atmospheres of Jupiter, Saturn, Neptune) are summarized, and the existence of similar structures in the atmospheres of stars is considered theoretically. The problem of vortex maintenance is addressed, including potential vorticity, numerical simulations of Jovian vortices, and cyclones and anticyclones; the Great Red Spot of Jupiter is described on the basis of Voyager data; the evidence for convective generation of vertical vorticity in the sun is examined; the possibly vortical nature of the large spots of RS CVn stars is discussed; and models of spots on rapidly rotating hot stars are surveyed.

Dowling, T. E.↗
NASA NTRS1989

Blow-up of unsteady two-dimensional Euler and Navier-Stokes solutions having stagnation-point form

The time-dependent form of the classic, two-dimensional stagnation-point solution of the Navier-Stokes equations is considered. If the viscosity is zero, a class of solutions of the initial-value problem can be found in closed form using Lagrangian coordinates. These solutions exhibit singular behavior in finite time, because of the infinite domain and unbounded initial vorticity. Thus, the blow-up found by Stuart in three dimensions using the stagnation-point form, also occurs in two. The singularity vanishes under a discrete, finite-dimensional 'point vortex' approximation, but is recovered as the number of vortices tends to infinity. We find that a small positive viscosity does not arrest the breakdown, but does strongly alter its form. Similar results are summarized for certain Boussinesq stratified flows.

Childress, S.↗
NASA NTRS1986

Lacunarity and intermittency in fluid turbulence

It is shown that oscillations in the high-order moments of turbulent velocity fields are inherent to the fractal character of intermittent turbulence and are a feature of the lacunarity of fractal sets. Oscillations in simple Cantor sets are described, and a single parameter to measure lacunarity is identified. The connection between oscillations in fractals and in the turbulent velocity correlations is discussed using the phenomenological beta model of intermittent turbulence (Frisch et al., 1978).

Smith, L. A.↗
NASA NTRS1985

Pattern formation by particles settling in viscous flows

Results are reported of several simulations of the motions of small objects in two-dimensional cellular flows performed to study the evolution of the distributions of particle flows over time in processes such as sedimentation. Stream functions are defined in the form of a Hamiltonian system for the particle motions, with inertial and particle acceleration being neglected. Conditions are found for which the particles will become trapped in an oscillatory motion or the particle orbits attain an oscillary motion. Various simulation images are provided to illustrate the usefulness of the technique for modeling fractal swarms.

Smith, L. A.↗
NASA NTRS1982

Time-dependent solutions of multimode convection equations

Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Numerical studies dealing with two or three modes with triad interactions are discussed. Rich time dependence was found in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favorably. Except at the highest Rayleigh number considered (10,000,000), the theoretical Nusselt numbers agree well with experiment.

Toomre, J.↗
NASA NTRS1981

A prospectus for a theory of variable variability

It is proposed that the kind of stellar variability exhibited by the Sun in its magnetic activity cycle should be considered as a prototype of a class of stellar variability. The signature includes long 'periods' (compared to that of the radial fundamental model), erratic behavior, and intermittency. As other phenomena in the same variability class we nominate the liminosity fluctuations of ZZ Ceti stars and the solar 160 m oscillation. We discuss the possibility that analogous physical mechanisms are at work in all these cases, namely instabilities driven in a thin layer. These instabilities should be favorable to grave modes (in angle) and should arise in conditions that may allow more than one kind of instability to occur at once. The interaction of these competing instabilities produces complicated temporal variations. Given suitable idealizations, it is shown how to begin to compute solutions of small, but finite, amplitude.

Childress, S.↗
NASA NTRS1977

Numerical solutions of single-mode convection equations

In the Boussinesq approximation, single-mode equations describing thermal convection are constructed by expanding the fluctuating velocity and temperature fields in a complete set of functions (or planforms) of the horizontal coordinates and retaining just one term. Numerical solutions of the single-mode equations are investigated, chief consideration being given to hexagonal planforms. Extensive surveys of steady solutions are presented for various Rayleigh numbers, Prandtl numbers, and horizontal wavenumbers. The dependences on Rayleigh number and Prandtl number at very large Rayleigh number are in satisfactory agreement with the results of asymptotic expansions.

Toomre, J.↗
NASA NTRS1976

Stellar convection theory. I - The anelastic modal equations

Methods are developed for dealing with the various dynamical problems that arise because of convective zones in stars. A system of equations for stellar convection is derived from the full equations of compressible fluid dynamics with the aid of two major approximations. The first of these is the anelastic approximation, which involves both the filtering out of acoustic waves and a suitable linearization of the fluctuating thermodynamic variables. The second one approximates the horizontal structure of convection by expanding the motion in a set of horizontal cellular platforms and severely truncating the expansion. The resulting system of partial differential equations, referred to as the anelastic modal equations, is outlined along with suggested boundary conditions and techniques for solving the equations. Ways of assessing the overall validity of the present treatment are discussed.

Latour, J.↗
NASA NTRS1975

Modal equations for cellular convection

We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.

Gough, D. O.↗
NASA NTRS1974

Nonlinear cellular motions in Poiseuille channel flow

In a number of nonlinear solutions to the equations of channel flow the velocity is decomposed into a mean part plus a nonlinear disturbance. The idea that nonlinear effects place a limitation on the amplitudes of the disturbance flow is considered. In the reported investigation the disturbance flow is represented by drastically limited Fourier expansions in the downstream coordinate. The resulting equations are solved numerically with high accuracy to obtain a good representation of the cross-stream structure of the solution. The results of the investigation show that indeed the nonlinear terms always limit the amplitude of the disturbance flow in this approximation.

Zahn, J.-P.↗
NASA NTRS1971

Aperiodic behaviour of a non-linear oscillator.

The aperiodic behavior of the solution of the equation of motion derived previously (1966) when considering a model thermomechanical oscillator is examined. Periodic solutions of this equation are studied numerically and analytically. Conditions for the instability of the solutions are determined. This instability seems to be the cause of the observed aperiodicity.

Baker, N. H.↗