Engineering topics

Toomre, J.

Publications and source records attributed to Toomre, J..

40 records · Page 3

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 NTRS1972

Galactic bridges and tails.

This paper argues that the bridges and tails seen in some multiple galaxies are just tidal relics of close encounters. These consequences of the brief but violent tidal forces are here studied in a deliberately simple-minded fashion. Each encounter is considered to involve only two galaxies and to be roughly parabolic; each galaxy is idealized as just a disk of noninteracting test particles which initially orbit a central mass point. As shown here, the two-sided distortions provoked by gravity alone in such circumstances can indeed evolve kinematically into some remarkably narrow and elongated features. Besides extensive pictorial survey of tidal damage, this paper offers reconstructions of the orbits and outer shapes of four specific interacting pairs: Arp 295, M51 + NGC 5195, NGC 4676, and NGC 4038/9.

Toomre, A.↗