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E. A. Spiegel

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

13 recordsLinked to original sources
arXiv2015

Generation of large-scale winds in horizontally anisotropic convection

We simulate three-dimensional, horizontally periodic Rayleigh-Bénard convection between free-slip horizontal plates, rotating about a distant horizontal axis. When both the temperature difference between the plates and the rotation rate are sufficiently large, a strong horizontal wind is generated that is perpendicular to both the rotation vector and the gravity vector. The wind is turbulent, large-scale, and vertically sheared. Horizontal anisotropy, engendered here by rotation, appears necessary for such wind generation. Most of the kinetic energy of the flow resides in the wind, and the vertical turbulent heat flux is much lower on average than when there is no wind.

physics.flu-dyn↗
arXiv2014

Uhlenbeck's Complaint

The passage from kinetic theory to fluid dynamics as discussed by Hilbert has perplexed Uhlenbeck. Herein, I try to smooth over the discord.

astro-ph.GA↗
arXiv2008

Modeling a Maunder Minimum

We introduce on/off intermittency into a mean field dynamo model by imposing stochastic fluctuations in either the alpha effect or through the inclusion of a fluctuating electromotive force. Sufficiently strong small scale fluctuations with time scales of the order of 0.3-3 years can produce long term variations in the system on time scales of the order of hundreds of years. However, global suppression of magnetic activity in both hemispheres at once was not observed. The variation of the magnetic field does not resemble that of the sunspot number, but is more reminiscent of the 10 Be record. The interpretation of our results focuses attention on the connection between the level of magnetic activity and the sunspot number, an issue that must be elucidated if long term solar effects are to be well understood.

astro-ph↗
arXiv2002

Luminosity Effects in Projected Fractals

We analyze examples of projected two dimensional fractals for the case where the objects studied have a Schechter luminosity function. Our results indicate that two dimensional catalogues of sources could be of value in detecting the effects of luminosity functions as well as of large scale structure.

astro-ph↗
arXiv2001

Radiative Bulk Viscosity

Viscous resistance to changes in the volume of a gas arises when different degrees of freedom have different relaxation times. Collisions tend to oppose the resulting departures from equilibrium and, in so doing, generate entropy. Even for a classical gas of hard spheres, when the mean free paths or mean flight times of constituent particles are long, we find a nonvanishing bulk viscosity. Here we apply a method recently used to uncover this result for a classical rarefied gas to radiative transfer theory and derive an expression for the radiative stress tensor for a gray medium with absorption and Thomson scattering. We determine the transport coefficients through the calculation of the comoving entropy generation. When scattering dominates absorption, the bulk viscosity becomes much larger than either the shear viscosity or the thermal conductivity.

astro-ph↗
arXiv1999

Particle Aggregation in a turbulent Keplerian flow

In the problem of planetary formation one seeks a mechanism to gather small solid particles together into larger accumulations of solid matter. Here we describe a scenario in which turbulence mediates this process by aggregating particles into anticyclonic regions. If, as our simulations suggest, anticyclonic vortices form as long-lived coherent structures, the process becomes more powerful because such vortices trap particles effectively. Even if the turbulence is decaying, following the upheaval that formed the disk, there is enough time to make the dust distribution quite lumpy.

astro-ph↗
arXiv1998

Negative Energy Modes and Gravitational Instability of Interpenetrating Fluids

We study the longitudinal instabilities of two interpenetrating fluids interacting only through gravity. When one of the constituents is of relatively low density, it is possible to have a band of unstable wave numbers well separated from those involved in the usual Jeans instability. If the initial streaming is large enough, and there is no linear instability, the indefinite sign of the free energy has the possible consequence of explosive interactions between positive and negative energy modes in the nonlinear regime. The effect of dissipation on the negative energy modes is also examined.

astro-ph↗
arXiv1998

Scaling Regimes in the Distribution of Galaxies

If we treat the galaxies in published redshift catalogues as point sets, we may determine the generalized dimensions of such sets by standard means, outlined here. For galaxy separations up to about 5 Mpc, we find the dimensions of the galaxy set to be about 1.2, with not a strong indication of multifractality. For larger scales, out to about 30 Mpc, there is also good scaling with a dimension of about 1.8. For even larger scales, the data seem too sparse to be conclusive, but we find that the dimension is climbing as the scales increase. We report simulations that suggest a rationalization of such measurements, namely that in the intermediate range the scaling behavior is dominated by flat structures (pancakes) and that the results on the smallest scales are a reflection of the formation of density singularities.

astro-ph↗
arXiv1998

Stellar Oscillons

We study the weakly nonlinear evolution of acoustic instability of a plane- parallel polytrope with thermal dissipation in the form of Newton's law of cooling. The most unstable horizontal wavenumbers form a band around zero and this permits the development of a nonlinear pattern theory leading to a complex Ginzburg-Landau equation (CGLE). Numerical solutions for a subcritical, quintic CGLE produce vertically oscillating, localized structures that resemble the oscillons observed in recent experiments of vibrated granular material.

astro-ph↗
arXiv1998

Spotted Disks

Rotating, turbulent cosmic fluids are generally pervaded by coherent structures such as vortices and magnetic flux tubes. The formation of such structures is a robust property of rotating turbulence as has been confirmed in computer simulations and laboratory experiments. We defend here the notion that accretion disks share this feature of rotating cosmic bodies. In particular, we show that the intense shears of Keplerian flows do not inhibit the formation of vortices. Given suitable initial disturbances and high enough Reynolds numbers, long-lived vortices form in Keplerian shear flows and analogous magnetic structures form in magnetized disks. The formation of the structures reported here should have significant consequences for the transport properties of disks and for the observed properties of hot disks.

astro-ph↗
arXiv1997

Density Singularities and Cosmic Structures

We show that an array of singular density concentrations accounts for the scaling exponents observed in the luminous matter distribution in the Universe for scales below 10Mpc. This model provides a good description of the matter distribution on those smaller scales.

astro-ph↗
arXiv1993

Chaotic Pulse Trains

We study a third-order nonlinear ordinary differential equation whose solutions, under certain specific conditions, are individual pulses. These correspond to homoclinic orbits in the phase space of the equation and we study the possible pulse types in some detail. Sufficiently close to the conditions under which a homoclinic orbit exists, the solutions take the form of trains of well-separated pulses. A measure of closeness to homoclinic conditions provides a small parameter for the development of an asymptotic solution consisting of superposed, isolated pulses. The solvability condition in the resulting singular perturbation theory is a {\its timing map} relating successive pulse spacings. This map of the real line onto itself, together with the known form of the homoclinic orbit, provides a concise and accurate solution of the equation.

chao-dyn↗