Engineering topics
Publications and source records attributed to Marcus, P. S..
Jupiter's Great Red Spot (GRS) is one of its most distinct and enduring features, having been continuously observed since the 1800's. It currently spans the smallest latitude and longitude size ever recorded. Here we show analyses of 2014 Hubble spectral imaging data to study the color, structure and internal dynamics of this long-live storm.
The fluid dynamics within a protoplanetary disk has been attracting the attention of many researchers for a few decades. Previous works include, to list only a few among many others, the well-known prescription of Shakura & Sunyaev, the convective and instability study of Stone & Balbus and Hawley et al., the Rossby wave approach of Lovelace et al., as well as a recent work by Klahr & Bodenheimer, which attempted to identify turbulent flow within the disk. The disk is commonly understood to be a thin gas disk rotating around a central star with differential rotation (the Keplerian velocity), and the central quest remains as how the flow behavior deviates (albeit by a small amount) from a strong balance established between gravitational and centrifugal forces, transfers mass and momentum inward, and eventually forms planetesimals and planets. In earlier works we have briefly described the possible physical processes involved in the disk; we have proposed the existence of long-lasting, coherent vortices as an efficient agent for mass and momentum transport. In particular, Barranco et al. provided a general mathematical framework that is suitable for the asymptotic regime of the disk; Barranco & Marcus (2000) addressed a proposed vortex-dust interaction mechanism which might lead to planetesimal formation; and Lin et al. (2002), as inspired by general geophysical vortex dynamics, proposed basic mechanisms by which vortices can transport mass and angular momentum. The current work follows up on our previous effort. We shall focus on the detailed numerical implementation of our problem. We have developed a parallel, pseudo-spectral code to simulate the full three-dimensional vortex dynamics in a stably-stratified, differentially rotating frame, which represents the environment of the disk. Our simulation is validated with full diagnostics and comparisons, and we present our results on a family of three-dimensional, coherent equilibrium vortices.
The Galerkin equations for convection in a sphere are examined to determine which physical processes are neglected by the severe truncation of the equations of motion. It is demonstrated that the gross features of the flow are affected by truncation in the horizontal direction, with all of the models considered being well resolved in the vertical direction. One of the effects of truncation is to enhance the high-wave number end of the kinetic energy and thermal variance spectra. The examples cited indicate that as long as the kinetic energy spectrum decreases with wave number, a truncation gives a qualitatively correct solution. Conclusions are tested by calculating solutions to the equations of motion for several values of the Rayleigh number and the limit of horizontal spatial resolution.
The results of a numerical, three-dimensional study of convection in a self-gravitating sphere of Boussinesq fluid with a Rayleigh number of 10-billion and a Prandtl number of 1 are presented. The velocity and temperature are computed by using spectral methods in the horizontal and finite-differencing in the radial directions. An eddy viscosity and diffusivity are needed to model the subresolution flow. For Rayleigh numbers much less than 10-billion the flows do not have well-defined inertial ranges, and an eddy viscosity and diffusivity cannot be assigned in this self-consistent manner. By computing the energy spectra as well as the detailed energy budgets as a function of wavenumber, it is shown that for Rs = 10-billion there is an inertial range for the modes corresponding to spherical harmonics with l greater than 6.
A stable, equilibrium solution for convection in a self-gravitating sphere of Boussinesq fluid was computed by using a modal analysis in which the theta, phi dependence of the fluid is expanded in a set of 168 spherical harmonics. The temperature, velocity, and convective flux of the fluid as well as the kinetic and thermal energy spectra as functions of wavelength are computed. The spectra are found to be in agreement with both experimental observations and analytic scaling laws. The dynamics of the energy cascade is examined by computing the ratio of the amount of energy dissipation at a particular wavelength to the amount of energy produced at that same wavelength. It is found that there is only a slight cascade of kinetic energy to smaller wavelengths but a large cascade of thermal energy.
The Galerkin (including single-mode and Lorenz) equations were examined for convection in a sphere to determine which physical processes are neglected when the equations of motion are truncated too severely. The conclusions were tested by calculating solutions to the equations of motion for different values of the Rayleigh number and for different values of the limit of the horizontal spatial resolution. It was shown that the transitions from steady state to periodic, then to aperiodic convection depend not only on the Rayleigh number but also very strongly on the horizontal resolution. One of the effects of truncation is to enhance the high wavenumber end of the kinetic energy and thermal variance spectra. The numerical examples indicate that as long as the kinetic energy spectrum decreases with wavenumber, a truncation gives a qualitatively correct solution.
The convective flow of a self gravitating sphere of Boussinesq fluid for small Reynolds and Peclet numbers is numerically determined. The decomposition of the equations of motion into modes is reviewed and a relaxation method is developed and presented to compute the solutions to these equations. The stable equilibrium flow for a Rayleigh number of 10 to the 4th power and a Prandtl number of 10 is determined. The 2 and 3 dimensional spectra of the kinetic and thermal energies and the convective flux as a function of wavelengths are calculated in terms of modes. The anisotropy of the flow as a function of wavelength is defined.
A three dimensional study of convection in a self gravitating sphere of Boussinesq fluid with a Rayleigh number of 10 to the 10th power and a Prandtl of 1 is presented. The velocity and temperature of the fluid are computed at the largest wavelengths using spectral methods. A confirmation that the fluid is anisotropic and that the energy spectra are not smooth functions of wavelength but have a large amount of fine structure is discussed. The parameterization of the transport properties of the unresolvable inertial subrange with eddy viscosities and diffusivities is described. The time dependent fluctuations in the energy spectra and how they cascade from large to small wavelengths is examined.