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Results for “dissipatively stabilized states”

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At least 19 records

A linear analysis of the transition curve for the baroclinic annulus

A primitive equation linear model is shown to be capable of quantitatively predicting the neutral curve for a baroclinic annulus. Flows unstable to small nonaxisymmetric perturbations are assumed to lie on the nonaxisymmetric side of a transition curve, while the stable flows are on the axisymmetric side. The stability in the presence of perturbations is tested with linearized hydrostatic primitive equations. Attention is given to the fastest growing eigenmodes, demonstrating that the linear and nonlinear wave have similar structures at a particular point in the nonaxisymmetric regime. All the waves are similar to the Eddy wave except at the extreme to the transition curve, where the waves maintain little structure with height. The eddy kinetic energy is baroclinic with a potential energy suppresed by the large static stability of the basic state. Eddy dissipation is noted to be significant near all boundaries.

Miller, T. L.↗

Finite volume computation of unsteady inviscid rotational transonic flows past airfoils in rigid body motion

Unsteady inviscid transonic flow over airfoils in arbitrary rigid body motion is analyzed numerically by solving the two-dimensional unsteady Euler equations in integral form using a finite volume scheme. The solution procedure is based on an explicit Runge-Kutta time-stepping scheme wherein the spatial terms are central-differenced and a combination of second- and fourth-differences in the flow variables are used to form the numerical dissipation terms to stabilize the scheme. Unsteady calculations are started from converged steady-state solutions as initial conditions. Nonreflective boundary conditions are imposed on the far-field boundaries. Results are presented and, where possible, validated against available numerical and experimental data for airfoils subjected to a step change in angle of attack, airfoils oscillating and plunging in transonic flow, and airfoils immersed in a time-varying free stream.

Damodaran, Murali↗

Damping of Quasi-stationary Waves Between Two Miscible Liquids

Two viscous miscible liquids with an initially sharp interface oriented vertically inside a cavity become unstable against oscillatory external forcing due to Kelvin-Helmholtz instability. The instability causes growth of quasi-stationary (q-s) waves at the interface between the two liquids. We examine computationally the dynamics of a four-mode q-s wave, for a fixed energy input, when one of the components of the external forcing is suddenly ceased. The external forcing consists of a steady and oscillatory component as realizable in a microgravity environment. Results show that when there is a jump discontinuity in the oscillatory excitation that produced the four-mode q-s wave, the interface does not return to its equilibrium position, the structure of the q-s wave remains imbedded between the two fluids over a long time scale. The damping characteristics of the q-s wave from the time history of the velocity field show overdamped and critically damped response; there is no underdamped oscillation as the flow field approaches steady state. Viscous effects serve as a dissipative mechanism to effectively damp the system. The stability of the four-mode q-s wave is dependent on both a geometric length scale as well as the level of background steady acceleration.

Duval, Walter M. B.↗

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems. II

The results of Goldberg and Tadmor (1985) are extended to achieve improved stability criteria for a large class of approximations to the initial boundary value problem associated with a particular hyperbolic system in a quarter plane. In a stability analysis, it is shown that the entire approximation is stable if and only if the scalar outflow components of its principal part are stable. Thus, the global stability question is reduced to that of a scalar, homogeneous outflow problem. The stability criteria for the reduced problem, which depend both on the basic scheme and the boundary conditions, but very little on the interaction between the two, are stated and used to establish previous examples and new ones, including a host of dissipative and nondissipative examples. There is no difficulty in extending the stability criteria to two-boundary problems and initial-boundary value problems with variable coefficients.

Goldberg, Moshe↗

Wavenumber selection for single-wave steady states in a nonlinear baroclinic system

The principles involved in the selection of a wavenumber for single-wave steady states are examined numerically and analytically in the framework of an Eady-type model with uneven Ekman dissipation. The process of selection involves the determination of the preferred wavenumber for a given parameter setting in the nonlinear system by testing the stability of steady single-wave states in a triad with wavenumbers n(0) - 1, n(0), and n(0) + 1, where n(0) may change successively in the selection procedure. In a given triad for a given parameter setting, the preferred wave is the wave with the nonlinear Eady angle that is last to vanish.

Weng, H.-Y.↗

A Self-Stabilizing Byzantine-Fault-Tolerant Clock Synchronization Protocol

This report presents a rapid Byzantine-fault-tolerant self-stabilizing clock synchronization protocol that is independent of application-specific requirements. It is focused on clock synchronization of a system in the presence of Byzantine faults after the cause of any transient faults has dissipated. A model of this protocol is mechanically verified using the Symbolic Model Verifier (SMV) [SMV] where the entire state space is examined and proven to self-stabilize in the presence of one arbitrary faulty node. Instances of the protocol are proven to tolerate bursts of transient failures and deterministically converge with a linear convergence time with respect to the synchronization period. This protocol does not rely on assumptions about the initial state of the system other than the presence of sufficient number of good nodes. All timing measures of variables are based on the node s local clock, and no central clock or externally generated pulse is used. The Byzantine faulty behavior modeled here is a node with arbitrarily malicious behavior that is allowed to influence other nodes at every clock tick. The only constraint is that the interactions are restricted to defined interfaces.

Malekpour, Mahyar R.↗

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Eliasson, Peter↗

Properties of earthquakes generated by fault dynamics

A model for fault dynamics consisting of a uniform chain of blocks and springs pulled slowly across a rough surface is presented. The only nonlinear element of the model is a slip-stick friction force between the blocks and the surface. It is found that this model gives rise to events of all sizes. The numerical evaluation of the distribution of earthquake magnitudes results in a power-law spectrum similar to what is observed in nature. Like certain other dissipative dynamical systems, the observed large fluctuations in earthquake magnitude persist because the system is in a state of marginal stability.

Carlson, J. M.↗

The use of superconductivity in magnetic balance design

The magnetic field and field gradient requirements for magnetic suspension in a Mach 3, 6-in. diameter wind tunnel are stated, along with the power requirements for gradient coil pairs wound of copper operating at room temperature and aluminum cooled to 20 K. The power dissipated is large enough that the use of superconductivity in the coil design becomes an attractive alternative. The problems of stability and ac losses are outlined along with the properties of stabilized superconductors. A brief review of a simplified version of the critical state model of C. P. Bean is presented, and the problems involved in calculations of the ac losses in superconducting coils are outlined. A summary of ac loss data taken on pancake coils wound of commercially available Nb3Sn partially stabilized tape is presented and shown as leading to the U.Va. gradient coil design. The actual coil performance is compared with predictions based on the BNL results. Finally, some remarks are presented concerning scaling of the ac losses to larger magnetic suspension systems as well as prospects for improved performance using newer multifilament superconductors.

Moss, F. E.↗

Extrema principles of entrophy production and energy dissipation in fluid mechanics

A survey is presented of several extrema principles of energy dissipation as applied to problems in fluid mechanics. An exact equation is derived for the dissipation function of a homogeneous, isotropic, Newtonian fluid, with terms associated with irreversible compression or expansion, wave radiation, and the square of the vorticity. By using entropy extrema principles, simple flows such as the incompressible channel flow and the cylindrical vortex are identified as minimal dissipative distributions. The principal notions of stability of parallel shear flows appears to be associated with a maximum dissipation condition. These different conditions are consistent with Prigogine's classification of thermodynamic states into categories of equilibrium, linear nonequilibrium, and nonlinear nonequilibrium thermodynamics; vortices and acoustic waves appear as examples of dissipative structures. The measurements of a typical periodic shear flow, the rectangular wall jet, show that direct measurements of the dissipative terms are possible.

Horne, W. Clifton↗

Extrema principles of entropy production and energy dissipation in fluid mechanics

A survey is presented of several extrema principles of energy dissipation as applied to problems in fluid mechanics. An exact equation is derived for the dissipation function of a homogeneous, isotropic, Newtonian fluid, with terms associated with irreversible compression or expansion, wave radiation, and the square of the vorticity. By using entropy extrema principles, simple flows such as the incompressible channel flow and the cylindrical vortex are identified as minimal dissipative distributions. The principal notions of stability of parallel shear flows appear to be associated with a maximum dissipation condition. These different conditions are consistent with Prigogine's classification of thermodynamic states into categories of equilibrium, linear nonequilibrium, and nonlinear nonequilibrium thermodynamics; vortices and acoustic waves appear as examples of dissipative structures. The measurements of a typical periodic shear flow, the rectangular wall jet, show that direct measurements of the dissipative terms are possible.

Horne, W. Clifton↗

Construction of Low Dissipative High Order Well-Balanced Filter Schemes for Non-Equilibrium Flows

The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. [26] to a class of low dissipative high order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. The class of filter schemes developed by Yee et al. [30], Sjoegreen & Yee [24] and Yee & Sjoegreen [35] consist of two steps, a full time step of spatially high order non-dissipative base scheme and an adaptive nonlinear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e., choosing a well-balanced base scheme with a well-balanced filter (both with high order). A typical class of these schemes shown in this paper is the high order central difference schemes/predictor-corrector (PC) schemes with a high order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady state solutions exactly; it is able to capture small perturbations, e.g., turbulence fluctuations; it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.

Wang, Wei↗

Finite element formulation for transient heat treat problems

The macrothermomechanical behavior of materials subjected to rapid thermal or mechanical loading such as occurs in most heat treatments is described. The equations are developed for Lagrangian, Eulerian, and intermediary kinematic descriptions and are independent of the constitutive laws and the equation of state; they can be solved numerically for a specified material and boundary conditions. The coupled transport effects between dissipation and energy are included. The conventional linearized stability approach indicates the numerical procedure to be stable, with certain restriction on the time step size.

Mullen, R. L.↗

Possible histories of the obliquity of Mercury

Possible evolutionary paths of the spin axis of Mercury are studied theoretically in terms of generalized Cassini's laws using the Hamiltonian approach. Three stable positions (Cassini states) of the spin axis are discerned. The Cassini states in which the spin axis remains fixed in the frame rotating with the orbit precession are extremes in the tide-free Hamiltonian under the condition of constant angular momentum. The stability of the 3/2 spin resonance for Mercury as a function of obliquity is discussed, and it is shown how control of the resonance is passed from one to another term in the averaged potential as the obliquity is increased with a corresponding loss of stability at each transfer. A sampling technique is used to infer the evolution due to tidal interaction. Two tidal models are used - one with a constant value of the specific dissipation function Q and the other with Q inversely proportional to frequency. An approximate analytic solution for precession trajectories very close to a Cassini state is developed.

Peale, S. J.↗

Proposed law of nature linking impacts, plume volcanism, and Milankovitch cycles to terrestrial vertebrate mass extinctions via greenhouse-embryo death coupling

A greenhouse-physiological coupling killing mechanism active among mammals, birds, and reptiles has been identified. Operating via environmental thermal effects upon the maternal core-skin blood flow critical to the survival and development of embryos, it reduces the flow of blood to the uterine tract. Today, during hot summers, this phenomena kills embryos on a vast, global scale. Because of sensitivity of many mammals to modern heat, a major modern greenhouse could reduce population numbers on a global scale, and potentially trigger population collapses in the more vulnerable parts of the world. In the geological past, the killing mechanism has likely been triggered into action by greenhouse warming via impact events, plume volcanism, and Earth orbital variations (Milankovitch cycles). Earth's biosphere is maintained and molded by the flow of energy from the solar energy source to Earth and on to the space energy sink (SES). This SES energy flow maintains Earth's biosphere and its living components, as open, intermediate, dissipative, nonequilibrium systems whose states are dependent upon the rate of energy flowing through them. Greenhouse gases such as CO2 in the atmosphere influence the SES energy flow rate. Steady-state flow is necessary for global ecological stability (autopoiesis). Natural fluctuations of the C cycle such as rapid releases of CO2 from the mantle, or oceans, disrupt steady-state SES flow. These fluctuations constantly challenge the biosphere; slowdown of SES energy flow drives it toward thermodynamical equilibrium and stagnation. Fluctuations induced by impact event, mantle plume volcanism, and Milankovitch cycles can grow into structure-breaking waves triggering major perturbations of Earth's C cycle and mass extinctions. A major C cycle perturbation involves readjustment of the outer physiochemical spheres of the Earth: the atmosphere, hydrosphere, and lithosphere; and by necessity, the biosphere. A greenhouse, one manifestation of a major C cycle perturbation, is the most dangerous natural phenomenon that life on Earth can experience. Greenhouse conditions existed during the KT mass extinctions of 65 m.y. ago, and the Pleistocene-Holocene (P-H) mammalian extinctions of 10,000-12,000 yr ago. Coupling climatology to reproductive physiology via effects of ambient air temperature upon uterine blood flow to developing embryos accounts for the extinctions via established physiological principles.

Mclean, D. M.↗

A high-order compact numerical algorithm for supersonic flows

A dissipative compact two-four scheme (second-order time, fourth-order space) similar to the original MacCormack scheme has been developed, that exhibits greater accuracy than conventional fourth-order schemes. The dissipative nature of the scheme allows it to resolve weak discontinuities without artificial damping. A derivation of the scheme is presented, as well as the theoretical stability characteristics. The temporal scheme is then generalized into a steady-state formulation which achieves fourth-order spatial accuracy at steady-state. Several test problems are used to show that the scheme is more accurate than the traditional MacCormack scheme, and is nearly as efficient.

Carpenter, M. H.↗

Preferred orbit planes in the gravitational field of a tumbling spheroidal galaxy

An analytic method is described by means of which the preferred planes into which gas will settle by dissipative differential precession in a slightly nonspherical, nonstatic potential can be determined. Attention is given to the analysis of circular orbit precession in the external potential of a slightly prolate spheroidal mass that is tumbling about a short axis, providing a crude model for barred spiral galaxies as well as for prolate elliptical ones. The results obtained agree with previous work on the existence, orientation, and stability of periodic orbits in triaxial potentials. Depending on the source and injection geometry of the gas and on the nature of dissipation in the gas, the orbital dynamics presented could lead to enhanced, or even catastrophic, radial inflow and to steady state warped structures.

Durisen, R. H.↗

Protostellar rotation - Turbulence and heating of molecular clouds

The formation of rapidly rotating protostellar objects in turbulent and clumpy molecular clouds is analyzed. It is shown that the early dissipation of the protostellar rotational energy via a rotationally driven wind can keep their parent molecular clouds at the observed temperatures and in the observed turbulent state. The model requires a low space density of protostellar shells in order to provide the energy requirements to stabilize molecular clouds against gravitational collapse in regions of star formation. The dependence of this mechanism on the star formation rate suggests that the star formation is self-regulated.

Franco, J.↗