Showing papers on "Hydrostatic equilibrium published in 1998"

Numerical simulation of 3d quasi-hydrostatic, free-surface flows

Abstract: Numerical models that assume hydrostatic pressure are usually sufficiently accurate for applications in civil engineering where the vertical component of the velocity is relatively small. Nevertheless, the vertical momentum, and, hence, the nonhydrostatic pressure component, cannot be neglected when the bottom topography of the domain changes abruptly, as in cases of short waves, or when the flow is determined by strong density gradients. In this paper a numerical method for the three-dimensional (3D) quasi-hydrostatic, free-surface flows is outlined. The governing equations are the Reynolds-averaged Navier-Stokes equations with the pressure decomposed into the sum of a hydrostatic component and a hydrodynamic component. The momentum equations, the incompressibility condition, and the equation for the free surface are integrated by a time-splitting method in such a fashion that the resulting numerical solution is mass conservative and stable at a minimal computational cost. Several applications serve to illustrate the effect of the deviation from the hydrostatic pressure.

Gas density and X-ray surface brightness profiles of clusters of galaxies from dark matter halo potentials: beyond the isothermal beta model

Abstract: We describe a theoretical framework to compute the cluster gas distribution in hydrostatic equilibrium embedded in a class of spherical dark matter halo potentials. Unlike the conventional isothermal $\beta$-model, the present method provides a physical basis to directly probe the shape of dark matter halo from the observed X-ray surface brightness and temperature profiles of clusters of galaxies. Specifically, we examine the extent to which the resulting gas density and X-ray surface brightness profiles are sensitive to the inner slope of the dark matter halo density and other more realistic effects including the self-gravity of the gas and the polytropic equation of state. We also discuss a practical strategy to apply the present methodology to the actual cluster profiles from future X-ray observations.

A robust, finite element model for hydrostatic surface water flows

Abstract: A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

Magnetohydrodynamic Modeling of a Galactic Spiral Arm as a Combination Shock and Hydraulic Jump

Abstract: We consider the interarm-to-arm transition for gas flow in the Galactic disk, modeled as a thick, magnetized, cloudless layer of gas in hydrostatic equilibrium with external gravity from stars, and having parameters appropriate to the solar neighborhood. We neglect the self-gravity of the gas and shear, and radial variations in gravity. We show that such a transition, if supersonic, must present characteristics of both a hydraulic jump (or bore) and a shock. Our numerical simulations confirm this prediction. Modeling the spiral perturbation as local, we find that flow passing through it builds dense, long-lived vertical structures with high velocity flow over the top, followed by a downstream shock, and sometimes secondary jumps. In addition, gravity waves generated in the thick disk appear to promote the formation of marked density enhancements in the midplane.

Ontogenetic scaling of hydrostatic skeletons: geometric, static stress and dynamic stress scaling of the earthworm lumbricus terrestris

Abstract: Soft-bodied organisms with hydrostatic skeletons range enormously in body size, both during the growth of individuals and in the comparison of species. Therefore, body size is an important consideration in an examination of the mechanical function of hydrostatic skeletons. The scaling of hydrostatic skeletons cannot be inferred from existing studies of the lever-like skeletons of vertebrates and arthropods because the two skeleton types function by different mechanisms. Hydrostats are constructed of an extensible body wall in tension surrounding a fluid or deformable tissue under compression. It is the pressurized internal fluid (rather than the rigid levers of vertebrates and arthropods) that enables the maintenance of posture, antagonism of muscles and transfer of muscle forces to the environment. The objectives of the present study were (1) to define the geometric, static stress and dynamic stress similarity scaling hypotheses for hydrostatic skeletons on the basis of their generalized form and function, and (2) to apply these similarity hypotheses in a study of the ontogenetic scaling of earthworms, Lumbricus terrestris, to determine which parameters of skeletal function are conserved or changed as a function of body mass during growth (from 0.01 to 8 g). Morphometric measurements on anesthetized earthworms revealed that the earthworms grew isometrically; the external proportions and number of segments were constant as a function of body size. Calculations of static stresses (forces per cross-sectional area in the body wall) during rest and dynamic stresses during peristaltic crawling (calculated from measurements of internal pressure and body wall geometry) revealed that the earthworms also maintained static and dynamic stress similarity, despite a slight increase in body wall thickness in segment 50 (but not in segment 15). In summary, the hydrostatic skeletons of earthworms differ fundamentally from the rigid, lever-like skeletons of their terrestrial counterparts in their ability to grow isometrically while maintaining similarity in both static and dynamic stresses.

Gravity Wave Perturbations of Minor Constituents: A Parcel Advection Methodology

Abstract: Existing analytical models of wave-induced minor constituent fluctuations result from linearized perturbation expansions of a rate equation governing either number density or mixing ratio, whereas many numerical models now use isentropic parcel advection methods to simulate these effects Exact relationships between the two approaches are not currently clear for gravity waves Here, the parcel advection method is formalized and applied to derive analytical formulas for the response of vertical constituent profiles of arbitrary shape to adiabatic gravity wave displacements These relations are compared to corresponding formulas from standard linearized perturbation analyses Both methods accurately model perturbations produced by nondissipating hydrostatic gravity waves within idealized vertical tracer profiles Both methods can also model wave-induced perturbations of minor constituents with shorter chemical lifetimes This is demonstrated by using the parcel method to reproduce previous results

Coulomb interactions in the intracluster medium

Abstract: In this paper we discuss the effect of Coulomb collisions on the temperature profiles of the intracluster medium in clusters of galaxies, motivated by recent reports of negative temperature gradients in some clusters by Markevitch et al. The timescale for electrons and protons to reach temperature equilibrium can exceed a few billion years beyond radii of a Mpc, if the intracluster gas is assumed to be at the usual cluster virial temperature. If a cluster merger has occurred within that time causing the protons, but not the electrons, to be rapidly heated then a small negative temperature gradient can result. This gradient is larger in clusters with high temperatures and steep density profiles. Applying these considerations to the cluster of galaxies A2163, we conclude that, more plausibly, the observed gradient is due to a lack of hydrostatic equilibrium following a merger.

Anomalous diffusion modifies solar neutrino fluxes

Abstract: Density and temperature conditions in the solar core suggest that the microscopic diffusion of electrons and ions could be nonstandard: Diffusion and friction coefficients are energy dependent, collisions are not two-body processes and retain memory beyond the single scattering event. A direct consequence of nonstandard diffusion is that the equilibrium energy distribution of particles departs from the Maxwellian one (tails go to zero more slowly or faster than exponentially) modifying the reaction rates. This effect is qualitatively different from temperature and / or composition modification: Small changes in the number of particles in the distribution tails can strongly modify the rates without affecting bulk properties, such as the sound speed or hydrostatic equilibrium, which depend on the mean values from the distribution. This mechanism can considerably increase the range of predictions for the neutrino fluxes allowed by the current experimental values (cross-sections and solar properties) and can be used to reduce the discrepancy between these predictions and the solar neutrino experiments.

Dissipative fluids out of hydrostatic equilibrium

Abstract: In the context of the Muller-Israel-Stewart second-order phenomenological theory for dissipative fluids, we analyse the effects of thermal conduction and viscosity in a relativistic fluid, just after its departure from hydrostatic equilibrium, on a time scale of the order of the relaxation times. Stability and causality conditions are contrasted with conditions for which the `effective inertial mass' vanishes.

Calculation of Pressure in Ocean Simulations

Abstract: Many state-of-the-art numerical ocean models calculate pressure using the hydrostatic balance, or an equation derived from it. The proper form of this deceptively simple-looking equation, ∂p/∂z = −gρ(S, T, p) (where notation is standard), is nonlinear in the pressure p. In contrast, most numerical models solve the linear equation ∂p/∂z = −gρ(S, T, z). This modification essentially replaces the total pressure, which includes a time-dependent signal, with an approximate time-independent pressure associated with the depth of a model grid point. In this paper, the authors argue that the inclusion of the total pressure when solving the hydrostatic equation can generate a depth-dependent baroclinic pressure gradient equivalent to a geostrophic velocity of several centimeters per second. Further, this effective velocity can increase with depth and is largest in dynamically important areas like western boundary currents. These points suggest that the full feedback of pressure on density should be include...

Nonhydrostatic haline convection under leads in sea ice

Abstract: The distribution of dense brine under leads in sea ice is associated with convective sinking of individual plumes and near-surface mixing associated with ice-water momentum flux. The processes have been studied in the recent Lead Experiment (LeadEx) field program and previously modeled using a two-dimensional hydrostatic numerical model. In this study these processes are reexamined using a nonhydrostatic model. It is shown that nonhydrostatic effects give rise to pressure distributions which counter hydrostatic pressure gradients in the fluid. These effects are largest in sinking plume events and can be substantial when plumes are free to sink to depths of 100 m. In the presence of the Arctic halocline (typically at 30–40 m), however, vertical accelerations of convective plumes are limited spatially and temporally, and nonhydrostatic effects are relatively small. It is the purpose of this paper to demonstrate that for realistic Arctic stratification, convective circulations under leads in sea ice are predominantly hydrostatic.

Methods for computing internal flattening, with applications to the Earth's structure and geodynamics

Abstract: After general comments (Section 1) on using variational procedures to compute the oblateness of internal strata in the Earth and slowly rotating planets, we recall briefly some basic concepts about barotropic equilibrium figures (Section 2), and then proceed to discuss several accurate methods to derive the internal flattening. The algorithms given in Section 3 are based on the internal gravity field theory of Clairaut, Laplace and Lyapunov. They make explicit use of the concept of a level surface. The general formulation given here leads to a number of formulae which are of both theoretical and practical use in studying the Earth's structure, dynamics and rotational evolution. We provide exact solutions for the figure functions of three Earth models, and apply the formalism to yield curves for the internal flattening as a function of the spin frequency. Two more methods, which use the general deformation equations, are discussed in Section 4. The latter do not rely explicitly on the existence of level surfaces. They offer an alternative to the classical first-order internal field theory, and can actually be used to compute changes of the flattening on short timescales produced by variations in the LOD. For short durations, the Earth behaves elastically rather than hydrostatically. We discuss in some detail static deformations and Longman's static core paradox (Section 5), and demonstrate that in general no static solution exists for a realistic Earth model. In Section 6 we deal briefly with differential rotation occurring in cylindrical shells, and show why differential rotation of the inner core such as has been advocated recently is incompatible with the concept of level surfaces. In Section 7 we discuss first-order hydrostatic theory in relation to Earth structure, and show how to derive a consistent reference Earth model which is more suitable for geodynamical modelling than are modern Earth models such as 1066-A, PREM or CORE11. An important result is that a consistent application of hydrostatic theory leads to an inertia factor of about 0.332 instead of the value 0.3308 used until now. This change automatically brings ‘hydrostatic’ values of the flattening, the dynamic shape factor and the precessional constant into much better agreement with their observed counterparts than has been assumed hitherto. Of course, we do not imply that non-hydrostatic effects are unimportant in modelling geodynamic processes. Finally, we discuss (Sections 7–8) some implications of our way of looking at things for Earth structure and some current problems of geodynamics. We suggest very significant changes for the structure of the core, in particular a strong reduction of the density jump at the inner core boundary. The theoretical value of the free core nutation period, which may be computed by means of our hydrostatic Earth models CGGM or PREMM, is in somewhat better agreement with the observed value than that based on PREM or 1066-A, although a significant residue remains. We attribute the latter to inadequate modelling of the deformation, and hence of the change in the inertia tensor, because the static deformation equations were used. We argue that non-hydrostatic effects, though present, cannot explain the large observed discrepancy of about 30 days.

Hydrostatic equilibrium conditions in the galactic halo

Abstract: The large scale distributions of gas, magnetic field and cosmic rays in the galactic halo are investigated. Our model is based on the analysis of all-sky surveys of H i gas (Leiden/Dwingeloo survey), soft X-ray radiation ( ROSATall-sky survey), high energy γ-ray emission ( EGRET> 100 MeV), and radio-continuum emission (408 MHz survey). We found a stable hydrostatic equilibrium configuration of the Galaxy which, on large scales, is consistent with the observations. Instabilities due to local pressure or temperature fluctuations can evolve only beyond a scale height of 4 kpc. We have to distinguish 3 domains, with different physical properties and scale heights: 1) The gaseous halo has an exponential scale height hz ' 4.4 kpc. Its radial distribution is characterised by a galactocentric scale length A1 ' 15 kpc. On large scales all components of the halo – gas, magnetic fields and cosmic rays – are in pressure equilibrium. The global magnetic field is regularly ordered and oriented parallel to the galactic plane. 2) The disk has a vertical scale height of about 0.4 kpc. Characteristic for this region is the high gas pressure. The associated magnetic field is irregularly ordered and its equivalent pressure is only' 1/3 of the gas pressure. The cosmic rays are decoupled from gas and magnetic fields. 3) The diffuse ionised gas layer with a vertical scale height of about 0.95 kpc and a radial scale length of A1 ' 15 kpc acts as a disk-halo interface. The magnetic field in this region has properties similar to that in the disk. However, here the cosmic rays are coupled to the magnetic fields in contrast to the situation within the galactic disk. The gas pressure in this transition region is essential for the stability of the galactic halo system. Applying the model we can derive some major properties of the Milky Way: Assuming that the distribution of the gas in the halo traces the dark matter, we derive for a flat rotation curve a total mass of M = 2.8 1011 M . The mass of the galactic halo is Mhalo ' 2.1 1011 M . We find that turbulent motions in the gaseous halo can be described by the Kolmogoroff relation. The smallest clouds, which are compatible with such a turbulent flow, are at temperatures close to 3 K. They have linear sizes of ∼ 20 au and masses of Send offprint requests to : P. Kalberla, (pkalberla@astro.uni-bonn.de) ∼ 2 10−3 M . A significant fraction of the galactic dark matter may be in this form.

The effect of gravity on the combustion synthesis of metal-ceramic composites

Abstract: The effects of gravity on the combustion characteristics and microstructure of metal-ceramic composites (HfB2/Al and Ni3Ti/TiB2 systems) were studied under both normal and low gravity conditions. Under normal gravity conditions, pellets were ignited in three orientations relative to the gravity vector. Low gravity combustion synthesis (SHS) was carried out on a DC-9 aircraft at the NASA-Lewis Research Center. It was found that under normal gravity conditions, both the combustion temperature and wave velocity were highest when the pellet was ignited from the bottom orientation; i.e., the wave propagation direction was directly opposed to the gravitational force. The SHS of 70 vol pct Al (in the Al-HfB2 system) was changed from unstable, slow, and incomplete when ignited from the top to unstable, faster, and complete combustion when ignited from the bottom. The hydrostatic force (height × density × gravity) in the liquid aluminum was thought to be the cause of formation of aluminum nodules at the surface of the pellet. The aluminum nodules that were observed on the surface of the pellet when reacted under normal gravity were totally absent for reactions conducted under low gravity. Buoyancy of the TiB2 particles and sedimentation of the Ni3Ti phase were observed for the Ni3Ti/TiB2 system. The possibility of liquid convective flow at the combustion front was also discussed. Under low gravity conditions, both the combustion temperature and wave velocity were lower than those under normal gravity. The distribution of the ceramic phase, i.e., TiB2 or HfB2, in the intermetallic (Ni3Ti) or reactive (Al) matrix was more uniform.

Polishing method using a hydrostatic fluid bearing support having fluctuating fluid flow

Abstract: A polishing system such as a chemical mechanical belt polisher includes a hydrostatic fluid bearing that supports polishing pads and incorporates one or more of the following novel aspects. One aspect uses compliant surfaces surrounding fluid inlets in an array of inlets to extend areas of elevated support pressure around the inlets. Another aspect modulates or reverses fluid flow in the bearing to reduce deviations in the time averaged support pressure and to induce vibrations in the polishing pads to improve polishing performance. Another aspect provides a hydrostatic bearing with a cavity having a lateral extent greater than that of an object being polished. The depth and bottom contour of cavity can be adjusted to provide nearly uniform support pressure across an area that is surrounded by a retaining ring support. Changing fluid pressure to the retaining ring support adjusts the fluid film thickness of the bearing. Yet another aspect of the invention provides a hydrostatic bearing with spiral or partial cardiod drain grooves. This bearing has a non-uniform support pressure profile but provides a uniform average pressure to a wafer that is rotated relative to the center of the bearing. Another aspect of the invention provides a hydrostatic bearing with constant fluid pressure at inlets but a support pressure profile that is adjustable by changing the relative heights of fluid inlets to alter local fluid film thicknesses in the hydrostatic bearing.

Hydrodynamics and stability of galactic cooling flows

Abstract: Using numerical techniques we study the global stability of cooling flows in X-ray luminous giant elliptical galaxies. As an unperturbed equilibrium state we choose the hydrostatic gas recycling model. Non-equilibrium radiative cooling, stellar mass loss, heating by type Ia supernovae, distributed mass deposition and thermal conductivity are included. Although the recycling model reproduces the basic X-ray observables, it appears to be unstable with respect to the development of inflow or outflow. In spherical symmetry the inflows are subject to a central cooling catastrophe, while the outflows saturate in a form of a subsonic galactic wind. Two-dimensional axisymmetric random velocity perturbations of the equilibrium model trigger the onset of a cooling catastrophe, which develops in an essentially non-spherical way. The simulations show a patchy pattern of mass deposition and the formation of hollow gas jets, which penetrate through the outflow down to the galaxy core. The X-ray observables of such a hybrid gas flow mimic those of the equilibrium recycling model, but the gas temperature exhibits a central depression. The mass deposition rate M˙ consists of two contributions of similar size: (i) a hydrostatic one resembling that of the equilibrium model, and (ii) a dynamical one which is related to the jets and is more concentrated towards the centre. For a model galaxy, like NGC 4472, our 2D simulations predict M˙ ≈ 2 M⊙ yr−1 within the cooling radius for the advanced non-linear stage of the instability. We discuss the implications of these results to Hα nebulae and star formation in cooling flow galaxies and emphasize the need for high-resolution 3D simulations.

Hydrodynamics and stability of galactic cooling flows

Abstract: Using numerical techniques we studied the global stability of cooling flows in giant elliptical galaxies. As an initial equilibrium state we choose the hydrostatic gas recycling model (Kritsuk 1996). Non-equilibrium radiative cooling, stellar mass loss, heating by type Ia supernovae, distributed mass deposition, and thermal conductivity are included. Although the recycling model reproduces the basic X-ray observables, it appears to be unstable with respect to the development of inflow or outflow. In spherically symmetry the inflows are subject to a central cooling catastrophe, while the outflows saturate in a form of a subsonic galactic wind. Two-dimensional axisymmetric random velocity perturbations of the equilibrium model trigger the onset of a cooling catastrophe, which develops in an essentially non-spherical way. The simulations show a patchy pattern of mass deposition and the formation of hollow gas jets, which penetrate through the outflow down to the galaxy core. The X-ray observables of such a hybrid gas flow mimic those of the equilibrium recycling model, but the gas temperature exhibits a central depression. The mass deposition rate M_dot consists of two contributions of similar size: (i) a hydrostatic one resembling that of the equilibrium model, and (ii) a dynamical one which is related to the jets and is more concentrated to the centre. For a model galaxy, like NGC 4472, our 2D simulations predict M_dot = 2 M_sun/yr within the cooling radius for the advanced non-linear stage of the instability. We discuss the implications of these results to H_alpha nebulae and star formation in cooling flow galaxies and emphasize the need for high-resolution 3D simulations.

Dynamic meteorology : a basic course

Abstract: Introduction - units and dimensions the thermodynamics of dry clan air the aerological diagram the thermodynamics of moist air hydrostatic equilibrium the equations of motion (1) - the Coriolos force the equations of motion (2) - derivation in various co-ordinates balanced flow unbalanced flow Euler and Lagrange vorticity the long wave equations the upper air synoptic chart friction in the boundary layer of the atmosphere some more advanced equations synoptic observations and analysis simple synoptic models the tropical cyclone radiant energy transfer the radiation balance of the Earth climate change.

The Active Gravitational Mass of a Heat Conducting Sphere Out of Hydrostatic Equilibrium

Abstract: We obtain an expression for the active gravitational mass of a relativistic heat conducting fluid, just after its departure from hydrostatic equilibrium, on a time scale of the order of relaxation time. It is shown that an increase of a characteristic parameter leads to larger (smaller) values of active gravitational mass of collapsing (expanding) spheres, enhacing thereby the instability of the system.

Clouds as Turbulent Density Fluctuations. Implications for pressure confinement and spectral line data interpretation

Abstract: We examine the idea that diffuse and giant molecular clouds and their substructure form as density fluctuations induced by large scale interstellar turbulence. We do this by investigating the topology of various fields in realistic simulations of the ISM. We find that a) the velocity field is continuous across threshold-defined cloud boundaries; b) such cloud boundaries are rather arbitrary, with no correspondence to any actual physical boundary, such as a density discontinuity; c) abrupt velocity jumps are coincident with the density maxima; d) the volume and surface kinetic terms in the Eulerian Virial Theorem for a cloud ensemble are comparable in general; e) the magnetic field exhibits bends and reversals highly correlated with similar density features. These results suggest that clouds are formed by colliding gas streams. Within this framework, we argue that thermal pressure equilibrium is irrelevant for cloud confinement in a turbulent medium, since inertial motions can still distort or disrupt a cloud. Turbulent pressure confinement appears self-defeating, because turbulence contains large-scale motions which necessarily distort cloud boundaries. Density-weighted velocity histograms show similar FWHMs and similar multi-component structure to those of observational line profiles, though the histogram features do not correspond to isolated "clumps", but rather to extended regions throughout a cloud. We argue that the results presented here may be also applicable to small scales with larger densities (molecular clouds and cores) and suggest that quasi- hydrostatic configurations cannot be produced from turbulent fluctuations unless the thermodynamic behavior of the flow becomes nearly adiabatic at late stages of collapse. We expect this to occur only at protostellar densities.

Particle Model for Simulating Flow Over Large Areas

Abstract: On the basis of traditional particle-in-cell methods, a particle model has been developed to simulate flow over large areas. Under the assumption that the fluid medium is an assembly of many small independent fluid particles, the momentum equation for a particle is derived for shallow-flow conditions. In the formulation used, only two forces are involved. One is the hydrostatic force arising from the accumulation of different numbers or particles at different locations. The other is a friction force that varies inversely with flow depth and quadratically with particle velocity and bed roughness. The velocity and spatial positions of all particles are averaged at fixed grid points to obtain the overall flow behavior. The particle model is demonstrated through an application to a documented 1954 flood in the Jingjiang River flood diversion area in Hubei, China. The flood lasted 300 h, with the total discharge volume being 4 billion m³. Good agreement between computed and observed water levels was obtained. Convergence of the method is demonstrated by repeatedly doubling the number of particles employed in the computation until there is little change between simulations.

Particle model for simulating flow over large areas. technical note

Abstract: On the basis of traditional particle-in-cell methods, a particle model has been developed to simulate flow over large areas. Under the assumption that the fluid medium is an assembly of many small, independent fluid particles, the momentum equation for a particle is derived for shallow-flow conditions. In the formulation used, only two forces are involved. One is the hydrostatic force arising from the accumulation of different numbers of particles at different locations. The other is a friction force that varies inversely with flow depth and quadratically with particle velocity and bed roughness. The velocity and spatial positions of all particles are averaged at fixed grid points to obtain the overall flow behavior. The particle model is demonstrated through an application to a documented 1954 flood in the Jingjiang River flood diversion area in Hubei, China. The flood lasted 300 hours, with the total discharge volume being 4 billion cu m. Good agreement between computed and observed water levels was obtained. Convergence of the method is demonstrated by repeatedly doubling the number of particles employed in the computation until little change was found between simulations.

Hydrostatic, wind and non-uniform lateral pressure solutions for containment vessels

Abstract: The governing Flugge stability equations in coupled form are used for cylinders subjected to external pressure that varies circumferentially. Three cases are considered: fluid (hydrostatic) pressure, wind pressure and partial (patch) circumferential pressure. The wind load follows the Australian Standard AS 1170.2 (1989). Longitudinal variation of the load is not considered. The numerical process gives the stagnation buckling pressure for different shell geometry and simple support conditions at each end. The Galerkin method is employed to orthogonalize the error made with the introduction of the finite series into the governing equations. The solutions are compared with a few published solutions in the literature.

Free wobble/nutation of the Earth : a new approach for hydroAppalachian Mountainsstatic Earth models

Abstract: One of the two conventional approaches to formulate a theory to describe the Earth's wobble/nutations is to regard these as among the set of free oscillations of a rotating oblate Earth model. This theory, now standard, predicts the eigenperiods of the Chandler wobble and free core nutation (FCN). Very-long-baseline interferometry and superconducting gravimetry data indicate a significant discrepancy between the inferred and theoretically-predicted values of FCN period. The widely-accepted explanation for this discrepancy is that the core-mantle boundary's ellipticity departs from its hydrostatic equilibrium value. However the standard theory for a hydrostatic Earth model has two mathematical shortcomings, which should be removed before abandoning hydrostatic equilibrium as the reference state. These shortcomings are: (1) the treatment of the governing equations in interior regions is not consistent with the treatment of the boundary conditions at surfaces of discontinuity in material properties; (2) formulation of the boundary conditions does not treat material properties properly. To remove these shortcomings, in this thesis spherical polar coordinates are replaced by a non-orthogonal coordinate system (ro,θ,o), named after Clairaut. A set of new variables in Clairaut coordinates is introduced, generalizing the conventional notation for a spherical-layered Earth model. The governing equations and boundary conditions, written in these new variables, give a consistent description of free wobble/nutation accurate to first order in ellipticity. A program to compute wobble/nutation eigenperiods has been written, and preliminary numerical results obtained, but either the program still contains errors or truncation is too severe.