Showing papers on "Hydrostatic equilibrium published in 2021"

Postbuckling analysis of hydrostatic pressurized FGM microsized shells including strain gradient and stress-driven nonlocal effects

Abstract: Herein, with the aid of the newly proposed theory of nonlocal strain gradient elasticity, the size-dependent nonlinear buckling and postbuckling behavior of microsized shells made of functionally graded material (FGM) and subjected to hydrostatic pressure is examined. As a consequence, the both nonlocality and strain gradient micro-size dependency are incorporated to an exponential shear deformation shell theory to construct a more comprehensive size-dependent shell model with a refined distribution of shear deformation. The Mori–Tanaka homogenization scheme is utilized to estimate the effective material properties of FGM nanoshells. After deduction of the non-classical governing differential equations via boundary layer theory of shell buckling, a perturbation-based solving process is employed to extract explicit expressions for nonlocal strain gradient stability paths of hydrostatic pressurized FGM microsized shells. It is observed that the nonlocality size effect causes to decrease the critical hydrostatic pressure and associated end-shortening of microsized shells, while the strain gradient size dependency leads to increase them. In addition, it is found that the influence of the internal strain gradient length scale parameter on the nonlinear instability characteristics of hydrostatic pressurized FGM microsized shells is a bit more than that of the nonlocal one.

Anisotropic compact stars in f(R) gravity

Abstract: We derive a new interior solution for stellar compact objects in $$f\mathcal {(R)}$$ gravity assuming a differential relation to constrain the Ricci curvature scalar. To this aim, we consider specific forms for the radial component of the metric and the first derivative of $$f\mathcal {(R)}$$ . After, the time component of the metric potential and the form of $$f({\mathcal {R}})$$ function are derived. From these results, it is possible to obtain the radial and tangential components of pressure and the density. The resulting interior solution represents a physically motivated anisotropic neutron star model. It is possible to match it with a boundary exterior solution. From this matching, the components of metric potentials can be rewritten in terms of a compactness parameter C which has to be $$C=2GM/Rc^2<<0.5$$ for physical consistency. Other physical conditions for real stellar objects are taken into account according to the solution. We show that the model accurately bypasses conditions like the finiteness of radial and tangential pressures, and energy density at the center of the star, the positivity of these components through the stellar structure, and the negativity of the gradients. These conditions are satisfied if the energy-conditions hold. Moreover, we study the stability of the model by showing that Tolman–Oppenheimer–Volkoff equation is at hydrostatic equilibrium. The solution is matched with observational data of millisecond pulsars with a withe dwarf companion and pulsars presenting thermonuclear bursts.

Dynamic Compression–Shear Response and Failure Criterion of Rocks with Hydrostatic Confining Pressure: An Experimental Investigation

Abstract: Rocks in the deep underground are likely subjected to both hydrostatic confining pressure and dynamic compression–shear load. Thus, accurately characterizing the dynamic properties and failure mechanism of hydrostatically confined rocks under combined compression–shear impacting is crucial for the stability assessment of deep underground rock structures. In this study, on the basis of an improved split Hopkinson pressure bar (SHPB) apparatus, the combined dynamic compression–shear tests are performed on inclined cylindrical sandstone specimens with hydrostatic confining pressures. During the test, the dynamic force balance of rock specimens can be well satisfied using the pulse shaping technique. Our results show that the hydrostatic confining pressure and dynamic loading rate help strengthen the load-carrying capacity of rocks. In contrast, the shear component in the dynamic load limits the dynamic peak stress of rocks. As hydrostatic confining pressure increases, the failure surface based on the Drucker–Prager criterion gradually expands outward. Under dynamic loading, the compressive deformation modulus of rocks decreases with increasing shear component in the dynamic load, contrary to its response to hydrostatic confining pressure. Fragmentation analysis indicates that the hydrostatic confining pressure and the shear component of dynamic loading restrict the fracture behavior of rocks. Besides, as the specimen inclination angle and the hydrostatic confining pressure increase, the failure pattern of rock specimens changes from the tensile-dominated failure with a truncated conical surface to the shear-dominated failure with a single shear plane along its short diagonal.

Interior solutions of relativistic stars with anisotropic matter in scale-dependent gravity

Abstract: We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton’s constant is allowed to vary with the radial coordinate throughout the star. Assuming (1) a linear equation-of-state in the MIT bag model for quark matter, and (2) a certain profile for the energy density, we integrate numerically the generalized structure equations, and we compute the basic properties of the strange quark stars, such as mass, radius and compactness. Finally, we demonstrate that stability criteria as well as the energy conditions are fulfilled. Our results show that a decreasing Newton’s constant throughout the objects leads to slightly more massive and more compact stars.

Characterizing hydrostatic mass bias with MOCK-X

Abstract: Surveys in the next decade will deliver large samples of galaxy clusters that transform our understanding of their formation. Cluster astrophysics and cosmology studies will become systematics limited with samples of this magnitude. With known properties, hydrodynamical simulations of clusters provide a vital resource for investigating potential systematics. However, this is only realized if we compare simulations to observations in the correct way. Here we introduce the \textsc{Mock-X} analysis framework, a multiwavelength tool that generates synthetic images from cosmological simulations and derives halo properties via observational methods. We detail our methods for generating optical, Compton-$y$ and X-ray images. Outlining our synthetic X-ray image analysis method, we demonstrate the capabilities of the framework by exploring hydrostatic mass bias for the IllustrisTNG, BAHAMAS and MACSIS simulations. Using simulation derived profiles we find an approximately constant bias $b\approx0.13$ with cluster mass, independent of hydrodynamical method or subgrid physics. However, the hydrostatic bias derived from synthetic observations is mass-dependent, increasing to $b=0.3$ for the most massive clusters. This result is driven by a single temperature fit to a spectrum produced by gas with a wide temperature distribution in quasi-pressure equilibrium. The spectroscopic temperature and mass estimate are biased low by cooler gas dominating the emission, due to its quadratic density dependence. The bias and the scatter in estimated mass remain independent of the numerical method and subgrid physics. Our results are consistent with current observations and future surveys will contain sufficient samples of massive clusters to confirm the mass dependence of the hydrostatic bias.

Anisotropic Strange Star in 5D Einstein-Gauss-Bonnet Gravity.

Abstract: In this paper, we investigated a new anisotropic solution for the strange star model in the context of 5D Einstein-Gauss-Bonnet (EGB) gravity. For this purpose, we used a linear equation of state (EOS), in particular pr=βρ+γ, (where β and γ are constants) together with a well-behaved ansatz for gravitational potential, corresponding to a radial component of spacetime. In this way, we found the other gravitational potential as well as main thermodynamical variables, such as pressures (both radial and tangential) with energy density. The constant parameters of the anisotropic solution were obtained by matching a well-known Boulware-Deser solution at the boundary. The physical viability of the strange star model was also tested in order to describe the realistic models. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified TOV equation and the dynamical stability through the critical value of the radial adiabatic index. The mass-radius relationship was also established for determining the compactness and surface redshift of the model, which increases with the Gauss-Bonnet coupling constant α but does not cross the Buchdahal limit.

Stability of hydrostatic equilibrium for the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity

Abstract: In mathematics and physics, the problem of the stability of perturbations near the hydrostatic balance is very important. Due to the classical tools designed for the fully dissipated systems are no longer apply, stability and global regularity problems on partially dissipated magnetic Benard fluid equations can be extremely challenging. This paper considers the stability problem on perturbations near the hydrostatic equilibrium for the 2D magnetic Benard fluid equations. We establish the global $$H^1$$ -stability of the 2D magnetic Benard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity and affirm the global stability in the Sobolev space $$H^1$$ setting.

Evaporation of dark matter from celestial bodies

Abstract: Scatterings of galactic dark matter (DM) particles with the constituents of celestial bodies could result in their accumulation within these objects. Nevertheless, the finite temperature of the medium sets a minimum mass, the evaporation mass, that DM particles must have in order to remain trapped. DM particles below this mass are very likely to scatter to speeds higher than the escape velocity, so they would be kicked out of the capturing object and escape. Here, we compute the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium, spanning the mass range $[10^{-10} - 10^2]~M_\odot$. We illustrate the critical importance of the exponential tail of the evaporation rate, which has not always been appreciated in recent literature, and obtain a robust result: for the geometric value of the scattering cross section and for interactions with nucleons, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by $E_c/T_\chi \sim 30$, where $E_c$ is the escape energy of DM particles at the core of the object and $T_\chi$ is the DM temperature. The minimum value of the DM evaporation mass is obtained for super-Jupiters and brown dwarfs, $m_{\rm evap} \simeq 0.7$ GeV. For other values of the scattering cross section, the DM evaporation mass only varies by a factor of two or less within the range $10^{-41}~\textrm{cm}^2 \leq \sigma_p \leq 10^{-31}~\textrm{cm}^2$, where $\sigma_p$ is the spin-independent DM-nucleon scattering cross section. Its dependence on parameters such as the local galactic DM density and velocity, or the scattering and annihilation cross sections is only logarithmic.

A depth integrated, coupled, two-phase model for debris flow propagation

Abstract: Debris flows are a type of fast landslides where a mixture of soil and water propagates along narrow channels. The main characteristics are (1) important relative displacements between the solid and fluid phases, and (2) development of pore-water pressures in excess to hydrostatic. The ratios between vertical and horizontal displacements of the flow, from the triggering point to the deposition, indicate that friction angles are much smaller than those measured in laboratories. Debris flows are modeled as two phases flow, but implementing pore-water pressure is an important issue. The purpose of this paper is to improve the existing two phases debris flow models by implementing pore-water pressures in excess to hydrostatic. It is found that pore pressure evolution depends on consolidation, changes in the flow depth, and changes and gradients of porosity. The proposed depth integrated mathematical model is discretized using two sets of SPH nodes (solid and fluid), with a set of finite difference meshes associated with each solid material SPH point. The paper presents two examples from where it is possible to gain insight into the differences between the models (with and without excess pore water pressure).

CFD-Based Investigation on Effects of Orifice Length–Diameter Ratio for the Design of Hydrostatic Thrust Bearings

Abstract: Orifice-restricted hydrostatic thrust bearings are broadly employed in ultra-precision machine tools, aerospace industries, and so forth. The orifice length–diameter ratio (OLDR) is one of the significant geometrical parameters of the orifice-restricted hydrostatic thrust bearing, which directly affects the performance of the bearing. To accurately guide the design of the hydrostatic thrust bearing, the effect of the OLDR on the performance of the hydrostatic thrust bearing needs to be thoroughly and scientifically investigated, especially for ultra-precision machine tools. In this paper, the influences of various OLDRs are comprehensively studied using the computational fluid dynamics (CFD) approach on the pressure pattern, velocity, turbulent intensity, and vortices, as well as the load capacity, stiffness, volume flow rate, and orifice flow resistance of the hydrostatic thrust bearing under identical operating conditions. The obtained results show that there are differences in performance behaviors of the hydrostatic thrust bearing caused by different OLDRs. Some new findings are obtained, particularly in the second-order small vortices which appear in the annular recesses with all OLDRs except that of 2, and the flow resistance does not always increase with increasing OLDRs. Finally, the proposed CFD approach is experimentally validated.

Blast waves in a paraxial fluid of light (a)

Abstract: We study experimentally blast wave dynamics on a weakly interacting fluid of light. The fluid density and velocity are measured in 1D and 2D geometries. Using a state equation arising from the analogy between optical propagation in the paraxial approximation and the hydrodynamic Euler's equation, we access the fluid hydrostatic and dynamic pressure. In the 2D configuration, we observe a negative differential hydrostatic pressure after the fast expansion of a localized over-density, which is a typical signature of a blast wave for compressible gases. Our experimental results are compared to the Friedlander waveform hydrodynamical model (Friedlander F. G., Proc. R. Soc. A: Math. Phys. Sci. , 186 (1946) 322). Velocity measurements are presented in 1D and 2D configurations and compared to the local speed of sound, to identify the supersonic region of the fluid. Our findings show an unprecedented control over hydrodynamic quantities in a paraxial fluid of light.

Stability and optimal decay for a system of 3D anisotropic Boussinesq equations

Abstract: This paper focuses on a system of three-dimensional (3D) Boussinesq equations modeling anisotropic buoyancy-driven fluids. The goal here is to solve the stability and large-time behavior problem on perturbations near the hydrostatic balance, a prominent equilibrium in fluid dynamics, atmospherics and astrophysics. Due to the lack of the vertical kinematic dissipation and the horizontal thermal diffusion, this stability problem is difficult. When the spatial domain is with being a 1D periodic box, this paper establishes the desired stability for fluids with certain symmetries. The approach here is to distinguish the vertical averages of the velocity and temperature from their corresponding oscillation parts. In addition, the oscillation parts are shown to decay exponentially to zero in time.

Blast waves in a paraxial fluid of light

Abstract: We study experimentally blast wave dynamics on a weakly interacting fluid of light. The fluid density and velocity are measured in 1D and 2D geometries. Using a state equation arising from the analogy between optical propagation in the paraxial approximation and the hydrodynamic Euler's equation, we access the fluid hydrostatic and dynamic pressure. In the 2D configuration, we observe a negative differential hydrostatic pressure after the fast expansion of a localized over-density, which is a typical signature of a blast wave for compressible gases. Our experimental results are compared to the Friedlander waveform hydrodynamical model. Velocity measurements are presented in 1D and 2D configurations and compared to the local speed of sound, to identify supersonic region of the fluid. Our findings show an unprecedented control over hydrodynamic quantities in a paraxial fluid of light.

Dynamically inflated wind models of classical Wolf-Rayet stars

Abstract: Context. Vigorous mass loss in the classical Wolf-Rayet (WR) phase is important for the late evolution and final fate of massive stars.Aims. We develop spherically symmetric time-dependent and steady-state hydrodynamical models of the radiation-driven wind outflows and associated mass loss from classical WR stars.Methods. The simulations are based on combining the opacities typically used in static stellar structure and evolution models with a simple parametrised form for the enhanced line opacity expected within a supersonic outflow.Results. Our simulations reveal high mass-loss rates initiated in deep and hot, optically thick layers around T ≈ 200 kK. The resulting velocity structure is non-monotonic and can be separated into three phases: (i) an initial acceleration to supersonic speeds (caused by the static opacity), (ii) stagnation and even deceleration, and (iii) an outer region of rapid re-acceleration (by line opacity). The characteristic structures seen in converged steady-state simulations agree well with the outflow properties of our time-dependent models.Conclusions. By directly comparing our dynamic simulations to corresponding hydrostatic models, we explicitly demonstrate that the need to invoke extra energy transport in convectively inefficient regions of stellar structure and evolution models, in order to prevent drastic inflation of static WR envelopes, is merely an artefact of enforcing a hydrostatic outer boundary. Moreover, the dynamically inflated inner regions of our simulations provide a natural explanation for the often-found mismatch between predicted hydrostatic WR radii and those inferred from spectroscopy; by extrapolating a monotonic β -type velocity law from the observable supersonic regions to the invisible hydrostatic core, spectroscopic models likely overestimate the core radius by a factor of a few. Finally, we contrast our simulations with alternative recent WR wind models based on co-moving frame (CMF) radiative transfer to compute the radiation force. Since CMF transfer currently cannot handle non-monotonic velocity fields, the characteristic deceleration regions found here are avoided in such simulations by invoking an ad hoc very high degree of clumping.

Optimal Decay Estimates for 2D Boussinesq Equations with Partial Dissipation

Abstract: Buoyancy-driven fluids such as many atmospheric and oceanic flows and the Rayleigh–Benard convection are modeled by the Boussinesq systems. By rigorously estimating the large-time behavior of solutions to a special Boussinesq system, this paper reveals a fascinating phenomenon on buoyancy-driven fluids that the temperature can actually stabilize the fluids. The Boussinesq system concerned here governs the motion of perturbations near the hydrostatic equilibrium. When the buoyancy forcing is not present, the velocity of the fluid obeys the 2D Navier–Stokes equation with only vertical dissipation and its Sobolev norm could potentially grow even though its precise large-time behavior remains open. This paper shows that the temperature through the coupling and interaction tames and regularizes the fluids, and causes the velocity (measured in Sobolev norms) to decay in time. Optimal decay rates are obtained.

A Weakly Non-hydrostatic Shallow Model for Dry Granular Flows

Abstract: A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration. A variable friction coefficient based on the $$\mu (I)$$ rheology is considered. The model is obtained from an asymptotic analysis in a local reference system, where the non-hydrostatic contribution is supposed to be small compared to the hydrostatic one. The non-hydrostatic counterpart of the pressure may be written as the sum of two terms: one corresponding to the stress tensor and the other to the vertical acceleration. The model introduced here is weakly non-hydrostatic, in the sense that the non-hydrostatic contribution related to the stress tensor is not taken into account due to its complex implementation. The motivation is to propose simple models including non-hydrostatic effects. In order to approximate the resulting model, a simple and efficient numerical scheme is proposed. It consists of a three-step splitting procedure and the resulting scheme is well-balanced for granular material at rest with slope smaller than the fixed repose angle. The model and numerical scheme are validated by means of several numerical tests, including a convergence test, a well-balanced test, and comparisons with laboratory experiments of granular collapse. The influence of non-hydrostatic terms and of the choice of the coordinate system (Cartesian or local) is also analyzed. We show that non-hydrostatic models are less sensitive to the choice of the coordinate system. In addition, the non-hydrostatic Cartesian model produces deposits similar to the hydrostatic local model as suggested by Denlinger and Iverson (J Geophys Res Earth Surf, 2004. https://doi.org/10.1029/2003jf000085 ), the flow dynamics being however different. Moreover, the proposed model, when written in Cartesian coordinates, can be seen as an improvement of their model, since the vertical velocity is computed and not estimated from the boundary conditions. In general, the non-hydrostatic model introduced here much better reproduces granular collapse experiments compared to hydrostatic models, especially at the beginning of the flow.

Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers

Abstract: Accurate simulations of flows in stellar interiors are crucial to improving our understanding of stellar structure and evolution. Because the typically slow flows are merely tiny perturbations on top of a close balance between gravity and the pressure gradient, such simulations place heavy demands on numerical hydrodynamics schemes. We demonstrate how discretization errors on grids of reasonable size can lead to spurious flows orders of magnitude faster than the physical flow. Well-balanced numerical schemes can deal with this problem. Three such schemes were applied in the implicit, finite-volume Seven-League Hydro (SLH) code in combination with a low-Mach-number numerical flux function. We compare how the schemes perform in four numerical experiments addressing some of the challenges imposed by typical problems in stellar hydrodynamics. We find that the $\alpha$-$\beta$ and deviation well-balancing methods can accurately maintain hydrostatic solutions provided that gravitational potential energy is included in the total energy balance. They accurately conserve minuscule entropy fluctuations advected in an isentropic stratification, which enables the methods to reproduce the expected scaling of convective flow speed with the heating rate. The deviation method also substantially increases accuracy of maintaining stationary orbital motions in a Keplerian disk on long timescales. The Cargo-LeRoux method fares substantially worse in our tests, although its simplicity may still offer some merits in certain situations. Overall, we find the well-balanced treatment of gravity in combination with low Mach number flux functions essential to reproducing correct physical solutions to challenging stellar slow-flow problems on affordable collocated grids.

Combining magneto-hydrostatic constraints with Stokes profiles inversions. II. Application to Hinode/SP observations

Abstract: Context. Inversion techniques applied to the radiative transfer equation for polarized light are capable of inferring the physical parameters in the solar atmosphere (temperature T , magnetic field B , and line-of-sight velocity v los ) from observations of the Stokes vector (i.e., spectropolarimetric observations) in spectral lines. Inferences are usually performed in the (x , y , τ c ) domain, where τ c refers to the optical-depth scale. Generally, their determination in the (x , y , z ) volume is not possible due to the lack of a reliable estimation of the gas pressure, particularly in regions of the solar surface harboring strong magnetic fields.Aims. We aim to develop a new inversion code capable of reliably inferring the physical parameters in the (x , y , z ) domain.Methods. We combine, in a self-consistent way, an inverse solver for the radiative transfer equation (Firtez-DZ) with a solver for the magneto-hydrostatic equilibrium, which derives realistic values of the gas pressure by taking the magnetic pressure and tension into account.Results. We test the correct behavior of the newly developed code with spectropolarimetric observations of two sunspots recorded with the spectropolarimeter (SP) instrument on board the Hinode spacecraft, and we show how the physical parameters are inferred in the (x , y , z ) domain, with the Wilson depression of the sunspots arising as a natural consequence of the force balance. In particular, our approach significantly improves upon previous determinations that were based on semiempirical models.Conclusions. Our results open the door for the possibility of calculating reliable electric currents in three dimensions, j (x , y , z ), in the solar photosphere. Further consistency checks would include a comparison with other methods that have recently been proposed and which achieve similar goals.

Properties of RbHgF3 fluoro-perovskite under growing hydrostatic pressure from first-principles calculations

Abstract: Mercury fluoro-perovskites based on Rubidium have a lot of technical relevance nowadays, especially in optical and semiconductive applications. A Cambridge Serial Total Energy Package code analysis using the Density Functional Theory was performed to calculate the structural, electronic, elastic, optical, and thermodynamic characteristics as well as the bonding nature of cubic fluoro-perovskites RbHgF3 under various hydrostatic pressures. To determine the total energy, the Perdew–Berke–Ernzerhof generalized gradient approximation was used to manage the exchange–correlation potential. The effects of hydrostatic pressure are studied in the region of 0–20 GPa, which maintains the cubic stable condition of RbHgF3 fluoro-perovskite. Experimental and prior theoretical results agree well with the calculated lattice parameters. When the pressure reached 20 GPa from 0 GPa, the volume, bond length, and lattice constant decreased. The bandgaps demonstrate an indirect band structure, with substantial reductions at various external forces. The total density of states reveals a non-metallic behavior. Mechanical properties satisfy the stability criteria until 20 GPa for this compound, and ductile behavior is also found within that pressure range. External stress modifies the optical characteristics a bit such as the complicated dielectric function, absorption, conductivity, and reflectivity. The presence of blue shift is confirmed by the movement of absorption edges toward higher energies, making this material an intriguing option for optical devices.

A robust method for quantification of surface elasticity in soft solids.

Abstract: We propose an approach to measure surface elastic constants of soft solids. Generally, this requires one to probe interfacial mechanics at around the elastocapillary length scale, which is typically microscopic. Deformations of microscopic droplets embedded in soft solids are particularly attractive, because they avoid intrinsic nonlinearities associated with previous experiments such as the equilibrium of contact lines and the relaxation of patterned surfaces. We derive analytical solutions for the shape of droplets under uniaxial deformation and for the radius of droplets upon hydrostatic inflation. We couple mechanical deformations to the dissolution of droplets to assess experimental sensitivities. Combined with experimental data from both modes of deformation, one should be able to reliably extract the complete set of isotropic surface material parameters following a specific minimization procedure.

Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers

Abstract: Context. Accurate simulations of flows in stellar interiors are crucial to improving our understanding of stellar structure and evolution. Because the typically slow flows are merely tiny perturbations on top of a close balance between gravity and the pressure gradient, such simulations place heavy demands on numerical hydrodynamics schemes.Aims. We demonstrate how discretization errors on grids of reasonable size can lead to spurious flows orders of magnitude faster than the physical flow. Well-balanced numerical schemes can deal with this problem.Methods. Three such schemes were applied in the implicit, finite-volume SEVEN-LEAGUE HYDRO code in combination with a low-Mach-number numerical flux function. We compare how the schemes perform in four numerical experiments addressing some of the challenges imposed by typical problems in stellar hydrodynamics.Results. We find that the α -β and deviation well-balancing methods can accurately maintain hydrostatic solutions provided that gravitational potential energy is included in the total energy balance. They accurately conserve minuscule entropy fluctuations advected in an isentropic stratification, which enables the methods to reproduce the expected scaling of convective flow speed with the heating rate. The deviation method also substantially increases accuracy of maintaining stationary orbital motions in a Keplerian disk on long timescales. The Cargo–LeRoux method fares substantially worse in our tests, although its simplicity may still offer some merits in certain situations.Conclusions. Overall, we find the well-balanced treatment of gravity in combination with low Mach number flux functions essential to reproducing correct physical solutions to challenging stellar slow-flow problems on affordable collocated grids.

Ocean dynamic equations with the real gravity

Abstract: Two different treatments in ocean dynamics are found between the gravity and pressure gradient force Vertical component is 5–6 orders of magnitude larger than horizontal components for the pressure gradient force in large-scale motion, and for the gravity in any scale motion The horizontal pressure gradient force is considered as a dominant force in oceanic motion from planetary to small scales However, the horizontal gravity is omitted in oceanography completely A non-dimensional C number (ratio between the horizontal gravity and the Coriolis force) is used to identify the importance of horizontal gravity in the ocean dynamics Unexpectedly large C number with the global mean around 24 is obtained using the community datasets of the marine geoid height and ocean surface currents New large-scale ocean dynamic equations with the real gravity are presented such as hydrostatic balance, geostrophic equilibrium, thermal wind, equipotential coordinate system, and vorticity equation

Conical hydrostatic journal bearings for high speeds

Abstract: Conventional conical hydrostatic bearings are compared with less conventional three-recess and four-recess designs for operation in hybrid hydrostatic/hydrodynamic mode. Design implications are dis...