Magnetic buoyancy and the Boussinesq approximation

Abstract

The full Boussinesq equations for hydromagnetic convection are derived and shown to include the effects of magnetic buoyancy. Instabilities caused by magnetic buoyancy are analyzed and their roles in double convection are brought out.     

Baroclinic nonlinear exchanges of energy and potential enstrophy in the quasi-geostrophic two-layer model

Abstract

Merilees and Warn's (1975) nonlinear interaction analysis of two-dimensional nondivergent flow is extended to examine the quasi-geostrophic two-layer model. Two sets of triads exist in this model (Salmon, 1978). The purely barotropic triads are the same as the triads examined by Merilees and Warn. Baroclinic-barotropic triads are found to exchange more energy or potential enstrophy with smaller or larger scales depending on the scale of motion as compared with the internal Rossby deformation radius and the relative wavenumber position of baroclinic and barotropic components.     

Three-dimensional primary instabilities of a stratified,dissipative, parallel flow

Abstract

We demonstrate the existence of a class of dissipative, stratified, parallel shear flows which, as a consequence of linear supercritical instability, evolve directly into three-dimensional flows without the requirement for an intermediate two-dimensional finite-amplitude state. This represents a counter-example to a common misinterpretation of Squire's theorm, namely that the fastest-growing unstable mode of a dissipative parallel shear flow must be two-dimensional.     

Effect of fracture pressure depletion regimes on the dual-porosity shape factor for flow of compressible fluids in fractured porous media

A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a dual-porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media. Adv Water Res 2011;34(5):627-39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.     

Baroclinic,Kelvin and inertia-gravity waves in the barostrat instability experiment

The differentially heated rotating annulus is a laboratory experiment historically designed for modelling large-scale features of the mid-latitude atmosphere. In the present study, we investigate a modified version of the classic baroclinic experiment in which a juxtaposition of convective and motionless stratified layers is created by introducing a vertical salt stratification. The thermal convective motions are suppressed in a central region at mid-depth of the rotating tank, therefore double-diffusive convection rolls can develop only in thin layers located at top and bottom, where the salt stratification is weakest. For high enough rotation rates, the baroclinic instability destabilises the flow in the top and the bottom shallow convective layers, generating cyclonic and anticyclonic eddies separated by the stable stratified layer. Thanks to this alternation of layers resembling the convective and radiative layers of stars, the planetary’s atmospheric troposphere and stratosphere or turbulent layers at the sea surface above stratified waters, this new laboratory setup is of interest for both astrophysics and geophysical sciences. More specifically, it allows to study the exchange of momentum and energy between the layers, primarily by the propagation of internal gravity waves (IGW). PIV velocity maps are used to describe the wavy flow pattern at different heights. Using a co-rotating laser and camera, the wave field is well resolved and different wave types can be found: baroclinic waves, Kelvin and Poincaré type waves. The signature of small-scale IGW can also be observed attached to the baroclinic jet. The baroclinic waves occur at the thin convectively active layer at the surface and the bottom of the tank, though decoupled they show different manifestation of nonlinear interactions. The inertial Kelvin and Poincaré waves seem to be mechanically forced. The small-scale wave trains attached to the meandering jet point to an imbalance of the large-scale flow. For the first time, the simultaneous occurrence of different wave types is reported in detail for a differentially heated rotating annulus experiment.     

Characteristics and origins of primary fluids and noble gases in mantle-derived minerals from the Yishu area, Shandong Province, China

springerlink.com Studies of mantle fluids are currently one of the hot topics in the earth science, greatly contributing to re-vealing origins and evolutions of fluids. In general, the concept of mantle fluids refers to their active compo-nents, such as CO2, H2O, N2, etc., while the noble gases inert in chemical properties belong to another research system. Due to their marked differences in various fluid sources of the Earth[1], the isotopic sig-natures of He and Ar have been widely used a…     

On the RH relations across weak and strong shocks in van der Waals gases

The Rankine–Hugoniot (RH) jump relations for normal shock waves in van der Waals fluids have been studied in order to improve a theoretical understanding of those shock related phenomena as observed in a real atmosphere which cannot be accounted for by the ideal gas model. The RH jump relations for the pressure, density, particle velocity, temperature, speed of sound, adiabatic compressibility and change-in-entropy across the shock front have been analysed in terms of the non-idealness parameter of the gas, downstream Mach number and adiabatic index of the gas. Further, as the strength of shock waves may range from weak to strong, the convenient forms of RH jump relations for weak and strong shock waves have been discussed, simultaneously. Finally, the effects on the flow-field behind the shock front have been explored due to the non-idealness parameter of the gas, downstream Mach number and adiabatic index of the gas.     

The Boussinesq and anelastic liquid approximations for convection in the Earth’s core

Convection in the Earth’s core is usually studied in the Boussinesq approximation in which the compressibility of the liquid is ignored. The density of the Earth’s core varies from ICB to CMB by approximately 20%. The question of whether we need to take this variation into account in core convection and dynamo models is examined. We show that it is in the thermodynamic equations that differences between compressible and Boussinesq models become most apparent. The heat flux conducted down the adiabat is much smaller near the inner core boundary than it is near the core-mantle boundary. In consequence, the heat flux carried by convection is much larger nearer the inner core boundary than it is near the core-mantle boundary. This effect will have an important influence on dynamo models. Boussinesq models also assume implicitly that the rate of working of the gravitational and buoyancy forces, as well as the Ohmic and viscous dissipation, are small compared to the heat flux through the core. These terms are not negligible in the Earth’s core heat budget, and neglecting them makes it difficult to get a thermodynamically consistent picture of core convection. We show that the usual anelastic equations simplify considerably if the anelastic liquid approximation, valid if αT?1, where α is the coefficient of expansion and T a typical core temperature, is used. The resulting set of equations are not significantly more difficult to solve numerically than the usual Boussinesq equations. The relationship of our anelastic liquid equations to the Boussinesq equations is also examined.     

A semi-analytical time integration for numerical solution of Boussinesq equation

A semi-analytical time integration method is proposed for the numerical simulation of transient groundwater flow in unconfined aquifers by the nonlinear Boussinesq equation. The method is based on the analytical solution of the system of ordinary differential equations with constant coefficients. While it is unconditionally stable and more accurate than the finite difference methods, the computational cost is much more expensive than (can be more than 10 times) that of the finite difference methods for a single time step. However, by partitioning the nonlinear parameters into linear and nonlinear parts, the costly computation can be performed only once. With larger and less variable time step sizes, the total computational cost can be significantly reduced. Three examples are included to illustrate the advantages and limitations of the proposed method.     

Penetrative convection in rotating fluids: A model for the base of stellar convection zones

Abstract

To model penetrative convection at the base of a stellar convection zone we consider two plane parallel, co-rotating Boussinesq layers coupled at their fluid interface. The system is such that the upper layer is unstable to convection while the lower is stable. Following the method of Kondo and Unno (1982, 1983) we calculate critical Rayleigh numbers R_c for a wide class of parameters. Here, R_c is typically much less than in the case of a single layer, although the scaling R_c～T^2/3 as T → ∞ still holds, where T is the usual Taylor number. With parameters relevant to the Sun the helicity profile is discontinuous at the interface, and dominated by a large peak in a thin boundary layer beneath the convecting region. In reality the distribution is continuous, but the sharp transition associated with a rapid decline in the effective viscosity in the overshoot region is approximated by a discontinuity here. This source of helicity and its relation to an alpha effect in a mean-field dynamo is especially relevant since it is a generally held view that the overshoot region is the location of magnetic field generation in the Sun.     

Effective probability distribution approximation for the reconstruction of missing data

Stochastic Environmental Research and Risk Assessment - Spatially distributed processes can be modeled as random fields. The complex spatial dependence is then incorporated in the joint probability...     

豫01井水位异常与地震的关系分析

分析豫01井与地震活动的对应关系,统计映震情况,发现该井地震响应比较灵敏。希望研究结果有助于今后对范县豫01井流体异常的识别,并增强对冀鲁豫交界区及邻区地震活动的监测与预测能力。     

The origin of the crustal conductive layer and the conductivity of supercritical brine (II)

This paper is the second one of a series of three papers on fluid evolution of the crust-upper mantle and the causes of earthquakes. Based on the first paper, two conductive mechanisms of the crustal conductive layer (CCL), graphite and supercritical saline aqueous fluids, are discussed. As there are difficulties for graphite model, the supercritical fluids are investigated in this paper concerning the phases, the electrically conductive behaviors, the evolution and the sealing mechanisms of the fluids. It is obvious that this model is reasonable to explain the geophysical and geochemical characteristics of the CCL presented in the first paper.     

Seismicity of the Koyna region and regional tectonomagmatism of the Western Margin (India)

Recent findings on the Meso-Cenozoic tectonomagmatism and deep-seated anomalous geophysical structures suggest a close linkage between the seismicity of the Koyna region, the Westernghat uplift (WG-U) and associated thermomechanical and fluid activities. The WG-U seems to be the result of late Cretaceous thermal mobilization, erosion of the Deccan trap cover and superposition of compressional stress. The association of seismicity with uplift seems to result from movement of deep-seated heat and fluids/volatiles along the edges (or boundary faults) of the uplift; because the force required for crustal deformation depends on the relief. Observed gradients in relief may be attributed to the differential erosion-rates and heat inputs, due to the time gap of 50 Ma in the break-ups and plume activities on the eastern and western sides and consequence magmatism. Further, the geology and tectonics strongly indicate that the western margin (WM) is a relic of a mobile arm (MA), that included Madagascar, and which formed a part of the Proterozoic mobile belt of greater India (fort>85 Ma). The mobile nature of the WM facilitates mantle upwellings and transient elevation of isotherms at depth, raising the possibility of intermittent metamorphism and greater deformation.Superposition of the ongoing compression and uplift-induced forces make local permeability and pore-fluid pressure vital in triggering the seismic slip over the Peninsular shield. Certain representative model calculations have been carried out to estimate change in the e.m. induction characteristics caused by an intermittent hydraulic connectivity. The results show a drop in the resistivity which could be a useful monitoring index. The close connection of uplift and fluid activity as discussed here seems applicable for other active parts of the South Indian Shield (SIS) also.     

An Asymptotic Analysis of a Simple Model for the Structure and Dynamics of the Ramdas Layer

This paper presents a complete asymptotic analysis of a simple model for the evolution of the nocturnal temperature distribution on bare soil in calm clear conditions. The model is based on a simplified flux emissivity scheme that provides a nondiffusive local approximation for estimating longwave radiative cooling near ground. An examination of the various parameters involved shows that the ratio of the characteristic radiative to the diffusive timescale in the problem is of order 10⁻³, and can therefore be treated as a small parameter (μ). Certain other plausible approximations and linearization lead to a new equation whose asymptotic solution as μ → 0 can be written in closed form. Four regimes, consisting of a transient at nominal sunset, a radiative-diffusive boundary (‘Ramdas’) layer on ground, a boundary layer transient and a radiative outer solution, are identified. The asymptotic solution reproduces all the qualitative features of more exact numerical simulations, including the occurrence of a lifted temperature minimum and its evolution during night, ranging from continuing growth to relatively sudden collapse of the Ramdas layer.     

Tracing the history of submarine hydrothermal inputs and the significance of hydrothermal hafnium for the seawater budget—a combined Pb-Hf-Nd isotope approach

Secular variations in the Pb isotopic composition of a mixed hydrogenous-hydrothermal ferromanganese crust from the Bauer Basin in the eastern Equatorial Pacific provide clear evidence for changes in hydrothermal contributions during the past 7 Myr. The nearby Galapagos Rise spreading center provided a strong hydrothermal flux prior to 6.5 Ma. After 6.5 Ma, the Pb became stepwise more radiogenic and more similar to Equatorial Pacific seawater, reflecting the westward shift of spreading to the presently active East Pacific Rise (EPR). A second, previously unrecognized enhanced hydrothermal period occurred between 4.4 and 2.9 Ma, which reflects either off-axis hydrothermal activity in the Bauer Basin or a late-stage pulse of hydrothermal Pb from the then active, but waning Galapagos Rise spreading center.Hafnium isotope time-series of the same mixed hydrogenous-hydrothermal crust show invariant values over the past 7 Myr. Hafnium isotope ratios, as well as Nd isotope ratios obtained for this crust, are identical to that of hydrogenous Equatorial Pacific deep water crusts and clearly indicate that hydrothermal Hf, similar to Nd, does not travel far from submarine vents. Therefore, we suggest that hydrothermal Hf fluxes do not contribute significantly to the global marine Hf budget.