共查询到20条相似文献，搜索用时 31 毫秒
1.
Abstract The equilibrium properties of the magnetic field of an axisymmetric star are studied. A family of analytical solutions to the magnetohydrostatic equations is found, which are used to model the slow evolution of the field through a series of equilibria. Firstly, a model is set up for a force-free dipole-like field, which has a toroidal field component; it is found that, as such a field is twisted up, a critical point is reached, at which the field topology changes. If the twist is increased beyond this point, there is no physically reasonable equilibrium. Next, an untwisted magnetostatic dipole-like field is studied, with an increasing pressure differential between pole and equator. A critical point again occurs when the pressure differential becomes too large. Finally a force-free quadrupole-like field is modelled, which is being twisted up, for example by differential rotation; this has similar properties to the dipole-like field. In each case, it is suggested that, when the critical point is reached, the field will no longer evolve smoothly, but will change catastrophically to a new stable, releasing energy. Such an event could represent the onset of a stellar flare or some other dynamic stellar process. 相似文献
2.
Abstract Modelling and prediction of hydrological processes (e.g. rainfall–runoff) can be influenced by discontinuities in observed data, and one particular case may arise when the time scale (i.e. resolution) is coarse (e.g. monthly). This study investigates the application of catastrophe theory to examine its suitability to identify possible discontinuities in the rainfall–runoff process. A stochastic cusp catastrophe model is used to study possible discontinuities in the monthly rainfall–runoff process at the Aji River basin in Azerbaijan, Iran. Monthly-averaged rainfall and flow data observed over a period of 20 years (1981–2000) are analysed using the Cuspfit program. In this model, rainfall serves as a control variable and runoff as a behavioural variable. The performance of this model is evaluated using four measures: correlation coefficient, log-likelihood, Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results indicate the presence of discontinuities in the rainfall–runoff process, with a significant sudden jump in flow (cusp signal) when rainfall reaches a threshold value. The performance of the model is also found to be better than that of linear and logistic models. The present results, though preliminary, are promising in the sense that catastrophe theory can play a possible role in the study of hydrological systems and processes, especially when the data are noisy. Citation Ghorbani, M. A., Khatibi, R., Sivakumar, B. & Cobb, L. (2010) Study of discontinuities in hydrological data using catastrophe theory. Hydrol. Sci. J. 55(7), 1137–1151. 相似文献
3.
Abstract In this paper we study the stability of an idealised magnetostatic coronal loop, incorporating both the effect of line-tying, due to the dense photosphere, and of pressure gradients. The stability equations may be solved analytically for our particular equilibrium. From the marginally stable case, the critical conditions separating instability from stability are derived. It is found that stretching or twisting a loop eventually makes it kink unstable. 相似文献
4.
Abstract This paper explores magnetic equilibria which could result from the kink instability in a cylindrical magnetic flux tube. We examine a variety of cylindrical magnetic equilibria which are susceptible to the kink, and simulate its evolution in a frictional fluid. We assume that the evolution takes place under conditions of helical symmetry, so the problem becomes effectively two-dimensional. The initial cylindrical equilibrium field is specified in terms of its twist function k(r) = B θ/(rBz ) and for a variety of k(r) functions we calculate linear growth rates for the kink instability, assuming that it develops under helical symmetry with pitch τ. We find that the growth rate is sensitive to the value of τ. We simulate nonlinear evolution of the kink using a Lagrangian frictional code which constrains the field to have helical symmetry of a given pitch τ. Ideal MHD is assumed and the plasma pressure is taken to be small in order to mimic conditions in the solar corona. In some cases the flux tube evolves to a new smooth helically symmetric equilibrium which involves a relatively small change in the maximum electric current. In other cases there is evidence of current-sheet formation. 相似文献
5.
P. F. Linden 《地球物理与天体物理流体动力学》2013,107(3-4):163-182
Abstract The flow of a two-layer flow in a rotating channel on an f-plane over topography with sinusoidal variation of height in a direction parallel to the flow is investigated. When the two layers flow in opposite directions a resonance is found when the topographic scale matches the free mode of the system. We examine the stability of the forced mode in the vicinity of this resonance by means of a perturbation expansion of the topographic height. Both subresonant and super-resonant instabilities are found and their equilibration is examined. For small values of the dissipation multiple equilibria are found. The topographic drag releases potential energy even when the flow is baroclinically stable. 相似文献
6.
Y. T. Fung 《地球物理与天体物理流体动力学》2013,107(1-4):57-69
Abstract A stratified parallel flow in a potential force field is investigated. The density, the velocity, and the potential field of the flow are allowed to vary in two directions. Three sufficient conditions are derived for guaranteed stability of the flow. Two are the classical stability conditions in their respective directions. The third, measured by a newly defined Richardson number, is a result of the shear interaction and the pressure balance condition for stability. Like the classical Richardson number which is always positive preceding stability, this new number acts as a constraint on the other two stability conditions. In addition to the above stability criteria, a semi-ellipse theorem is derived for the present flow. 相似文献
7.
The cross-sectional stability of double inlet systems is investigated using an exploratory model that combines Escoffier’s stability concept for the evolution of the inlet’s cross-sectional area with a two-dimensional, depth-averaged (2DH) hydrodynamic model for tidal flow. The model geometry consists of four rectangular compartments, each with a uniform depth, associated with the ocean, tidal inlets and basin. The water motion, forced by an incoming Kelvin wave at the ocean’s open boundary and satisfying the linear shallow water equations on the f -plane with linearised bottom friction, is in each compartment written as a superposition of eigenmodes, i.e. Kelvin and Poincaré waves. A collocation method is employed to satisfy boundary and matching conditions. The analysis of resulting equilibrium configurations is done using flow diagrams.
Model results show that internally generated spatial variations in the water motion are essential for the existence of stable equilibria with two inlets open. In the hydrodynamic model used in the paper, both radiation damping into the ocean and basin depth effects result in these necessary spatial variations. Coriolis effects trigger an asymmetry in the stable equilibrium cross-sectional areas of the inlets. Furthermore, square basin geometries generally correspond to significantly larger equilibrium values of the inlet cross-sections. These model outcomes result from a competition between a destabilising (caused by inlet bottom friction) and a stabilising mechanism (caused by spatially varying local pressure gradients over the inlets).
相似文献8.
ABSTRACTThe problem of transmission of pressure head through the zone of tension saturation in the Lisse effect (LE), i.e., the rapid response of groundwater level to pressurized pore air in the unsaturated zone, is investigated theoretically and experimentally. From the law of conservation of energy and the continuity equation, a one-dimensional diffusion equation is derived for transmission of pressure head through the zone of tension saturation. The solution to the equation is the pressure head at any point below the upper boundary of the zone of tension saturation and at any time after the compressed pore air pressure is imposed on the boundary. The key parameter, which determines the behaviour of transmission of pressure head, is the newly proposed pressure head diffusivity coefficient. The theoretical results agree with the experimental results, obtained from laboratory column experiments in three physically different soils.
Editor Demetris Koutsoyiannis Associate editor Xi Chen 相似文献
9.
Abstract Many advances in simulating single and two-phase fluid flow and heat transport in porous media have recently been made in conjunction with geothermal energy research. These numerical models reproduce system thermal and pressure behaviour and can be used for heat-transport problems other than those associated with geothermal energy development, such as high-level radioactive waste disposal and heat-storage projects. Although these models are general, additional research is necessary before they can be applied to certain site-specific problems that are concerned with additional processes, such as mass transport and flow in fractured media. 相似文献
10.
Abstract It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov et al. (1999) are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime β0 ≈ γ0 ≈ δ0 ≈ ε0 ? 1, where β0, γ0, δ0, and ε0 are related to the thermal, poloidal-current, flow and gravitating energies normalized to the poloidal-magnetic-field energy, respectively, and (b) in the high-energy regime β0 ≈ γ0 ≈ δ0 ≈ ε0 ? 1. It turns out that in the high-energy regime all four forces, pressure-gradient, toroidal-magnetic-field, inertial, and gravitating contribute equally to the formation of magnetic surfaces very extended and localized about the symmetry plane such that the resulting equilibria resemble the accretion disks in astrophysics. 相似文献
11.
Abstract The behaviour of the shear velocity along a gravel-bed channel is investigated experimentally in the presence of a negative pressure gradient (accelerating flow). Different methods of estimation of the shear velocity, derived from vertical profiles of the mean longitudinal point velocity, are examined and a new method is proposed. Results show that the proposed method of estimation is comparable to the St Venant and Clauser's methods. At a specific cross section, for constant bottom slope and relative roughness, shear velocity increases with discharge. 相似文献
12.
《水文科学杂志》2013,58(2):349-362
Abstract A methodology of time-step estimation for numerically solving the Richards equation is discussed. Its importance in simulating water movement in unsaturated—saturated soils is shown for infiltration into a soil profile by applying various time-step estimations and boundary conditions for different soils. In order to test the results of the computations, infiltration theory was applied. According to infiltration theory, the pressure head in the initially unsaturated part will not take positive values as long as the moisture front has not reached the phreatic level, or, in the case of a profile with a free-draining lower boundary, it is not saturated at the base. In other cases, the appearance of positive values of the pressure head produces incorrect values for the inflow rate q. 相似文献
13.
Brian H. Fiedler 《地球物理与天体物理流体动力学》2013,107(4):195-201
Abstract This paper explores the properties of a two-dimensional, Boussinesq convection model with an ad hoc term in the buoyancy tendency equation that represents a positive external feedback process acting on the buoyancy fluctuations. Linear stability analyses and nonlinear integrations are presented for the case of constant heat flux boundary conditions. Although the large wavenumber modes grow the fastest from a state of rest, the nonlinear solutions progressively evolve to cells of small wavenumber. Applications to mesoscale cellular convection in the atmosphere are discussed. 相似文献
14.
Abstract A new tracer technique for the direct observation of movement and dispersion of estuarine and inshore waters is described. The method utilizes the fluorescent organic pigment, rhodamine B, together with a very stable, compact filter fluorometer. The tracer is very satisfactory with regard to stability, cost, toxicity, and detectability. Its nearly unique fluorescent and absorption spectra minimize the effect of natural background so that concentrations as low as 2 × 10?11 have been observed in the field, with expectations that this detection limit can be lowered to 4 × 10?12. Advection and diffusion from approximate point sources discharged in Baltimore Harbor, in Conowingo Lake, and in Chesapeake Bay were measured. Theoretical models of horizontal diffusion are compared to the observed decrease in concentration with time. 相似文献
15.
Abstract Accretion discs in astrophysics are fundamental for converting gravitational binding energy into observed electromagnetic radiation. We study the behavior of waves in a two dimensional supersonic Keplerian flow inside a given gravitational potential. We present the effects of shearing and rotation on short waves, and the numerical study of the dynamical stability of such flows with respect to various perturbations. We show that a large class of dynamical effects, due to pressure and associated to short time scales, may be excited. 相似文献
16.
Abstract One-dimensional solute transport, originating from a continuous uniform point source, is studied along unsteady longitudinal flow through a heterogeneous medium of semi-infinite extent. Velocity is considered as directly proportional to the linear spatially-dependent function that defines the heterogeneity. It is also assumed temporally dependent. It is expressed in both the independent variables in degenerate form. The dispersion parameter is considered to be proportional to square of the velocity. Certain new independent variables are introduced through separate transformations to reduce the variable coefficients of the advection–diffusion equation to constant coefficients. The Laplace Transformation Technique (LTT) is used to obtain the desired solution. The effects of heterogeneity and unsteadiness on the solute transport are investigated. Editor D. Koutsoyiannis; Associate editor F.F. Hattermann Citation Kumar, A., Jaiswal, D.K., and Kumar, N., 2012. One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity. Hydrological Sciences Journal, 57 (6), 1223–1230. 相似文献
17.
John D. HEM 《水文科学杂志》2013,58(3):30-37
Abstract The solubility of manganese in natural water is strongly influenced bychemical equilibria involving Mn+2, Mn+3 and Mn+4 species, redox potential, pH, and dissolved species of bicarbonate and sulfate. The solubility of manganese is shown by graphs as a function of Eh and pH in the absence of sulfate and in the presence of several different fixed activities of bicarbonate and sulfate ranging from 10 to 2,000 ppm (parts per million). Solubility is increased by the complexes MnHCO+ 3 and MnSO4 aq. whose association constants are 63 and 190, respectively. Divalent manganese is soluble to the extent of 0.10 to 1.0 ppm at equilibrium in most ground and surface water. Manganese is more soluble than iron under most possible conditions, especially inthe Eh-pH range common in river water. 相似文献
18.
I. C. Walton 《地球物理与天体物理流体动力学》2013,107(1-4):81-103
Abstract The stability of a zonal shear flow to symmetric baroclinic perturbations is examined when the Ekman number, E, is asymptotically small. It is assumed, following Antar and Fowlis (1982), that the zonal Row is generated by imposing a constant horizontal temperature gradient γ* at the horizontal boundaries, and by maintaining a constant temperature difference δT* between them. The boundaries are at rest relative to a rotating frame. Features of the neutral stability curve are determined for several ranges of values of δT/E 1/3, where δT = δT*/Hγ* and H is the depth of the fluid layer, and all values of the Prandtl number, [sgrave]. In some cases it is possible to determine the whole curve analytically. The most important feature of the results is that the neutral stability curve is closed. The results are compared to the numerical integrations of Antar and Fowlis (1982). The qualitative features of the solutions are in accord and the quantitative results are, in most cases, as good as can be expected for E only as small as ～ 10?4. The implications of the results for experimental observations of symmetric baroclinic instability are explored. 相似文献
19.
Lorna Richardson 《地球物理与天体物理流体动力学》2013,107(1-4):169-182
Abstract We establish a nonlinear stability result for convection in a generalized incompressible fluid. Both numerical calculations and an asymptotic analysis are carried out. The linear and nonlinear results are shown to be very close in both cases, implying that the region of possible subcritical instabilities is very small. During this work I was supported by a research studentship awarded by the Science and Engineering Council of the United Kingdom. 相似文献
20.
Abstract We impose a surface forcing on the 2D, Boussinesq, thermohaline equations in a rectangular domain, in the form of equatorially symmetric cosine distributions of salinity flux and temperature. This system may be seen as an idealization of the ocean thermohaline circulation on the global scale over intervals of centuries or millenia. Multiple steady states are found numerically. They reflect the competition between the opposite signs of the temperature and salinity-driven equatorially symmetric circulations. There are also pole-to-pole, equatorially asymmetric circulations. In the control space of the temperature and salinity-flux forcing amplitudes, these equilibria form two cusp catastrophes, and transitions between stable equilibria occur through several distinct bifurcations. These catastrophes can be reproduced in simple box models connecting stirred reservoirs through capillary pipes. This steady-state analysis may provide a framework for a better understanding of climatic transitions between different stable regimes of the ocean-atmosphere system. 相似文献