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1.
Non-linear Rayleigh-Bénard convection in a fluid layer is considered as a model of convection in the Earth's upper mantle. Previous studies have shown that when the temperature is held fixed at one of the boundaries of the layer, convection takes place in cells of width of the order of the layer depth or less. We investigate the effects of a different thermal boundary condition, in which the flux of heat is held fixed on both layer boundaries; then if this flux is just greater than that required for the onset of convection, motion takes place on horizontal scales much greater than the layer depth. An analytical treatment of the equations, based on an expansion in the depth-to-width ratio of the cells, shows that cells of a definite horizontal scale are the fastest growing according to linearised theory, but that these cells are unstable to ones of larger wavelength than themselves. Thus the dominant wavelength lengthens with time. The results hold whether the heat flux is generated internally of comes from beneath the layer. These results produce flow patterns similar to those found when the heat flux is much greater than the critical value. The results have important consequences for the understanding of mantle convection. 相似文献
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WANG Xingtao ZHAI Shikui MENG Fanshun LI Huaiming YU Zenghui SUN Ge XUE Gang 《中国科学D辑(英文版)》2006,49(7):773-784
1 Introduction Hydrothermal circulation is the key process of hydrothermal activity. Modern seafloor hydrothermal circulation can be divided into three parts: convective cells in the oceanic curst, interface between seafloor and ocean and hydrothermal plume. Hydrothermal convection in the crust is the dominant part of the whole seafloor hydrothermal circulation. The distribu-tion and nature of hydrothermal system in the oceanic crust are controlled by crust thermal structures and permeability … 相似文献
4.
B. I. Birger 《Izvestiya Physics of the Solid Earth》2011,47(6):541-554
Stationary solutions including wave solutions with constant amplitudes are found for nonlinear equations of thermal convection
in a layer with nonlinear rheology. The solution is based on the Fourier expansion of unknown velocities and temperatures
with only the first and first two terms retained in the velocity and temperature series, respectively. This method, which
can be regarded as the Lorenz method, yields the Lorenz equations that fairly well describe the thermal convection in a layer
with Newtonian rheology if the Rayleigh number is not very large. The obtained generalization of the Lorenz equations to the
case of an integral (having a memory) nonlinear rheology implies that only the first term is retained in the Fourier series
for the stress components, i.e., the nonlinear rheological equation is harmonically linearized. However, in the Fourier series
of temperature, it is essential to keep the second term: this term, which is independent of the horizontal coordinate, models
the thermal boundary layer that characterizes the developed convection. We constructed the bifurcation curves that describe
the stationary convection in the nonlinear integral medium simulating the rheology of the mantle, and analyzed the stability
of stationary convective flows. The Lorenz method is applied to study small-scale thermal convection in the lithosphere of
the Earth. 相似文献
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Abstract This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress—Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of order unity, as is the ratio of thermal to magnetic diffusivity. Attention is focused on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection. The case of main interest is the layer confined between electrically-insulating no-slip walls, but the analysis is guided by a parallel study based on illustrative boundary conditions that are mathematically simpler. 相似文献
6.
Observations suggest that the interannual variability of wintertime convection in Wilkinson Basin (WB) during 1977–2005 is related to the variation in the surface layer salinity in the western Gulf of Maine (wGOM). When the winter convection is stronger (weaker), the resulting deep-layer temperatures in the wGOM are colder (warmer), and the likelihood of deep winter mixing is greater when the wGOM salinities are high. This hypothesis was tested using a one-dimensional mixed layer model to simulate the water column structure over the cooling period. Comparisons were made between the convection potential for the range of observed late-fall salinity values. Model results indicated that the mixed layer depth could deepen by as much as 50% when the surface layer salinities in the wGOM were high. Sensitivity tests revealed that the surface layer salinity variability, and its influence on the water column density structure, was a significant factor, along with local climate variability, in determining the observed time series trend in springtime bottom layer temperatures. 相似文献
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Thermal and compositional evolution of magmas after emplacement of basalt into continental crust has been investigated by means of fluid dynamic experiments using a cold solid mixture with eutectic composition and a hot liquid with higher salinity in the NH4Cl–H2O binary eutectic system. The experiments were designed to simulate cases where crystallization of a basalt magma is accompanied by melting at both the roof and floor of a crustal magma chamber. The results show that thermal and compositional convection occur simultaneously in the solution; the thermal convection is driven by cooling at the roof and the compositional convection is driven by melting and crystallization at the floor. The roof was rapidly melted by the convective heat flux, which resulted in formation of a separate eutectic melt layer (the upper liquid layer) with negligible mixing of the underlying liquid (the lower liquid layer). On the other hand, a mushy layer formed at the floor. The compositional convection at the floor carried a low heat flux, so that the heat transfer at the floor was basically explained by simple heat conduction. The thermal boundary layer in the lower liquid layer at the interface with the upper liquid layer became thicker with time and subsequently temperature decreased upward throughout the lower liquid layer. Compositional gradient with NH4Cl content decreasing upward formed by compositional convection in the lower liquid layer. The formation of these gradients resulted in formation of double-diffusive convecting layers in the lower liquid layer. The upward heat transfer was suppressed when compared with the case where the liquid region is homogenized by vigorous convection.These experimental results imply that, when a basalt magma is emplaced in continental crust, floor melting does not always enhance the cooling of the magma, but it may even reduce the total heat loss from the magma to the crusts due to suppression of convection by formation of a stabilizing compositional gradient. 相似文献
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Takehiro Koyaguchi Mark A. Hallworth Herbert E. Huppert 《Journal of Volcanology and Geothermal Research》1993,55(1-2)
The effect of phenocrysts on convection in magma chambers is investigated experimentally using small heavy particles in convecting fluids. The particles are initially uniformly distributed in a fluid which is either heated from below or cooled from above. The system is allowed to evolve, and temperature and particle concentration profiles are measured as functions of time. When the concentration of particles is sufficiently small, convection is basically unaffected by their presence. When the concentration is above a critical value, however, the convective motion is considerably altered. The effect of particles on the subsequent fluid behaviour is different in the cases of heating from below and cooling from above. In the former case, there are strong convective motions confined to a sedimentary layer of decreasing thickness beneath a clear layer which displays rather weak convective motions. With time, the destabilizing increase of temperature in the lower layer overcomes the stabilizing contribution to the bulk density due to the particles and the layer overturns quite suddenly. In the situation of cooling from above, a critical condition separates a case of continual overturn from a case of no overturn at all, with the sedimentary layer falling unimpeded to the bottom. Theoretical analysis suggests that the critical value is determined primarily by the ratio of the contribution to the bulk density of the suspension due to particles to the change in fluid density due to the thermal effect. The size distribution of the particles can also modify the fluid behaviour. Applying our general results to geological situations, we suggest that the presence of relatively small concentrations of phenocrysts can critically influence the mode of convection in magmas. 相似文献
9.
Numerical analysis for cooling effect of open boundary ripped-rock embankment on Qinghai-Tibetan railway 总被引：6，自引：0，他引：6
At present, the Qinghai-Tibetan railway is being built, and it will pass across more than 550-km perma-frost regions. Therefore, the key to the stability of therailway embankment lies in solving the permafrost problem. Because global warming and existence of railway tend to degrade the permafrost in these re-gions[1], more difficulties and problems are induced in the construction and maintenance of railway. In the area where the mean annual air temperature is higher than a certain value, the … 相似文献
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《Physics of the Earth and Planetary Interiors》2004,141(4):269-279
We investigate the stability of hypothetical layered convection in the mantle and the mechanisms how the downwelling structures originating in the lower layer are generated. The stability is studied by means of numerical simulations of the double-diffusive convection in a 2D spherical model with radially dependent viscosity. We demonstrate that the stability of the layering strongly depends not only on the density contrast between the layers but also on the heating mode and the viscosity profile. In the case of the classical Boussinesq model with an internally heated lower layer, the density contrast of about 4% between the compositionally different materials is needed for the layered flow to be maintained. The inclusion of the adiabatic heating/cooling in the model reduces the temperature contrast between the two layers and, thus, enhances the stability of the layering. In this case, a density contrast of 2-3% is sufficient to preserve the layered convection on a time scale of billions of years. The generation of the downwelling structures in the lower layer occurs via mechanical or thermal coupling scenarios. If the viscosity dependent on depth and average temperature at each depth is considered, the low viscosity zone develops at a boundary between the two convecting layers which suppresses mechanical coupling. Then the downwelling structures originating in the lower layer develop beneath upper layer subductions, thus resembling continuous slab-like structures observed by seismic tomography. 相似文献
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The onset of convection in a layer of an electrically conducting fluid heated from below is considered in the case when the layer is permeated by a horizontal magnetic field of strength B 0 the orientation of which varies sinusoidally with height. The critical value of the Rayleigh number for the onset of convection is derived as a function of the Chandrasekhar number Q. With increasing Q the height of the convection rolls decreases, while their horizontal wavelength slowly increases. Potential applications to the penumbral filaments of sunspots are briefly discussed. 相似文献
12.
平流层-对流层物质交换是影响全球大气成分收支的重要过程.过去的研究认为大尺度的交换过程在平流层-对流层物质交换中最为重要,但是近些年的研究表明,中小尺度过程对平流层-对流层物质交换也有重要贡献.本文利用OMI和MLS数据、ERA-Interim再分析资料,结合中尺度WRF模式综合分析了东北地区发生在冷涡前部和冷涡后部的两次强对流天气过程.结果表明：发生在冷涡前部暖锋云系中的强对流持续时间长,对流垂直尺度小,下平流层静力稳定度高;发生在冷涡后部的孤立强对流持续时间短,水平尺度较小,且在对流层顶附近,静力稳定度小,对流可穿出热力学对流层顶.从示踪物分布情况来看,两次强对流都可将示踪物输送到对流层顶附近,但是冷涡前部对流可将示踪物从边界层输送到整个对流层,而孤立对流是把示踪物输送到对流层顶,而不与自由对流层空气发生混合. 相似文献
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《Advances in water resources》2004,27(5):547-562
This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA––A model for saturated–unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4π2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. 相似文献
14.
Theodore D. Foster 《地球物理与天体物理流体动力学》2013,107(1):201-217
Abstract A theoretical analysis of pseudo two-dimensional, finite-amplitude, thermal convection is made for an infinite Prandtl number fluid which is subjected to a constant heat flux out of the top boundary and insulated at the bottom. For large Rayleigh numbers the convective flow becomes intermittent and the system is characterized by the following cyclic process: the formation of a thermal boundary layer by diffusion, the instability of this layer when it becomes sufficiently thick, the destruction of the layer by the convective flow, the dying down of the convection, and the reforming of the thermal boundary layer by diffusion. The periodicity and the horizontal wave number of the intermittent convective flow are found to be independent of the depth of the fluid layer but depend on the rate of cooling and the properties of the fluid. 相似文献
15.
We have performed laboratory experiments using a Hele-Shaw cell to model a saturated, porous layer with various sinusoidal upper boundaries. Our intent was to determine the range of conditions over which boundary topography can control the pattern of thermal convection within a porous layer, and thereby take the first step toward understanding why heat flow seems correlated with hypsography in many areas of the ocean floor.These experiments indicate that above the critical Rayleigh number, topography does not control the convection pattern, except when the topographic wavelength is comparable to the depth of water penetration. Scaled to the depth of the layer, the convective wavenumbers are restricted to values between 2.5 and 4.8—a range which brackets π, the natural wavenumber for convection in a porous slab with planar, isothermal, impermeable boundaries. Topographies within this range control the circulation pattern perfectly, with downwelling under valleys and upwelling aligned with topographic highs. Other topographies do not force the pattern, although in some cases, the convection wavenumber may be a harmonic of the topographic wavenumber. Unforced circulation cells wander and vary in size, because they are not locked to the topography.For these experiments we employed eight different topographies with non-dimensional wavenumbers between 1.43 and 8.17, and we studied the flow at Rayleigh numbers between zero and five times the critical Rayleigh number. The amplitude of each topography tapered linearly (over a factor of three to six) from one end of the apparatus to the other, and the mean topographic amplitude was 0.05 times the depth of the layer. Under these conditions, amplitude has only a minor effect on the structural form and vigor of supercritical convection.Our results may apply to submarine geothermal systems, sealed by a thin layer of impermeable sediment draped over the basement topography. In this case, the convection wavelength—as measured perhaps by the spatial periodicity of conductive heat flow—may be a good measure of the depth to which water penetrates the crust. Where the circulation correlates with the bottom topography, it may be because the topographic wavelength is comparable to the depth to which water penetrates the porous crust. 相似文献
16.
The paper presents results obtained in experiments on a horizontal layer heated from below in its central part and cooled from above; the layer models the oceanic asthenosphere. Flow velocity and temperature profiles are measured and the flow structure under boundary layer conditions is determined (at Rayleigh numbers Ra > 5 × 105). The flow in the core of a plane horizontal layer heated laterally and cooled from above develops under conditions of a constant temperature gradient averaged over the layer thickness. The flow core is modeled by a horizontal layer with a moving upper boundary and with adiabatic bounding surfaces under conditions of a constant horizontal gradient of temperature. Exact solutions of free convection equations are found for this model in the Boussinesq approximation. Model results are compared with experimental data. Temperature and flow velocity ranges are determined for the boundary layer regime. Based on the experimental flow velocity profiles, an expression is found for the flow velocity profile in a horizontal layer with a mobile upper boundary heated laterally and cooled from above. Free convection velocity profiles are obtained for the asthenosphere beneath a mid-ocean ridge (MOR) with a mobile lithosphere. An expression is obtained for the tangential stress at the top of the asthenosphere beneath an MOR and the total friction force produced by the asthenospheric flow at the asthenosphere-lithosphere boundary is determined. 相似文献
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Results are presented from both linear stability analysis and numerical simulations of three-dimensional nonlinear convection in a Boussinesq fluid in an annular channel, under experimental boundary conditions, rotating about a vertical axis uniformly heated from below. The focus is placed on the Prandtl number Pr = 7.0, representing liquid water at room temperature. The linear analysis shows that, when the aspect ratio is sufficiently small, there exists only one stationary mode that occupies the whole fluid container. When the aspect ratio is moderate or large, however, there exist three different linear solutions: (i) the outer sidewall-localized traveling wave propagating against the sense of rotation; (ii) the inner sidewall-localized traveling wave propagating in the same sense as rotation; and (iii) both the counter-traveling waves occurring simultaneously. Guided by the result of the linear stability analysis, fully three-dimensional simulations are then performed for a channel with a moderate aspect ratio. It is found that neither the prograde nor the retrograde mode is physically realizable near threshold and beyond. The dynamics of nonlinear convection in a rotating channel are chiefly characterized by the interaction between the sidewall-localized waves and the interior convection cells/rolls, producing an interesting and unusual nonlinear phenomenon. In order to compare with the classical Rayleigh–Bénard problem without vertical sidewalls, we also study linear and nonlinear convection at exactly the same parameters but in an infinitely extended layer with periodic horizontal conditions. This reveals that both the linear instability and nonlinear convection in a rotating channel are characteristically different from those in a rotating layer with periodic horizontal conditions. 相似文献
18.
Abstract This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress-Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of unit order. In Part I of this series, it was also supposed that the ratio thermal diffusivity diffusivity/magnetic diffusivity is O(1), but here we suppose that this ratio is large. The character of the solution is changed in this limit. In the case of main interest, when the layer is confined between electrically-insulating no-slip walls, the solution is significantly different from the solution when the mathematically simpler, illustrative boundary conditions also considered in Part I are employed. As in Part I, attention is focussed on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection. 相似文献
19.
A wide class of equations is defined for a high pressure and subcritical temperature range of a fluid state whose thermodynamic properties enable the construction of a polytropic model of the mantle. A variant of deep convection equations of the Ogura and Phillips type is substantiated in terms of the polytropic mantle model. The proposed system of the deep convection equations includes fluctuation of the generalized potential temperature, has a quasi-incompressible form, and is transformed into Mihaljan’s system of shallow convection equations with a decrease in the layer depth. This circumstance is of great importance because it validates the use of the same dimensionless parameters as in the shallow convection model. The advantage of the proposed variant of the deep convection equations is its complete conservatism, which allows one to gain constraints on the efficiency of energy conversion in deep mantle processes and the thermal energy power expended on the generation rate of the convection kinetic energy and associated processes. This power is shown to be of the order of half the geothermal flux measured on the Earth’s surface. 相似文献