Showing papers on "Convection published in 1970"
611 citations
TL;DR: In this paper, the Galerkin method is used to predict convective instability of a ferromagnetic fluid in the presence of a uniform vertical magnetic field, where the magnetization of the fluid is a function of temperature and a temperature gradient is established across the layer.
Abstract: Convective instability of a ferromagnetic fluid is predicted for a fluid layer heated from below in the presence of a uniform vertical magnetic field. Convection is caused by a spatial variation in magnetization which is induced when the magnetization of the fluid is a function of temperature and a temperature gradient is established across the layer. A linearized convective instability analysis predicts the critical temperature gradient when only the magnetic mechanism is important, as well as when both the magnetic and buoyancy mechanisms are operative. The magnetic mechanism predominates over the buoyancy mechanism in fluid layers about 1 mm thick. For a fluid layer contained between two free boundaries which are constrained flat, the exact solution is derived for some parameter values and oscillatory instability cannot occur. For rigid boundaries, approximate solutions for stationary instability are derived by the Galerkin method for a wide range of parameter values. It is shown that in this case the Galerkin method yields an eigenvalue which is stationary to small changes in the trial functions, because the Galerkin method is equivalent to an adjoint variational principle.
465 citations
TL;DR: In this article, it was shown that large heat generation along the deep-earthquake fault zone and effective heat transfer in the upper mantle above the deep earthquake zone is required to explain the heat flow pattern across island arcs and marginal seas.
281 citations
TL;DR: In this article, the so-called conservative or flux form of the finite difference formulation of convection terms is shown to be inadequate for preventing nonlinear instability in some cases, and a preferred scheme for the convection term which has the property of absolute spatial conservation is obtained.
271 citations
TL;DR: Plasmasphere bulge region morphology from hydrogen ion concentration measurement by mass spectrometer on OGO 5 satellite was obtained from the OGO-5 satellite as mentioned in this paper, which was used for the measurement.
Abstract: Plasmasphere bulge region morphology from hydrogen ion concentration measurement by mass spectrometer on OGO 5 satellite
233 citations
TL;DR: In this article, the onset of axisymmetric convection in cylindrical layers of fluid heated from beneath is investigated for various radius-to-height ratios and upper and lower bounds on the critical Rayleigh number for such flows are computed, and the structure of the convective flow is investigated.
203 citations
TL;DR: In this article, it was shown theoretically and observed experimentally that spontaneous motions are set up in a stably stratified diffusive fluid in a container whose side-walls are not vertical, and the fluid streams up or down the inclined walls in a kind of boundary layer whose Reynolds number is inversely proportional to the Prandtl number.
191 citations
TL;DR: In this article, the authors compared the stability of the boundary layer of two Australian expeditions with the use of four stability classifications: deep convection, sub-geostrophic wind, convective flow, and a spiral of the expected sense.
Abstract: Winds and temperatures in the boundary layer measured during two Australian expeditions are analysed according to the similarity scheme, with the use of four stability classifications.
Under conditions of deep convection there is a minimum potential temperature and a maximum velocity component in the direction of the surface wind, at a height of about 0.12 u*/f. In the very stable cases, the temperature gradient follows rather closely a z−2 law for a considerable height range from 0.08 u*/f upwards. An expression closely fitting the mean data in stable conditions is suggested for the vertical temperature structure at all levels in the boundary layer.
Wind data processed in this way show, for all four stability classes, a rudimentary Ekman spiral. With deep convection the spiral is found to be reversed in sense, but the flow in the convecting layer is down the gradient of pressure. If the convective limit lies broadly within the Ekman layer, a spiral of the expected sense is found. The upper limit of the Ekman layer (as defined by the ‘spiral’) is found to lie at a height of 0.17 to 0.24 (increasing with stability) in units of u*/f. Stress and heat-flux are apparently considerable above this level, with sub-geostrophic wind, when deep convection is occurring.
Approximations to the universal distributions of stress, eddy coefficients, mixing length and rate of degradation of mean flow kinetic energy are computed for the various stabilities. The mixing length in unstable conditions increases almost as height up to a level of about 0.08 u*/f, and then decreases, but in general appears not to vanish in stable layers above the boundary layer. In the unstable boundary layer with deep convection, the eddy transfer coefficient for heat exceeds that for momentum up to 0.12 u*/f, where it becomes infinite, and is negative at higher levels. In stable conditions the transfer coefficients for a small sample of soundings were estimated to be closely similar.
The universal functions of stability, A, B and C, which enable one to compute free atmosphere wind vector and temperature, given surface conditions, have been evaluated with moderate success, although B, which essentially describes the change of wind direction with height, exhibits excessive variability. A method is suggested for computing horizontal advection in the boundary layer when this is to be ‘parameterized’ in mathematical models.
The drag coefficient, in terms of free atmosphere wind, has almost a 50-fold range, due to stability variation only. Most of the variation occurs relatively close to neutral, so warning against too ready an assumption of neutrality in practical applications.
It is suggested that, for modelling purposes, it is preferable to adopt boundary layer formulations which are not too sensitive to departures from ideal conditions, and eddy coefficients, perhaps based on mixing lengths, may well provide the best approach currently available.
182 citations
TL;DR: In this article, the authors extended the analysis of Busse l970a to include the detailed spatial dependence of the meridional circulation as well as of the differential rotation, and the thin shell approximation for a rotating spherical convection layer of a Boussinesq fluid is used.
Abstract: The analysis of an earlier paper (Busse l970a) in which the differential rotation of the Sun was explained as the result of large scale convection in the solar convection zone is extended to include the detailed spatial dependence of the meridional circulation as well as of the differential rotation The thin shell approximation for a rotating spherical convection layer of a Boussinesq fluid is used The asymptotic representation of large order spherical harmonlcs by Hermite functions permits a simple integration of the equations for the meridional circulation and the differential rotation Explicit analytical solutions are given for the case of stressfree boundaries and numerical results are shown in the case of a rigid inner and a free outer boundary The case of stressfree boundaries is rather exceptional and the magnitude of the differential rotation is reduced for more general boundary conditions However, the differential rotation still exhibits the characteristic equatorial acceleration in the case of an inner rigid boundary (auth)
173 citations
TL;DR: In this paper, numerical methods are used to solve the field equations for heat transfer in a porous medium filled with gas and bounded by plane rectangular surfaces at different temperatures, and the relative increases in heat transfer rate, corresponding to natural convection, are obtained as functions of 3-dimensional parameters: the Darcy number Da, the Rayleigh number Ra and a geometric aspect ratio L/D.
Abstract: Numerical methods are used to solve the field equations for heat transfer in a porous medium filled with gas and bounded by plane rectangular surfaces at different temperatures. The results are presented in terms of theoretical streamlines and isotherms. From these the relative increases in heat transfer rate, corresponding to natural convection, are obtained as functions of 3- dimensionless parameters: the Darcy number Da, the Rayleigh number Ra, and a geometric aspect ratio L/D. A possible correlation using the lumped parameter Da Ra is proposed for Da Ra greater than about 40. (33 refs.)
155 citations
TL;DR: In this paper, a simple model with constant convection electric field and a dipole magnetic field was used to calculate the plasma flow patterns with the convection fields as scale factors, which indicated that protons of a few hundred electron volts convected in from the tail to L = 3-4 could be responsible for the storm-time ring currents.
Abstract: By using a simple model with constant convection electric field and a dipole magnetic field, plasma flow patterns are calculated with the convection fields as scale factors. Unlike other particle trajectories, the flow patterns for protons with certain relative magnetic moments show double forbidden regions: one is composed of orbits that circle the earth; the other is composed of orbits that do not circle the earth. These protons can penetrate very close to the earth through the space between the two forbidden regions. The calculations based on the model of constant electric field with charge exchange as a loss mechanism indicate that protons of a few hundred electron volts convected in from the tail to L = 3–4 could be responsible for the storm-time ring currents.
TL;DR: In this article, a case study of a cold front has shown that, although appreciable ascent occurred over a deep layer, practically all precipitation growth was associated with the ascent of air which originated within the friction layer ahead of the front, and the overall efficiency of precipitation production was high, 60 per cent of the water vapour flux in the rising air reaching the ground as precipitation.
Abstract: A case study of a cold front has shown that, although appreciable ascent occurred over a deep layer, practically all precipitation growth was associated with the ascent of air which originated within the friction layer ahead of the front. Doppler radar observations showed that the ascent was accomplished in two phases; first through near-vertical line convection to between 1 and 3 km at the surface cold front, and thence through shallow-slope convection of the same air to between 3 and 6 km. The line convection was 2-dimensional rather than cellular and occurred in the absence of appreciable hydrostatic instability. Horizontal convergence at low levels was very intense (10−2 s−1 averaged over 500 m vertically and horizontally), so that despite the shallowness of the line convection, the updraught attained a rising speed of 8 m s−1 which was sufficient to generate hail and thunder. The subsequent slope convection produced a period of moderate precipitation behind the surface cold front, and was associated with a pronounced transverse circulation, with strong gradients of velocity separating the weak downdraughts in (and beneath) the sloping frontal zone from the overlying updraught. The overall efficiency of precipitation production was high, 60 per cent of the water vapour flux in the rising air reaching the ground as precipitation.
TL;DR: In this paper, the critical Rayleigh number for convective flow in a porous two-dimensional channel is found when there is a net flow of fluid up through the channel, where the critical number is defined as the ratio of the number of convective flows in the channel to the amount of fluid passing through it.
Abstract: The critical Rayleigh number for convective flow in a porous two‐dimensional channel is found when there is a net flow of fluid up through the channel.
TL;DR: In this paper, the authors applied the theory of moving heat sources to two models to determine the effect of convective surface cooling on temperature distributions, which can be used to predict temperature distributions occurring in certain machining processes or other processes involving heat sources.
Abstract: The theory of moving heat sources is applied to two models to determine the effect of convective surface cooling on temperature distributions. The models chosen consist of a translating semi-infinite body and a rotating cylindrical body, each having a band heat source acting on a portion of the surface and convective cooling acting over the entire surface. The analytical results can be utilized to predict temperature distributions occurring in certain machining processes or other processes involving heat sources.
TL;DR: In this article, the authors considered the problem of fully developed free convection in the atmospheric boundary layer and derived an expression for the height of unstable Ekman layers, as a function of the time of day and the stability conditions at the top of the boundary layer.
Abstract: This paper deals with the problem of fully developed free convection in the atmospheric boundary layer. In free convection, the height of the Ekman layer is much larger than the absolute value of the Monin-Oboukhov length. The kinetic energy budget of the turbulence above the surface layer shows that the standard deviations of vertical velocity and of temperature are related to h/L by σw/u*∝(−h/L)⅓ and σθ/θ*∝(−h/L)⅓. Because convection has no natural length scale, the height of the neutral Ekman layer (h∝u*/f) is used to explore the consequences of the proposed expressions for σw and σθ. The dissimilarity between the heat flux and the momentum flux is studied in terms of time- and length-scale ratios and in terms of a flux Richardson number. A definitive solution of the problem, however, cannot be formulated until an expression for the height of unstable Ekman layers, as a function of the time of day and the stability conditions at the top of the boundary layer, can he found.
TL;DR: In this paper, a finite difference solution in the laminar flow field was achieved by modifying the potential flow field to yield convective terms equivalent to the LQE terms in the energy equation.
TL;DR: In this article, a surface-tension-driven liquid flow, induced by the temperature profile ahead of a spreading flame, is analyzed and velocities, pressures and surface heights are determined for a two-dimensional flame spreading at a steady rate.
Abstract: Convective heat transfer through the liquid fuel below a spreading flame is considered as a rate controlling mechanism. Thus, a surface-tension-driven liquid flow, induced by the temperature profile ahead of a spreading flame, is analyzed. Velocities, pressures and surface heights are determined for a two-dimensional flame spreading at a steady rate. It is demonstrated that convection can occur near the suface ahead of the flame and in the direction of propagation and, thus, that liquid-phase convective heat transfer can be a plausible rate-controlling mechanism for flame propagation.
TL;DR: In this article, the wall temperatures of a 4·56 m long, 2·28 × 10−2 m dia. tube with heat transfer to turbulent flow of CO2 at supercritical pressure were measured.
TL;DR: Investigation of the equation of motion, and the equations of species transport, indicate that the plasma mixing is important only in the transfer of materials such as macromolecules, which may diffuse more slowly than dissolved gases.
TL;DR: In this article, the authors describe a representation of the distribution of sensible and latent heat from the surface through the atmospheric boundary layer which has been formulated for use in a 10-level primitive equation model atmosphere.
Abstract: This paper describes a representation of the distribution of sensible and latent heat from the surface through the atmospheric boundary layer which has been formulated for use in a 10-level primitive equation model atmosphere. The transfer process is represented in two parts : (i) the transfer of energy across the Earth's surface into the lowermost 100 mb layer of the model atmosphere; and (ii) the subsequent redistribution of this energy through two or more such layers by small-scale convection. The fluxes of energy across the surface are calculated using empirical ‘bulk aerodynamic’ relationships. In land regions consideration of the energy balance at the surface is also necessary, and diurnal variations of radiation are taken into account. The redistribution of energy by small-scale convection is represented by convective adjustments which ensure that a certain neutral lapse rate of temperature is never exceeded. Some results of the incorporation of these effects into the 10-level model are described.
01 Aug 1970
TL;DR: In this article, a formulation is given and computed solutions are presented for transient solidification accompanied by natural convection in a vertical slot, where the simplifying assumptions made limit the validity of the solutions to systems where GrPr < 500, i.e., to narrow slots or to low values of the superheat.
Abstract: A formulation is given and computed solutions are presented for transient solidification accompanied by natural convection in a vertical slot. It was found that appreciable fluid velocities may be produced by natural convection, the values of which could be comparable to the terminal rising velocities of typical nonmetallic inclusions. The simplifying assumptions made limit the validity of the solutions to systems where GrPr < 500,i.e., to narrow slots or to low values of the superheat; nonetheless, the results should be indicative of the effects of convection at much higher values of GrPr.
TL;DR: In this article, the critical Rayleigh number of the supercritical convective motion of vertical jets of cool surface fluid which plunged downward into the interior of the fluid was investigated, where the jets were not arranged in an orderly lattice and each jet had a tendency to merge with a close neighbour.
Abstract: Results of linear stability calculations and post-stability experimental observations are reported for horizontal fluid layers with upward heat flux bounded below by a stably stratified fluid. Stability calculations were done for several families of continuous and discontinuous temperature distributions, and it was found that as a rule the flow originating in the unstable layer penetrates into the stably stratified region, resulting in increased critical cell size and correspondingly decreased critical Rayleigh number. A notable exception to this occurs for an unstable layer with a linear temperature distribution adjacent to a stable layer of very high stable density gradient. In this case energy pumped from the unstable to the stable region is sufficient to raise the critical Rayleigh number above that of a solid boundary. It is also found that, for density distributions with a more gradual transition between the stable and the unstable regions, the effect of increased cell size upon the critical Rayleigh number is sometimes masked by effects of curvature in the density profile of the unstable region, which tends to increase the critical Rayleigh number. The inadequacy of the usual definition of Rayleigh number to characterize the stability of such complex systems is discussed. Experimentally, such a temperature distribution was produced by radiant energy from above as it was absorbed by the top few centimetres of the fluid. Within an uncertainty of ± 20%, it was found that the critical experimental Rayleigh number agreed with neutral stability calculations. The supercritical convective motion consisted of vertical jets of cool surface fluid which plunged downward into the interior of the fluid. The jets were not arranged in an orderly lattice but were in a constant state of change, each jet having a tendency to merge with a close neighbour. The net loss of jets due to merging was balanced by new jets spontaneously appearing. As Rayleigh number was increased, the mean number of jets and the intermittancy increased proportionally. Temperature scans taken with a movable probe showed that cool surface fluid plunging downward in the jets was confined to a fairly restricted region, the surrounding fluid being quite isothermal.