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Showing papers on "Convection published in 1969"


Journal ArticleDOI
TL;DR: In this article, an experimental study of the response of a thin uniformly heated rotating layer of fluid is presented, and it is shown that the stability of the fluid depends strongly upon the three parameters that described its state, namely the Rayleigh number, the Taylor number and the Prandtl number.
Abstract: An experimental study of the response of a thin uniformly heated rotating layer of fluid is presented. It is shown that the stability of the fluid depends strongly upon the three parameters that described its state, namely the Rayleigh number, the Taylor number and the Prandtl number. For the two Prandtl numbers considered, 6·8 and 0·025 corresponding to water and mercury, linear theory is insufficient to fully describe their stability properties. For water, subcritical instability will occur for all Taylor numbers greater than 5 × 104, whereas mercury exhibits a subcritical instability only for finite Taylor numbers less than 105. At all other Taylor numbers there is good agreement between linear theory and experiment.The heat flux in these two fluids has been measured over a wide range of Rayleigh and Taylor numbers. Generally, much higher Nusselt numbers are found with water than with mercury. In water, at any Rayleigh number greater than 104, it is found that the Nusselt number will increase by about 10% as the Taylor number is increased from zero to a certain value, which depends on the Rayleigh number. It is suggested that this increase in the heat flux results from a perturbation of the velocity boundary layer with an ‘Ekman-layer-like’ profile in such a way that the scale of boundary layer is reduced. In mercury, on the other hand, the heat flux decreases monotonically with increasing Taylor number. Over a range of Rayleigh numbers (at large Taylor numbers) oscillatory convection is preferred although it is inefficient at transporting heat. Above a certain Rayleigh number, less than the critical value for steady convection according to linear theory, the heat flux increases more rapidly and the convection becomes increasingly irregular as is shown by the temperature fluctuations at a point in the fluid.Photographs of the convective flow in a silicone oil (Prandtl number = 100) at various rotation rates are shown. From these a rough estimate is obtained of the dominant horizontal convective scale as a function of the Rayleigh and Taylor numbers.

584 citations


Journal ArticleDOI
TL;DR: In this article, the effect of continuous convection from small sources of buoyancy on the properties of the environment when the region of interest is bounded is considered, assuming that the entrainment into the turbulent buoyant region is at a rate proportional to the local mean upward velocity, and that the buoyant elements spread out at the top of the region and become part of the non-turbulent environment at that level.
Abstract: This paper considers the effect of continuous convection from small sources of buoyancy on the properties of the environment when the region of interest is bounded. The main assumptions are that the entrainment into the turbulent buoyant region is at a rate proportional to the local mean upward velocity, and that the buoyant elements spread out at the top of the region and become part of the non-turbulent environment at that level. Asymptotic solutions, valid at large times, are obtained for the cases of plumes from point and line sources and also periodically released thermals. These all have the properties that the environment is stably stratified, with the density profile fixed in shape, changing at a uniform rate in time at all levels, and everywhere descending (with ascending buoyant elements).The analysis is carried out in detail for the point source in an environment of constant cross-section. Laboratory experiments have been conducted for this case, and these verify the major predictions of the theory. It is then shown how the method can be extended to include more realistic starting conditions for the convection, and a general shape of bounded environment. Finally, the model is applied quantitatively to a variety of problems in engineering, the atmosphere and the ocean, and the limitations on its use are discussed.

441 citations


Journal ArticleDOI
TL;DR: In this paper, a formal scale analysis of the equations of motion in a plane parallel atmosphere is made, assuming conditions to be such that relative fluctuations in density and temperature are small.
Abstract: A formal scale analysis of the equations of motion in a plane parallel atmosphere is made, assuming conditions to be such that relative fluctuations in density and temperature are small. It is found that an energetically consistent set of approximate equations can be derived which preclude the existence of acoustic motions. Such equations can be used to describe subsonic convection or internal gravity waves. Under certain conditions the analysis can be generalized to include vertical pulsations of the atmosphere.

301 citations


Journal ArticleDOI
TL;DR: In this paper, the authors performed laboratory experiments of non-steady penetrative convection in water that closely simulate the lifting of an atmospheric inversion above heated ground and found that the rate at which kinetic energy is destroyed by the downward heat flux in the vicinity of the inversion base is a very small fraction of the rate that is generated in the lower convective region.
Abstract: Laboratory experiments of non-steady penetrative convection in water are performed that closely simulate the lifting of an atmospheric inversion above heated ground. Vertical profiles of horizontally averaged temperature and heat flux are measured and interpreted. The rate at which kinetic energy is destroyed by the downward heat flux in the vicinity of the inversion base is found to be a very small fraction of the rate at which it is generated in the lower convective region. The interface separating the convective region from the stable region is examined and its rate of rise explained.

279 citations


01 Jan 1969
TL;DR: In this paper, the authors discuss thermal convection currents and stress propagation in upper earth mantle, and discuss the dynamics of the upper earth's mantle, including dynamic processes in the lower earth mantle.
Abstract: Dynamic processes in upper earth mantle, discussing thermal convection currents and stress propagation

254 citations


Journal ArticleDOI
TL;DR: In this paper, the stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures.
Abstract: The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The effects of the oscillating temperature field are treated by a perturbation expansion in powers of the amplitude of the applied field. The shift in the critical Rayleigh number is calculated as a function of frequency, and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures.

253 citations


Journal ArticleDOI
TL;DR: In this paper, the convective flow in an infinite horizontal fluid layer rotating rigidly about a normal axis was investigated for the special case of infinite Prandtl number and free boundary conditions.
Abstract: The convective flow in an infinite horizontal fluid layer rotating rigidly about a normal axis is investigated for the special case of infinite Prandtl number and free boundary conditions. For slightly supercritical Rayleigh numbers the solutions of the non-linear steady-state equations are derived approximately by an amplitude expansion. A stability calculation shows that no stable steady-state convective flow exists if the Taylor number exceeds the critical value 2285.

219 citations


Journal ArticleDOI
TL;DR: Heat finite propagation velocity effects on temperature distribution and heat flux for step temperature change at semi-infinite body surface were studied in this article, where the authors considered a semi-inverse body surface.
Abstract: Heat finite propagation velocity effects on temperature distribution and heat flux for step temperature change at semiinfinite body surface

210 citations


Journal ArticleDOI
TL;DR: In this paper, an exact solution for the equations for free convection in a planar horizontal layer of liquid with a constant temperature gradient at the boundaries is found for two cases of boundary conditions for the velocity: 1) the liquid is bounded by two solid planes, 2) the upper surface of the liquid was free, and the surface tension is a function of temperature.
Abstract: An exact solution is found for the equations for free convection in a planar horizontal layer of liquid with a constant temperature gradient at the boundaries. Two cases of boundary conditions for the velocity are considered: 1) the liquid is bounded by two solid planes, 2) the upper surface of the liquid is free, and the surface tension is a function of temperature.

194 citations


Journal ArticleDOI
TL;DR: In this article, the stability of natural convection of a viscous fluid in a vertical slot having isothermal side walls of different temperatures is investigated analytically, and both the conduction and boundary-layer regimes are found to be unstable with respect to stationary disturbances in the form of multicellular secondary flows.
Abstract: The stability of natural convection of a viscous fluid in a vertical slot having isothermal side walls of different temperatures is investigated analytically. Both the conduction and boundary-layer regimes are found to be unstable with respect to stationary disturbances in the form of multicellular secondary flows. Theoretical predictions of the critical Rayleigh number and of the form of the secondary flow are verified by experimental measurements.

193 citations


Journal ArticleDOI
TL;DR: In this article, the effects of viscous dissipation are considered for external natural convection flow over a surface and a class of similar boundary-layer solutions is given and numerical results are presented for a wide range of the dissipation and Prandtl numbers.
Abstract: The effects of viscous dissipation are considered for external natural convection flow over a surface. A class of similar boundary-layer solutions is given and numerical results are presented for a wide range of the dissipation and Prandtl numbers. Several general aspects of similarity conditions for flow over surfaces and in convection plumes are discussed and their special characteristics considered. The general equations including the dissipation effect are given for the non-similar power law surface condition.

Journal ArticleDOI
TL;DR: In this paper, an equation for population distribution is derived for olivine and quartz crystals in ultramafic and granitic magmas, in agreement with observed distribution of these minerals in corresponding solidified intrusions.
Abstract: Normal heat fluxes from the Earth are sufficient to cause magma convection in plutons greater than 15 m for magma viscosities to 10 (super -8) poise. Convection increases markedly with size of the magma chamber and becomes the dominant method of heat transfer within the magma. Large solidifying intrusions have an approximately isothermal temperature distribution during part of the crystallization history. Natural convection also redistributes settling crystals. The population distribution (differentiation) of crystals in the vertical direction depends on the settling and convective back diffusion fluxes. An equation for population distribution is derived, and calculations made for olivine and quartz crystals in ultramafic and granitic magmas are in agreement with observed distribution of these minerals in corresponding solidified intrusions.


Book ChapterDOI
TL;DR: In this paper, the authors summarized results of more recent studies of convective heat transfer in rotating systems and showed that the results for convection heat transfer of a disk rotating in an infinite environment can not be applied to shrouded or corotating disks, and also dealt with heat transfer by convection in systems in which the fluids also have an independent axial motion superimposed on the rotating motion.
Abstract: Publisher Summary Because the convective heat transfer phenomena in rotating systems are intimately related to the flow characteristics, they too are quite complex and offer challenges to theoreticians as well as experimenters. Heat transfer by convection to or from bodies of revolution spinning about their axes of symmetry in an otherwise undisturbed fluid has been studied analytically and experimentally by numerous authors. This chapter summarizes results of more recent investigations. The flow and heat transfer characteristics of spinning bodies of revolution in a forced flow field are important for projectiles or re-entry missiles with spin as well as for certain other engineering problems. The fluid-mechanical phenomena of enclosed rotating disks and of parallel corotating disks are distinctly different from those of disks rotating in an infinite environment. In general, the results for convection heat transfer of a disk rotating in an infinite environment can, therefore, not be applied to shrouded or corotating disks. When a quiescent horizontal layer of fluid is heated from below, the fluid at the bottom becomes lighter than the fluid at the top and convection currents are set into motion. The chapter deals with convection in fluids that are set in motion principally by rotating bounding surfaces, but that do not have an independent axial flow. It also deals with heat transfer by convection in systems in which the fluids also have an independent axial motion superimposed on the rotating motion.

Journal ArticleDOI
TL;DR: In this article, the authors describe the three dimensional airflow and precipitation within small polar depressions which sometimes cross Britain during northerly outbreaks and which in winter can be responsible for heavy snowfalls.
Abstract: This paper describes the three dimensional airflow and precipitation within small ‘polar’ depressions which sometimes cross Britain during northerly outbreaks and which in winter can be responsible for heavy snowfalls. The data used in the study consist of Doppler and conventional radar information, together with routine synoptic data and sequential radiosonde ascents from the radar station. Three dimensional airflow was derived from the radiosonde data assuming that wet bulb potential temperature was conserved. Horizontal and vertical air velocities were also derived from the Doppler radar measurements. Previous knowledge of polar lows is meagre; they are generally thought to be shallow features resulting from enhanced convection within cold air flowing over a warm sea. However, the well-developed polar low which is the main subject of this paper is shown to have been an essentially baroclinic disturbance. Although enhanced small-scale convection occurred in one sector, the main area of widespread precipitation associated with the polar low was produced not by small-scale convective overturning but rather by slantwise convection within a narrow tongue of air ascending steadily at about 10 cm s−1. The speed of travel and short wavelength (900 km) of the polar low in this study are consistent with its having formed in a region of enhanced baroclinicity within the polar air below 850 mb rather than in the major baroclinic zone bounding the polar air mass. Considerable low-level baroclinicity within the polar air is also shown to have been present during the formation of other intense polar lows.

Journal ArticleDOI
TL;DR: In this paper, a temperature distribution in the upper mantle is obtained by matching the boundary-layer profiles to adiabatic profiles consistent with the boundary layer theory for finite amplitude convection.
Abstract: The aspects of mantle convection that do not require a knowledge of the viscosity are considered first. Using spreading rates obtained from magnetic anomaly data, the temperature distribution in the thermal boundary layers adjacent to the ocean floors is determined. The values of the surface heat flux are compared with measurements. A temperature distribution in the upper mantle is obtained by matching the boundary-layer profiles to adiabatic profiles consistent with the boundary-layer theory for finite amplitude convection. Mechanisms for a fluid-like mantle are considered. Assuming that diffusion creep is occurring, a semi-empirical expression for the temperature and pressure dependence of the viscosity is given. The viscosity is found to have a strong minimum near a 100-km depth. The effect of a strong temperature-dependent viscosity on the ascending, diverging flow near ocean ridges is studied. The topography of ocean ridges is attributed to the hydrostatic head required for the horizontal flow. The excess temperature associated with the ascending flow is found to be of the order of 50°K.


Journal ArticleDOI
TL;DR: In this paper, it was found that the onset of manifest convection was independent of the thermal boundary layer depth and that the horizontal spacing of the convection cells should vary with the rate of bottom surface temperature increase within reasonable limits.
Abstract: Experiments have been performed in deep layers of fluid in which the bottom surface temperature was increased at a constant rate. It was found that when the thermal boundary layer was only a small fraction of the total depth of the fluid layer, the onset of manifest convection was independent of the layer depth. The predictions of linear time‐dependent theory that the time of onset of manifest convection should vary with the ‐ 25 power of the rate of bottom surface temperature increase and that the horizontal spacing of the convection cells should vary with the ‐ 15 power of the rate of bottom surface temperature increase were verified within reasonable limits.

Journal ArticleDOI
TL;DR: Onset times for convection induced by buoyancy forces have been measured in three aqueous systems in terms of a critical value for a time-dependent Rayleigh number as mentioned in this paper.
Abstract: Onset times for convection induced by buoyancy forces have been measured. Results on three aqueous systems are summarized in terms of a critical value for a time-dependent Rayleigh number. Because of the presence of minute traces of unavoidable surface-active contaminants, a ‘free’ water surface behaved as if it were inflexible and laterally rigid so far as determining first convective motion was concerned. The form of the onset motion was observed with schlieren photography for both top and side view. The pattern at onset was frequently in the form of plunging rings. Surface effects were demonstrated with an organic liquid layer in which onset times were measured for convection driven by surface tension gradients as well as by buoyancy forces. The data are compared with some recent predictions of linear stability analyses.

Journal ArticleDOI
TL;DR: In this paper, the authors explore the possible importance of time-dependent convection electric fields as an agent for diffusing trapped magnetospheric radiation inward toward the earth, and derive a one-dimensional diffusion equation to describe statistically the loss-free motion of mirroring particles with arbitrary but conserved values of the first two adiabatic invariants M and J.
Abstract: We explore here the possible importance of time-dependent convection electric fields as an agent for diffusing trapped magnetospheric radiation inward toward the earth. By using a formalism (Birmingham, Northrop, and Falthammar, 1967) based on first principles, and by adopting a simple model for the magnetosphere and its electric field, we succeed in deriving a one-dimensional diffusion equation to describe statistically the loss-free motion of mirroring particles with arbitrary but conserved values of the first two adiabatic invariants M and J. Solution of this equation bears out the fact that reasonable electric field strengths, correlated in time for no longer than the azimuthal drift period of an average particle, move particles toward the earth at a rate at least an order of magnitude faster than electric fields whose source is a fluctuating current on the magnetopause.

Journal ArticleDOI
TL;DR: In this paper, numerical solutions to the Boussinesq equations containing a temperature-dependent viscosity are presented for the case of axisymmetric buoyancy-driven convective flow in a cylindrical cell.
Abstract: Numerical solutions to the Boussinesq equations containing a temperature-dependent viscosity are presented for the case of axisymmetric buoyancy-driven convective flow in a cylindrical cell. Two solutions, one with upflow and the other with downflow at the centre of the cell, were found for each set of boundary conditions that were considered. The existence of these two steady-state regimes was verified experimentally for the case of a cylindrical cell having rigid insulating lateral boundaries and isothermal top and bottom planes.Using a perturbation expansion it is also shown that only one of these solutions remains stable in the subcritical regime. This, however, seems to be confined to a very narrow range of Rayleigh numbers, beyond which, according to all the evidence presently at hand, both solutions are equally stable for those values of the Rayleigh and Prandtl numbers for which axisymmetric motions occur.Finally, certain fundamental differences between the problem considered here and that of thermal convection in a layer of infinite horizontal extent are briefly discussed.

Journal ArticleDOI
TL;DR: In this article, the effect of longitudinal combustion-driven oscillations on convective heat transfer rates was studied using a tubular, propane-fired combustor which resonated as a quarter-wavelength organ pipe at a frequency of 100 cps.
Abstract: The effect of longitudinal combustion-driven oscillations on convective heat transfer rates was studied using a tubular, propane-fired combustor which resonated as a quarter-wavelength organ pipe at a frequency of 100 cps. The combustor was provided with damping tubes of variable length which enabled the amplitude of the oscillations to be varied, to the extent of damping them out completely. Heat transfer coefficients were measured with and without the presence of combustion-driven oscillations. It was found that heat transfer coefficients were highest at a position of maximum velocity amplitude, where improvements of over 100 percent were obtained. Satisfactory prediction of the effects of the oscillations was obtained by using the quasisteady-state theory.

Journal ArticleDOI
TL;DR: The acceleration of the earth's rotation averaged over the past 3000 years has been re-studied using a new analysis of the ancient eclipses as mentioned in this paper, which seems to require a viscosity for the deep mantle of ∼1022 poises, permitting the convective transport of heat from the deep interior of earth.
Abstract: The acceleration of the earth's rotation averaged over the past 3000 years has been re-studied using a new analysis of the ancient eclipses. The relaxation time for a second-order harmonic distortion of the earth has been calculated to fall in the range 870–1600 years. This short relaxation time seems to require a viscosity for the deep mantle of ∼1022 poises, permitting the convective transport of heat from the deep interior of the earth. If the viscosity is this low, deep convective currents are required to support the excess equatorial bulge.

Journal ArticleDOI
TL;DR: In this paper, a theoretical analysis of two-dimensional, finite-amplitude, thermal convection is made for a fluid which has an infinite Prandtl number, and the vertical velocity disturbance is expanded in a double Fourier series which satisfies the horizontal and lateral boundary conditions.
Abstract: A theoretical analysis of two-dimensional, finite-amplitude, thermal convection is made for a fluid which has an infinite Prandtl number. The vertical velocity disturbance is expanded in a double Fourier series which satisfies the horizontal and lateral boundary conditions. The resulting coupled sets of non-linear differential equations are solved numerically. It is found that for a particular Rayleigh number the number and size of the convection cells that form depend upon the ratio of the distance between the lateral boundaries to the depth of the fluid layer and on the initial conditions. The steady-state solutions are not unique and the solution for which the heat transport is a maximum is not necessarily the solution that results. Where there are no lateral boundaries, the lateral edges of the cells tend to tilt and the Nusselt number increases slightly.


Journal ArticleDOI
TL;DR: In this article, columnar, counterrotating, vertical vortices were produced on a heated, vertical, flat plate under free-convection conditions in air using a high-voltage d-c electric field.
Abstract: Experimental results are presented to show that columnar, counterrotating, vertical vortices can be produced on a heated, vertical, flat plate under free-convection conditions in air using a high-voltage d-c electric field. The vortices result from the corona discharge on 0.002-in.-dia parallel wires of alternate high voltage and ground potential placed vertically on the surface of a phenolic laminate plate. Heat-transfer rates are measured using an energy-balance method, and the thermal boundary layer is made visible using a Mach-Zehnder interferometer. Experimental curves are presented to illustrate the increase in the heat-transfer rate with increase in the electric-field power. Interference photographs and frames from a motion picture show the effects of the vortices on the thermal boundary layer. The convective part of the heat transfer from the 10 × 10 in. plate is more than doubled before the electric-field power becomes as large as 5 percent of the increase in the heat-transfer rate. Local heat-transfer rates are highest at the high-voltage wires and lowest at the grounded wires.

Journal ArticleDOI
TL;DR: In this article, experimental evidence is presented showing that density gradients developed during the transfer of a solute across a liquid interface exert a strong influence on convection generated by interfacial tension variations.

Journal ArticleDOI
TL;DR: In this article, a schlieren optical system was used to observe the haline convection of long vertical filaments with a horizontal spacing of 0.2 to 0.3 cm, in good agreement with the predictions of linear theory.
Abstract: Laboratory experiments were performed in which sea water was frozen from above at controlled rates. The resulting haline convection was observed by using a schlieren optical system. Salinity of the sea water was varied from about 20‰ to 35‰. Freezing rates up to about 1.5 × 10−4 g/cm2 sec were used. The resultant salt fluxes varied from about 2 × 10−7 to 2 × 10−6 g/cm2 sec. The haline convection took the form of long vertical filaments with a horizontal spacing of 0.2 to 0.3 cm, in good agreement with the predictions of linear theory.

Journal ArticleDOI
TL;DR: In this paper, heat transfer by combined free and forced convection from a heated tube to a transverse air stream has been experimentally studied over a wide range of Grashof and Reynolds numbers.
Abstract: Heat transfer by combined free and forced convection from a heated tube to a transverse air stream has been experimentally studied over a wide range of Grashof and Reynolds numbers. The data obtained have been correlated with Gr/Re2.5 as the correlating parameter. Criteria for transition from free convection to combined convection and from combined convection to forced convection have also been obtained.

Journal ArticleDOI
TL;DR: In this article, a non-linear profile of solute concentration is presented, and observations of this phenomenon are compared with calculations based on a simple model, and it is concluded that the model contains the essential features of the process.