Showing papers on "Convection published in 1971"
TL;DR: In this paper, the root-mean-square fluctuating concentration is supposed to obey a parabolic differential equation containing terms for convection, diffusion, generation and dissipation, and the initial and boundary conditions are appropriate to the steady injection of fluid from a nozzle of circular cross-section into a reservoir containing stagnant fluid of equal density.
404 citations
TL;DR: In this paper, the authors take the optimistic view that present convective models are qualitatively reasonable, what can one expect of an improved theory? One desirable feature would be the prediction of convective transfer with, in addition, some reasonable estimate of the accuracy of the prediction.
Abstract: Convection occurs somewhere in most stars, yet our lack of understanding of convection has not seemed a major impediment to progress in stellar structure in recent years. In part this is true because convection often achieves the idealized adiabatic limit that is expected in convective cores of stars. I t has also been true that uncertainties in the other physical processes in stars have been reduced considerably, and this has permitted a better empirical determination of the arbitrary parameters used in stellar convec tion theory. Of course, there is always the possibility that things are not as satisfactory as one thinks. But if we take the optimistic view that present convective models are qualitatively reasonable, what can one expect of an improved theory? One desirable feature would be the prediction of convective transfer with, in addition, some reasonable estimate of the accuracy of the prediction. For this, a minimal but inadequate test is found in laboratory convection for which some quantitative data are available. Thus, a principal goal of stellar convection theory should be the development of a reasonable deductive theory whose reasonability can be minimally established by laboratory tests. Having obtained a theory at this level we would next be interested in finer details that characterize stellar convection. That is, we would like to be able to be quantitative about the time dependence and scales of the con vection motion and to compare these with solar observations; we would like to know how far convection may penetrate beyond the regions of in stability and by large-scale mixing remove chemical inhomogeneities; we would be interested in the precise temperature variations at the tops of convective envelopes to have better input for model atmospheres. And these are only a sample of some of the questions that one would hope to answer at this level of difficulty. There is, in addition, a series of dynamical questions which raise problems about the interaction of convection with other processes of stellar fluid dynamics. These bring in new instabilities and are probably the most in-
309 citations
TL;DR: In this paper, the effect of sloping boundaries on thermal convection is studied theoretically and in the laboratory in the context of a model in which fluid is contained in a differentially heated rectangular box of small aspect ratio (depth/length), inclined at an angle δ to the vertical.
Abstract: The effect of sloping boundaries on thermal convection is studied theoretically and in the laboratory in the context of a model in which fluid is contained in a differentially heated rectangular box of small aspect ratio (depth/length), inclined at an angle δ to the vertical. Like its two limiting cases, Benard convection and convection in the vertical slot, a basic state which exists for low Rayleigh numbers becomes unstable as this parameter is increased. The types of instability and indeed the manner in which the motions become turbulent depend crucially on δ. In our work with water the following general picture of the primary instabilities applies:
For 90° > δ > 10° with the bottom plate hotter, the instabilities are stationary longitudinal convectively driven rolls with axes oriented up the slope. Near δ = 10° there is an upper and lower Rayleigh number cut off. If the Rayleigh number is too small diffusion damps the instabilities, but if it is too large they are damped by the development of a stable upslope temperature gradient in the mean flow.For 10° > δ > −10° (negative angles imply a hotter upper plate), transverse travelling waves oriented across the slope are the first instabilities of the mean flow. They obtain their kinetic energy via the working of the upslope buoyancy force.For - 10° > δ > −85° longitudinal modes are again observed. These are rather curious in that they may exist when the stratification is everywhere positive. The necessary energy for these modes comes out of the mean velocity field and out of the mean available potential energy.Agreement between the stability theory and the experiments is generally quite good over the whole range of δ, considering the approximations involved in finding a suitable basic flow solution.For Rayleigh numbers less than ∼ 106 turbulence is only possible for positive angles. For 85° > δ > 20° the development of unsteadiness involves the occurrence and the breaking of wavy longitudinal vortices in a manner reminiscent of the development of turbulence in cylindrical Couette flow.
257 citations
TL;DR: The influence of large variations of viscosity on convection in a layer of fluid heated from below has been investigated in this paper, where solutions for the flow and temperature fields were obtained numerically assuming infinite Prandtl number, free-surface boundary conditions, and two-dimensional motion of fixed horizontal wavelength.
Abstract: The influence of large variations of viscosity on convection in a layer of fluid heated from below has been investigated. Solutions for the flow and temperature fields were obtained numerically assuming infinite Prandtl number, free-surface boundary conditions, and two-dimensional motion of fixed horizontal wavelength. The effects of a temperature-dependent and a depth-dependent viscosity were each studied; calculations were also carried out using a temperature- and depth-dependent viscosity model appropriate to the earth's mantle.
221 citations
TL;DR: In this article, the authors show that the mid-latitude ionosphere may be in a continual dynamic state if the storms occur sufficiently often and that the density and flux profiles expected during the subsonic phase of the recovery are still not reached after an elapsed time of 10 days and correspondingly there is still a net loss of plasma from the ionosphere to the magnetosphere.
175 citations
TL;DR: In this paper, the authors studied the behavior of the flow field induced by lateral heating in a stably stratified fluid of constant gradient and found that the critical Rayleigh number above which cellular convection occurs has been experimentally determined to be 15000 ± 2500.
171 citations
TL;DR: In this paper, the authors describe the behavior of thermodynamic and transport properties near the critical point and examine the equations of continuity, momentum, and energy with a view to revealing the effect of variable properties and deciding whether the same simplifications can be made as are common with a constant property fluid.
Abstract: Publisher Summary This chapter describes the behavior of thermodynamic and transport properties near the critical point. The near-critical region may be thought of as that region, in which boiling and convection merge. When the pressure is sufficiently subcritical or supercritical, the problem tends toward either a boiling problem or a constant property convection problem. Under such conditions, existing theoretical and empirical methods are generally adequate. The chapter concentrates on the region rather close to the critical point where the property variations are severe and where there are very significant heat transfer effects. The equations of continuity, momentum, and energy are examined with a view to revealing the effect of variable properties and deciding whether the same simplifications can be made as are common with a constant property fluid. Various modes of heat transfer are also discussed, particular attention being given to the interaction between forced and free convection.
158 citations
TL;DR: In this article, the authors investigated the effect of the observed profile curvature neglecting linear wind shear effects on convective streeting and showed that the curvature itself enforces alignment of ccnvective cells with the flow direction.
Abstract: It is now well known that parallel cloud bands are widespread in the earth's atmosphere Observations from manned and unmanned spacecraft and from high-altitude aircraft in connection with soundings from ships and ground stations have shed light on their origin These and a special investigation of tropical cloudstreets during the BOMEX Project suggest the following typical characteristics of convective cloudstreets: Length = 20 to 500 km; spacing = 2 to 8 km; layer height = 08 to 2 km; width-to-height ratio = 2 to 4; wind structure: little change of direction with height; vertical gradient of wind shear (profile curvature) = 10?7 to 10?6 cm?1 sec?1; alignment: along the mean wind of the convective layer On the theoretical side, linear wind shear is known to favor convective “streeting” The present theory investigates the effect of the observed profile curvature neglecting linear shear effects It shows that the curvature itself enforces alignment of ccnvective cells with the flow direction Inertial forces arising from the vorticity field counteract buoyancy forces Their ratio as expressed in a modified Froude numer determines the value of the critical Rayleigh number responsible for the onset of convection In a flowing medium this number is raised, often by several orders of magnitude, over that of a resting medium for all convective modes, except the longitudinal mode Some three-dimensional computer presentations illustrate these results A quantitative application of the simplified theory to actual atmospheric conditions is attempted It indieates that in strong flows heated from below longitudinal rolls may double their amplitude in a matter of 10 minutes while transverse rolls decay at a similar rate with symmetric cells having nearly neutral stability The relations of this concept to other hypotheses and to the Goertler/Taylor rolls are discussed Finally it is speculated that the formation of wind streaks on water surfaces may be related to a similar mechanism DOI: 101111/j2153-34901971tb00585x
153 citations
TL;DR: Magnetospheric plasma convection electric field double-probe measurement at high latitude by Injun-5 satellite, noting east-west velocity reversals or discontinuities at auroral zone.
Abstract: Magnetospheric plasma convection electric field double-probe measurement at high latitude by Injun-5 satellite, noting east-west velocity reversals or discontinuities at auroral zone
130 citations
TL;DR: In this article, the critical Rayleigh number is determined as a function of the properties of the phase transition in the olivine-spinel phase change in the mantle, and it is concluded that this phase change, in the presence of a negative temperature gradient may intensify deep mantle convection.
Abstract: In a two-phase fluid layer heated from below, two instability mechanisms are present, the ordinary Rayleigh instability associated with thermal expansion and a phase change instability driven by the density difference between the phases. A stability analysis is presented for the combined effects of these instability mechanisms, and the critical Rayleigh number is determined as a function of the properties of the phase transition. The results are applied to the olivine-spinel phase change in the mantle, and it is concluded that this phase change in the presence of a negative temperature gradient may intensify deep mantle convection. The elevation of the phase-change boundary within the descending cold lithospheric plate at ocean trenches is a finite amplitude example of the phase-change instability. The additional gravitational body force on the slab due to the elevation of the phase boundary is comparable to that of thermal contraction.
TL;DR: In this paper, the authors matched the temperature distribution in wells with published type curves to obtain solutions for vertical groundwater velocity, if the thermal conductivity of the solid-fluid complex is known or can be estimated.
Abstract: Vertically moving groundwater transports heat by convection and causes curvature in the earth's thermal profile. Dimensionless plots of the temperature distribution in wells can be matched with published type curves to obtain solutions for vertical groundwater velocity, if the thermal conductivity of the solid-fluid complex is known or can be estimated. Rates of upward movement through semiconfining beds determined from temperature studies in the San Luis valley of Colorado and the Roswell basin of New Mexico were in good agreement with rates computed from pumping tests and water budget methods. Limitations of the method result from instability in borehole fluids, measurement detail required, and magnitudes of flow that can be detected.
TL;DR: In this paper, a two-dimensional model of a precipitating convective cloud is simulated by numerical integration of the hydrodynamic and thermodynamic equations, including condensation, evaporation, coagulation, breaking, and the terminal fall velocity of water drops relative to the air.
Abstract: A precipitating convective cloud is simulated in a two-dimensional model by numerical integration of the hydrodynamic and thermodynamic equations. Cloud physical processes included in the model are condensation, evaporation, coagulation, breaking, and the terminal fall velocity of water drops relative to the air. The size distribution of water drops is described in terms of seven discrete radii at every grid point and at every time step. Cloud and rainwater contents, rainfall intensity and radar reflectivity are computed directly from the size distributions. The numerical experiments show that precipitating convective clouds may be grouped into three types according to the way the cloud develops. 1) If the atmosphere has sufficient conditional instability and if vertical shear in the ambient wind field is weak, new convective clouds form on both sides of the initial cloud mainly due to the diverging cold downdraft. 2) When the direction of the vertical wind shear is constant with height and the s...
TL;DR: In this paper, the effect of ionic migration on free convection and free convective limiting currents is investigated, and the presence of supporting electrolyte lowers the electric field, as in stagnant or forced convective systems.
Abstract: Free convection and ionic migration effects are reviewed. Electrolytic free convection is treated theoretically for solutions and for solutions without added electrolyte and with additions of or . The effect of ionic migration on limiting currents is investigated. The presence of supporting electrolyte lowers the electric field, as in stagnant or forced convective systems. In addition, the concentration distributions of added electrolytes affect the density distribution, hence, the velocity profile in free convection, and, indirectly, the value of the calculated limiting currents.
TL;DR: In this article, an exact solution for the problem of fully developed, radiating, laminar convective flow in a vertical heated channel was obtained for the case of a convective gas.
Abstract: An exact solution is obtained for the problem of fully-developed, radiating, laminar convective flow in a vertical heated channel. The effect of radiation is to decrease the temperature difference between the gas and the wall, thereby reducing the influence of natural convection. Thus, the reduction in velocity occurring in a heated upflow is less for a radiating gas. Graphs are presented for the dimensionless velocity and temperature profiles and for the volume and heat fluxes.
TL;DR: In this article, the authors demonstrate the feasibility of using numerical calculations to determine the structure of convection cells within the mantle and demonstrate that large flow velocities and small temperature differences are associated with ascending convection and significant flows extend to a depth of 300 km.
Abstract: This paper demonstrates the feasibility of using numerical calculations to determine the structure of convection cells within the mantle. A temperature and depth-dependent viscosity appropriate for diffusion creep is employed. The upper boundary is a rigid surface moving at constant speed; this boundary condition is compatible with plate tectonics. It is found that large flow velocities and small temperature differences are associated with ascending convection, and significant flows extend to a depth of 300 km. The surface heat flow and topography are determined and are in reasonable agreement with observations.
TL;DR: The extent of injury is predicted under certain controlled conditions, and these conditions may be used to disclose protection principles appropriate to each mode of transfer.
Abstract: Heat is transferred through fabrics by convection, conduction, and radiation and, under certain circumstances, by vaporization. Each mode is subject to different physical principles, but the effect of the total heat absorbed by underlying skin is the same: If the resultant skin temperature rise is sufficiently high and maintained sufficiently long, injury results. The extent of injury is predicted under certain controlled conditions, and these conditions may be used to disclose protection principles appropriate to each mode of transfer.
TL;DR: In this paper, a straight circular pipe rotating around an axis perpendicular to its own axis, there occurs a secondary flow caused by Coriolis force, by which the flow resistance and the heat-transfer rate are increased.
TL;DR: In this article, atmospheric structure revealed by a high-resolution FM/CW radar sounder is compared with hypothetical models of internal wave structure and convection, and it is concluded that the multiple layers result from untrapped internal gravity waves, whose propagation vector is directed vertically, within very stable height regions.
Abstract: In the present paper, atmospheric structure revealed by a high-resolution FM/CW radar sounder is compared with hypothetical models of internal wave structure and convection. Special attention is given to the distribution of Richardson's number in trapped and untrapped gravity waves. It is concluded that the multiple layers result from untrapped internal gravity waves, whose propagation vector is directed newly vertically, within very stable height regions. In contrast to the convective instability proposed by Orlanski and Bryan, it is concluded that the layers are caused by Kelvin-Helmholtz instability resulting from the reduction in the Richardson's number due to growth of the amplitude-to-wavelength ratio as the waves propagate into thermally stable height regions of the atmosphere.
TL;DR: In this article, an experimental study of thermal convection in a horizontal porous layer bounded by isothermal planes has been performed with and without a mean flow of the saturating fluid phase.
Abstract: An experimental study of thermal convection in a horizontal porous layer bounded by isothermal planes has been performed with and without a mean flow of the saturating fluid phase. The temperature distribution and heat transfer resulting from convection have been determined. The theoretical criterion for the onset of convection (Rayleigh number NDRaU > 4piU2D) has been verified. For low values of NDRaU (<260) a regular pattern of convection cells has been observed which may be motionless or moving depending on the experimental conditions. For NDRaU values higher than 260, another convective state has been found that is mainly unstable. Numerical computations have been worked out that confirm the experimental results on the heat transfer and size of convective cells. (23 refs.)
TL;DR: In this paper, the authors measured convection, production, diffusion, and dissipation of temperature fluctuations in a turbulent wake behind a headed circular cylinder 1140 diameters downstream from the cylinder at a Reynolds number of 960.
Abstract: Convection, production, diffusion, and dissipation of temperature fluctuations have been measured in the dynamically similar turbulent wake behind a headed circular cylinder 1140 diameters downstream from the cylinder at a Reynolds number of 960. The measurements show strong production and dissipation and moderate convection and diffusion. In addition, the dependence of one‐dimensional spectra of temperature fluctuations on wake parameters and the skewness of the temperature derivative have been measured for the Reynolds number range 440‐69 000. All measurements are consistent with the assumption of local isotropy except for the skewness of the temperature derivative.
TL;DR: In the evolutionary phase of central helium burning, models of horizontal-branch stars reach a stage at which an intermediate region is unstable against convection, due to the progressive increase of the core mass by overshooting during the previous evolutionary stages and to the behaviour of the radiative temperature gradient at the core boundary as mentioned in this paper.
Abstract: In the evolutionary phase of central helium burning, models of horizontal-branch stars reach a stage at which an intermediate region is unstable against convection. This feature is due to the progressive increase of the core mass by overshooting during the previous evolutionary stages and to the behaviour of the radiative temperature gradient at the core boundary. By consideration of the typical time scales of propagation of convection and nuclear burning, a partial mixing (semi-convection) can be induced in a region around the convective core.
TL;DR: In this paper, planar flow is considered in a stable atmosphere with a constant stability and a constant effective eddy diffusivity for heat transfer, and linearized flow calculations are carried out to estimate vertical temperature profiles over a heated area representing a city.
Abstract: Steady, linearized flow calculations are carried out to estimate vertical temperature profiles over a heated area representing a city. Initially, planar flow is considered in a stable atmosphere with a constant stability and a constant effective eddy diffusivity for heat transfer. The calculations predict the main effects observed over urban areas: 1) positive temperature perturbations near the ground which will tend to cancel the early morning radiation inversion, and 2) negative temperature perturbations aloft which will tend to produce one or more weak inversions several hundred meters above the city. This idealized calculation gives better results than expected, with appropriate values for the flow parameters yielding the approximate mean magnitude and height of the main (lowest) layer of negative temperature perturbations. The computed flow field shows a downward velocity directly over the upwind portion of the heat island, similar to nonlinear calculations and observations for ocean islands...
01 Jan 1971
TL;DR: In this article, an analytical and experimental investigation of flame spread over the surface of a solid-fuel bed in an oxygen-inert environment is presented, in which the processes controlling the flame-spreading phenomenon occur in a very small "ignition region" at the leading edge of the spreading flame adjacent to the surface, and attention is focused on this small region.
Abstract: This paper reports on an analytical and experimental investigation of flame spread over the surface of a solid-fuel bed in an oxygen-inert environment. It is postulated that the processes controlling the flame-spreading phenomenon occur in a very small “ignition region” at the leading edge of the spreading flame adjacent to the surface, and attention is focused on this small region. The solid-phase energy equation is uncoupled from the gas-phase conservation equations and solved separately, retaining as a boundary condition the heat flux into the surface from the adjacent gas phase. The resulting solutions, in the form of simple algebraic equations, show clearly the different relationships between the physically important parameters associated with flame propagation over: (1) a “thick” fuel bed (thermal wave penetration into the solid beneath the ignition region much less than the fuel-bed depth), and (2) a “thin” fuel bed (subsurface temperature gradients negligible). The “critical thickness” criterion for separating the regions of thin and thick fuel-bed flame-spreading characteristics evolves as a naturally occurring parameter of the problem. The main dependence of heat flux on environmental parameters is obtained from consideration of the gas-phase conservation equations in a quiescent environment. By combining the results from the gas-phase and solid-phase analyses, simple algebraic relationships are obtained between flame-spreading velocity and parameters of theoretical and practical interest. Experimentally, using the techniques described in Ref. 1, the dependence of flame-spreading velocity on pressure level, oxidant mole fraction, diluent gas, initial temperature and fuel-bed depth is determined for polymeric and cellulosic materials. In addition, the influence of forced convective motion of the environment on flame spreading velocity is investigated experimentally. The analytical results provide excellent correlation for all data obtained in a quiescent environment, with the exception of the influence of initial temperature. Data obtained by other investigators are shown to be correlated as well. It is concluded that the role played by the solid phase in the over-all flame-spreading mechanism is generally understood, but the gas-phase processes require further definition.
TL;DR: In this article, the interaction of rotation and turbulent convection is assumed to give rise to an inhomogeneous, but isotropic, latitude dependent turbulent energy transport, which is described by a convective conduction coefficient κ¯¯c which varies with latitude.
Abstract: The interaction of rotation and turbulent convection is assumed to give rise to an inhomogeneous, but isotropic, latitude dependent turbulent energy transport, which is described by a ‘convective conduction coefficient κ
c’ which varies with latitude. Energy balance in the convective zone is then possible only with a slow meridian circulation in the outer convective zone of the sun. The angular momentum transported by this circulation is balanced in a steady state by turbulent viscous transport down an angular velocity gradient. A detailed model is constructed allowing for the transition from convective transport to radiative transport at the boundaries of the convective zone, by using a perturbation analysis in which the latitude variation of κ
c is small. The solution for a thin compressible shell gives equatorial acceleration and a hotter equator than pole, assuming that the convection is preferentially stabilised at the equator. For agreement with the sun's equatorial acceleration the model predicts an equatorial temperature excess of 70 K and a surface meridional velocity of 350 cm/sec from pole to equator.
TL;DR: In this article, the authors considered the instability of a horizontal fluid layer with a univariant phase transition and found that the layer can be unstable even when the less dense phase lies above the dense phase and can be stable in the opposite case.
Abstract: The gravitational instability of a horizontal fluid layer with a univariant phase transition is considered It is found that the layer can be unstable even when the less dense phase lies above the dense phase and can be stable in the opposite case Applications of the theory to convection with phase transitions in astrophysical and geophysical problems are briefly discussed
TL;DR: In this paper, a detailed heating function is designed for use in the ω equation and primitive equation prediction models, which permits stable or unstable heating to occur in a given region and also allows for the simultaneous occurrence of both kinds of heating in the same region.
Abstract: Convective adjustment procedures remove conditional instability in a vertical sounding preserving the total energy (latent, internal and potential). It is shown that this procedure has very undesirable properties in the very first time step in numerical weather prediction, e.g., large-scale temperature and moisture distributions are greatly altered. If, on the other hand, convective adjustment is carried out on a mesoscale, as is the case for the Kuo parameterization procedure, then the large-scale conditional instability is preserved and the changes in initial data are small in the first (and subsequent) time steps. The latter procedure is used to evaluate convective precipitation in the vicinity of a squall line. A detailed heating function is designed for use in the ω equation and primitive equation prediction models. This function permits stable or unstable heating to occur in a given region and also allows for the simultaneous occurrence of both kinds of heating in the same region. Precipita...
TL;DR: In this article, Tritton and Zarraga conducted experiments with electrolytically heated fluid layers to investigate the reported phenomena, which were hitherto unknown and which contradicted a corresponding theory of Roberts, and concluded that no drastic differences between theory and experiments, and between internal and external heating, exist.
Abstract: Convection experiments described by Tritton & Zarraga (1967) with electrolytically heated fluid layers were renewed in order to investigate the reported phenomena, which were hitherto unknown and which contradicted a corresponding theory of Roberts. While the apparatus was essentially unchanged, provisions were incorporated to study the possible influence of several flow and equipment parameters on the convection pattern. With the exception of the temperature dependence of the electric conductivity, the new experiments displayed no essential effects of the convection parameters. Experiments with shallow fluid layers revealed a clear co-orientation of the convection flows with the electric current and a strong time dependence of the hexagonal patterns. Experiments with deeper fluid layers exhibited a considerably diminished time and direction dependence of the convection flow, and a significant reduction of the dilation of the cells. Based on these observations, it is concluded that no drastic differences between theory and experiments, and between internal and external heating, exist, provided the heating is sufficiently uniform.