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Showing papers on "Convection published in 1986"


Journal ArticleDOI
John Goldak1, Malcolm Bibby1, J. Moore1, R. House1, B. Patel1 
TL;DR: In this paper, a nonlinear transient finite element analysis (FEA) is used to solve the fundamental equations for heat transfer in welds and a formulation for a non-linear finite element analyzer to solve them is described.
Abstract: This paper summarizes progress in the development of methods, models, and software for analyzing or simulating the flow of heat in welds as realistically and accurately as possible. First the fundamental equations for heat transfer are presented and then a formulation for a nonlinear transient finite element analysis (FEA) to solve them is described. Next the magnetohydrodynamics of the arc and the fluid mechanics of the weld pool are approximated by a flux or power density distribution selected to predict the temperature field as accurately as possible. To assess the accuracy of a model, the computed and experimentally determined fusion zone boundaries are compared. For arc welds, accurate results are obtained with a power density distribution in which surfaces of constant power density are ellipsoids and on radial lines the power density obeys a Gaussian distribution. Three dimensional, in-plane and cross-sectional kinematic models for heat flow are defined. Guidelines for spatial and time discretization are discussed. The FEA computed and experimentally measured temperature field,T(x, y, z, t), for several welding situations is used to demonstrate the effect of temperature dependent thermal properties, radiation, convection, and the distribution of energy in the arc.

335 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe results from 200 heat flow measurements across the Cape Verde Rise in the North Atlantic and show that the heat flow through normal, 125 Myr-old crust is 45.5 ± 3.4mWm-2, close to the prediction for a lithospheric plate model.
Abstract: Summary. We describe results from 200 heat flow measurements across the Cape Verde Rise in the North Atlantic. They show that the heat flow through normal, 125 Myr-old crust is 45.5 ± 3.4mWm-2, close to the prediction for a lithospheric plate model. Heat flow increases towards the centre of the Rise, reaching a maximum of 16 ± 4 mW m-2 above the normal oceanic value. The concommitant geoid anomaly at the centre of the Rise is 7.6 ± 0.3 m and the depth anomaly is 1900 ± 200 m. The anomalous heat flow, geoid and bathymetric values are used to constrain a variety of theoretical models of hot spot mechanisms. Lithospheric reheating models alone, whether involving transient or sustained thinning of the lithosphere, fail to model the broad heat flow anomaly and the long duration of uplift and volcanism observed on the Cape Verde Rise. Axisymmetric convection models provide a better fit to the observed data, and suggest that the swell is a consequence primarily of dynamic uplift generated by an ascending thermal plume in the underlying mantle. Uplift caused by expansion of the solid lithosphere is of smaller importance. The observed geoid, bathymetry and heat flow anomalies are reproduced well using convection models with upper mantle viscosities of 2-4 times 1020 Pa s and a coefficient of thermal expansion in the range 2.0 - 2.5 times 10-5 K-1. The effect of melting in the ascending plume is to buffer the heat flow anomalies. In the case of the Cape Verde Rise, partial melting is minimal, but its effect on other hotspots will be to limit observed heat flow anomalies at the surface to less than 20-25 mW m-2.

320 citations


Journal ArticleDOI
TL;DR: In this article, a precipitation index is described which quantifies the intensity and spatial extent of high-latitude particle precipitation based on observations made along individual satellite passes, and average patterns of the ionospheric convection electric field have been derived from a data set consisting of five years' observations by the Millstone Hill radar.
Abstract: A precipitation index is described which quantifies the intensity and spatial extent of high-latitude particle precipitation based on observations made along individual satellite passes. By sorting plasma convection data according to this index, average patterns of the ionospheric convection electric field have been derived from a data set consisting of five years' observations by the Millstone Hill radar. Reference to the instantaneous precipitation index, and the average patterns keyed to it, provides a means of characterizing the global precipitation and convection patterns throughout an event.

290 citations


Book
01 Jan 1986
TL;DR: In this paper, an analytical method of solution for two-dimensional problems is proposed for a single-dimensional problem with constant internal and surface resistances, where the model is based on the Fourier's Law of Heat Conduction.
Abstract: Fundamental Concepts Mechanisms of Heat Transfer Dimensions and Units Fourier's Law of Heat Conduction Thermal Conductivity Convection Heat Transfer Convection Heat-Transfer Coefficient Radiation Heat Transfer Emissivity and Other Radiative Properties Combined Heat-Transfer Mechanisms Steady-State Conduction in One Dimension One-Dimensional Conduction Equation Plane Geometry Systems Polar Cylindrical Geometry Systems Spherical Geometry Systems Thermal Contact Resistance Heat Transfer from Extended Surfaces Steady-State Conduction in Multiple Dimensions General Conduction Equation Analytical Method of Solution Graphical Method of Solution Conduction Shape Factor Solution by Numerical Methods (Finite Differences) Numerical Method of Solution for Two-Dimensional Problems Methods of Solving Simultaneous Equations Unsteady-State Heat Conduction Systems with Negligible Internal Resistance Systems with Finite Internal and Surface Resistances Solutions to Multidimensional Geometry Systems Approximate Methods of Solution to Transient-Conduction Problems Introduction to Convection Fluid Properties Characteristics of Fluid Flow Equations of Fluid Mechanics Thermal-Energy Equation Applications to Laminar Flows Applications to Turbulent Flows Natural-Convection Problem Dimensional Analysis Convection Heat Transfer in a Closed Conduit Heat Transfer to and from Laminar Flow in Circular Conduit Heat Transfer to and from Turbulent Flow in Circular Conduit Heat-Transfer Correlations for Flow in Noncircular Ducts Convection Heat Transfer in Flows Past Immersed Bodies Boundary-Layer Flow Turbulent Flow over Flat Plate Flow Past Various Two-Dimensional Bodies Flow Past a Bank of Tubes Flow Past a Sphere Natural-Convection Systems Natural Convection on a Vertical Surface: Laminar Flow Natural Convection on a Vertical Surface: Transition and Turbulence Natural Convection on an Inclined Flat Plate Natural Convection on a Horizontal Flat Surface Natural Convection on Cylinders Natural Convection around Spheres and Blocks Natural Convection about an Array of Fins Combined Forced- and Natural-Convection Systems Heat Exchangers Double-Pipe Heat Exchangers Shell-and-Tube Heat Exchangers Effectiveness-Number of Transfer Units Method of Analysis Crossflow Heat Exchangers Efficiency of a Heat Exchanger Condensation and Vaporization Heat Transfer Condensation Heat Transfer Boiling Heat Transfer Introduction to Radiation Heat Transfer Electromagnetic Radiation Spectrum Emission and Absorption at the Surface of an Opaque Solid Radiation Intensity Irradiation and Radiosity Radiation Laws Characteristics of Real Surfaces Radiation Heat Transfer between Surfaces View Factor Methods for Evaluating View Factors Radiation Heat Transfer within Enclosure of Black Surfaces Radiation Heat Transfer within an Enclosure of Diff use-Gray Surfaces Bibliography and Selected References Appendices Index

274 citations


Journal ArticleDOI
TL;DR: In this paper, stable state two-dimensional results obtained from numerical solutions to the transient Navier-Stokes equations are given for laminar convective motion of a gas in an enclosed vertical slot with large horizontal temperature differences.
Abstract: Steady-state two-dimensional results obtained from numerical solutions to the transient Navier-Stokes equations are given for laminar convective motion of a gas in an enclosed vertical slot with large horizontal temperature differences. We present results for air using the ideal-gas law and Sutherland-law transport properties, although the results are also valid for hydrogen. Wide ranges of aspect-ratio, Rayleigh-number and temperature-difference parameters are examined. The results are compared in detail with the exact solution in the conduction and fully developed merged boundary-layer limits for arbitrary temperature difference, and to the well-established Boussinesq limit for small temperature difference. It is found that the static pressure, and temperature and velocity distributions are very sensitive to property variations, even though the average heat flux is not. In addition we observe a net vertical heat flux to be the same as that obtained from the Boussinesq equations. We concentrate on the boundary-layer regime, but we present a rather complete picture of different flow regimes in Rayleigh-number, aspect-ratio and temperaturedifference parameter space. We observe that, with increasing temperature difference, lower critical Rayleigh numbers for stationary and oscillatory instabilities are obtained. In addition we observe that in some cases the physical nature of the instability changes with increasing temperature difference.

253 citations



Journal ArticleDOI
TL;DR: In this article, two-dimensional numerical simulations were performed to investigate the nature of tropospheric internal gravity waves of the type which are observed to occur above active thermal convection over an unstable boundary layer.
Abstract: Two-dimensional numerical simulations were performed to investigate the nature of tropospheric internal gravity waves of the type which are observed to occur above active thermal convection over an unstable boundary layer. These gravity waves are believed to be excited by a combination of pure thermal forcing and by the boundary layer eddies and cumulus clouds acting as obstacles to the flow in the presence of mean environmental wind shear. Large amplitude internal gravity waves were obtained in the simulations with amplitudes and horizontal scales similar to the 12 June 1984 aircraft observations over western Nebraska. This was a day with strong wind shear in the lowest 3 km above the ground and with scattered cumulus clouds topping the boundary layer. The simulations show that there is significant difference between the early time solutions (as might be predicted by linear theory) and late time solutions for the boundary layer eddy structure. A layer interaction occurs in which gravity waves of the stable layer are excited by the boundary layer convection. There is evidence to suggest that this layer interaction occurs both with and without shear but that it is stronger in the presence of low-level shear. Results indicate that shear (or the obstacle) effect is a more efficient generator of gravity waves than is the pure thermal forcing. The simulations show that the gravity waves initially forced by the boundary layer eddies lead to a feedback mechanism that acts to organize the boundary layer eddies and the cumulus convection. The solutions suggest that the character of fair weather convection (moist or dry) is a non-local problem involving at times the full depth of the troposphere. The clouds produced in the simulations have very little influence on the wave field or boundary layer eddy structure as they are relatively small cumuli. On the other hand the clouds are strongly influenced by the interactions between the wave and eddy fields. Upshear growth of cumulus clouds similar to that which is frequently observed in nature is reproduced in the simulations. The development of feeder (‘feeder’ is used here in a dynamical sense only) clouds on (typically) the upshear side of the cloud is found to be a result of the interaction between the gravity wave field and the dry and moist convection. The relative phase velocity between the gravity waves and the cloud plays a crucial role in determining the character of the cumulus cloud growth in the present simulations. These simulations suggest that the dynamics both internal and external to the boundary of a cumulus cloud is a complicated mix between wave dynamics and the usually considered convection dynamics. A brief discussion of the implications of the present results to cloud boundary baroclinic instability dynamics is also presented.

212 citations


Journal ArticleDOI
Abstract: Recent advances in heat transfer are discussed, providing data and methodology to solve a wide range of heat transfer problems. The topics considered include: basic concepts of heat transfer, mathematical methods, thermophysical properties, conduction, numerical methods in heat transfer, natural convection, and internal duct flow and external flows in forced convection. Also addressed are: rarefied gases, electric and magnetic fields, condensation, boiling, two-phase flow, and radiation.

195 citations


Journal ArticleDOI
TL;DR: In this paper, small-scale convection under the oceanic lithosphere which begins in the first 5 m.y.p. of cooling can produce a gravity signal with the amplitude and wavelength observed for large areas of the central Pacific and southern Indian oceans using Seasat altimeter data.
Abstract: Small-scale convection under the oceanic lithosphere which begins in the first 5 m.y. of cooling can produce a gravity signal with the amplitude and wavelength observed for large areas of the central Pacific and southern Indian oceans using Seasat altimeter data. The trend of the observed anomalies is parallel to the direction of plate motion as might be expected if they were produced by small-scale convection. Models predict that the wavelengths of gravity anomalies increase more rapidly with age than is observed. The persistence of short relatively uniform wavelength anomalies (less than 200 km) to crustal ages of 50 Ma may indicate that they were produced when the lithosphere was very young and thin and were 'frozen in' as cooling thickened the elastic lithosphere. Small-scale convection which begins under very young lithosphere does not violate other geophysical data such as the rate of seafloor subsidence and variations of geoid height with age. After convection has begun, the subsidence due to thermal contraction within the lithosphere varies linearly with age, in the absence of mantle heat sources, although the rate of change of these quantities is affected by convection. Much of the variation of the geoid height across fracture zones can be fit by a model which includes small-scale convection.

193 citations


Journal ArticleDOI
TL;DR: In this paper, a simple stellar envelope consisting of three layers: a convectively unstable middle layer bounded above and below by stably stratified polytropes is studied, and two-dimensional numerical simulations are used to investigate the fully compressible nonlinear motions that ensue.
Abstract: Penetrative convection spanning multiple scale heights is studied within a simple stellar envelope consisting of three layers: a convectively unstable middle layer bounded above and below by stably stratified polytropes. Two-dimensional numerical simulations are used to investigate the fully compressible nonlinear motions that ensue. The cellular flows display prominent downward-directd plumes surrounded by broader regions of upflow. Such asymmetry arises because pressure fluctuations accentuate buoyancy driving in the concentrated plumes and can even lead to weak buoyancy braking in the surrounding ascending flows. As the plumes plunge downward into a region of stable stratification, they serve to excite a broad spectrum of internal gravity waves there. The induced waves are not passive, for they feed back upon the plumes by deflecting them sideways, thereby modulating the amplitude of the convection in time even in the unstable layer. The penetrative motions that billow upward into the upper stable zone are distinctly weaker, and they cascade back downward toward the unstable zone over a broad horizontal scale. The strong excitation of gravity waves by the convection has implications for gradual mixing deep within a star.

176 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigate the interaction of thermal convection and crystallization in large aspect-ratio magma chambers and show that the convective instability occurs at different stages of crystallization.

Journal ArticleDOI
TL;DR: In this article, a series of laboratory experiments were conducted to study convective structures in rotating fluids (distilled water) in ranges of Rayleigh flux number Raf from 106 to 2 × 1011 and of Taylor number Ta from 106-1012.
Abstract: We describe a series of laboratory experiments to study convective structures in rotating fluids (distilled water) in ranges of Rayleigh flux number Raf from 106 to 2 × 1011 and of Taylor number Ta from 106 to 1012. An intermediate quasi-stationary ring pattern of convection was found to arise from the interaction of the onset of convection with the fluid spin-up, for which we determined the times of origin and destruction, the distances between the rings, and the diameter of the central ring in terms of Raf and Ta. The ring structure evolves into a vortex grid which can be regular or irregular. In terms of Raf and Ta the regular grid exists in the linear regime, when the number of vortices N is in accord with the linear theory, when , or in the nonlinear regime when N ∝ h−2Ta½Raf−⅙ ∝ where Ω is the angular velocity and h is the fluid depth. In the irregular regime we always have N ∝ Ω. The transition from the regular regime to the irregular one is rather gradual and is determined by the value of the ordinary Rayleigh number, which we found to be greater than the first critical number Ra ∝ Ta2/3 by a factor about 25–40. In the transition region vortex interactions are observed, which start with rotation of two adjacent vortices around a common axis, then the vortices come closer and rotation accelerates, following which the vortices form a double helix and then coalesce into one stronger vortex.Some other qualitative experiments show that if the rotating vessel with the convective fluid is inclined to the horizontal, the vortex grid is formed along the rotation axis in accordance with the Proudman–Taylor theorem.

Journal ArticleDOI
TL;DR: In this paper, a mathematical model of convection, obtained by truncation from the two-dimensional Boussinesq equations, is shown to exhibit a bifurcation from symmetrical cells to tilted non-symmetrical ones.
Abstract: A mathematical model of convection, obtained by truncation from the two-dimensional Boussinesq equations, is shown to exhibit a bifurcation from symmetrical cells to tilted non-symmetrical ones. A subsequent bifurcation leads to time-dependent flow with similarly tilted transient plumes and a large-scale Lagrangian mean flow. This change of symmetry is similar to that occurring with the advent of a large-scale flow and transient tilted plumes seen in laboratory experiments on turbulent convection at high Rayleigh number. Though not intended as a description of turbulent convection, the model does bring out in a theoretically tractable context the possibility of the spontaneous change of symmetry suggested by the experiments.Further bifurcations of the model lead to stable chaotic phenomena as well. These are numerically found to occur in association with heteroclinic orbits. Some mathematical results clarifying this association are also presented.

Journal ArticleDOI
TL;DR: The flight of the Spacelab 3 microgravity laboratory onboard the Space Shuttle Challenger in May 1985 enabled electroconvection experiments to be conducted using the goephysical fluid flow cell instrument as mentioned in this paper.
Abstract: The flight of the Spacelab 3 microgravity laboratory onboard the Space Shuttle Challenger in May 1985 enabled electroconvection experiments to be conducted using the goephysical fluid flow cell instrument. Experimental results are presented which illustrate the variety of convection achieved by varying the imposed radial and latitudinal temperature gradients, rotation rates, and the strength of the electrostatic gravity. These results are compared with those obtained from nonlinear three-dimensional simulations and good agreement is found.

Journal ArticleDOI
TL;DR: In this article, a quantitative computer model of the convection surge mechanism is constructed, which incorporates the dipolarization of the field line shapes as well as the results of recent transient electric field measurements by the AST-6 satellite.
Abstract: To explore the properties of the 'convection surge' mechanism postulated by Quinn and Southwood (1982), a quantitative computer model of the mechanism is constructed. The model incorporates the dipolarization of the field line shapes as well as the results of recent transient electric field measurements by the AST-6 satellite. The computer model numerically integrates the equations of motion of ensembles of ions populating a single flux tube that goes through the convection surge or 'dipolarization' transformation. The numerical results confirm that the mechanism easily generates the bounce-phase-bunched ion distributions in question, and show that the convection surge can generate dramatically field-aligned ion distributions. It is hypothesized that the convection surge mechanism is fundamentally associated with the processes responsible for transporting tail ion populations to the geosynchronous regions of the earth's magnetosphere.


Journal ArticleDOI
TL;DR: In this paper, computer simulation was carried out to describe three-dimensional convection in laser melted pools, i.e., for the case where the workpiece is moving with respect to the laser beam.
Abstract: Computer simulation was carried out to describe three-dimensional convection in laser melted pools,i.e., for the case where the workpiece is moving with respect to the laser beam. Two different types of driving forces for flow were considered in the model,i.e., the buoyancy force and the surface tension gradient at the pool surface. Laser surface melting of 6063 aluminum alloy was carried out using a continuous-wave CO2 laser, and the power delivered to the workpiece was measured calorimetrically. The calculated and observed fusion boundaries were compared and very good agreement was obtained. Finally, the effect of the surface tension temperature coefficient δγ/δT on the convection pattern and penetration of laser melted pools was demonstrated with the model.

Journal ArticleDOI
TL;DR: In this paper, a qualitative model is developed to interpret the sometimes peculiar and spectacular-phenomena caused by the simultaneous cooperative effects of chemical reaction, diffusion, heat conduction, and fluid convection.
Abstract: A variety of experiments are presented to illustrate that chemical wave velocities in the iron(I1)-nitric acid and in the chlorite-thiosulfate reactions are profoundly affected by the convective motion of the solutions. A qualitative model is developed to interpret the-sometimes peculiar and spectacular-phenomena caused by the simultaneous cooperative effects of chemical reaction, diffusion, heat conduction, and fluid convection.


Journal ArticleDOI
TL;DR: In this article, an experimental investigation of the onset of convection in shallow fluid layers heated uniformly from below and cooled from above by an air layer has been made, and it has been shown that if the depth of the silicone layer is smaller than 2 mm, then convection takes place in two stages.
Abstract: An experimental investigation of the onset of convection in shallow fluid layers heated uniformly from below and cooled from above by an air layer has been made. If the depth of the silicone layer is smaller than 2 mm the onset of convection takes place in two stages. There is first a weak pattern, which is characterized by its appearance at ever smaller temperature gradients as the depth of the fluid is decreased. When the temperature difference across the fluid is increased a second strong pattern forms near the predicted critical Marangoni number. The cells in this pattern are hexagonal and seem to be what one has always referred to as Benard cells. The temperature gradient at which this pattern appears increases with decreased depth. The heat transfer through the fluid has been measured. The critical temperature gradient for the formation of the hexagonal pattern has been determined from the break of the heat transfer curve.

Proceedings ArticleDOI
01 Jan 1986
TL;DR: In this article, a finite difference method based on flux-corrected transport (FCT) is applied to natural convective flow in a porous medium at large Rayleigh number.
Abstract: A numerical technique designed to solve a wide class of convectively dominated flow problems is applied to natural convective flow in a porous medium at large Rayleigh number. The technique is a finite difference method based on flux-corrected transport (FCT) and possesses four desirable numerical properties: stability, accuracy, monotonicity, and conservation. Steady natural convection is investigated for Rayleigh numbers as large as 10,000. An efficient methodology for obtaining steady state solutions is illustrated. A simulation is performed for transient thermal convection at a Rayleigh number of 2500. Transient natural convection involving both heat and mass transfer is illustrated for a Rayleigh number of 2500, Lewis number of 2, and buoyancy ratio of 0.1. All simulations are performed in a square cavity with heated vertical side walls. 17 refs.

Journal ArticleDOI
TL;DR: In this paper, a simple turbulence model is used to study the moist convective boundary layer, in which a prognostic equation is applied to calculate the turbulent kinetic energy E. The eddy coefficient is proportional to El.
Abstract: A simple turbulence model is used to study the moist convective boundary layer, in which a prognostic equation is applied to calculate the turbulent kinetic energy E. An observational length scale of the vertical velocity component, l, is used in the mixed layer, while a length scale associated with gravity waves is applied in the stable layer. The eddy coefficient is proportional to El. This model simulates well the temperature, mixing ratio and mean wind observed in the Wangara experiments. The turbulent kinetic energy and eddy fluxes generated are also in good agreement with those observed, as well as with those obtained from other more complicated models. Furthermore, the parameterization and results generated are used in a pollution model, which will be presented in Part II of this study.

Journal ArticleDOI
TL;DR: In this article, a pseudo-spectral numerical scheme is used to study two-dimensional, single-cell, time-dependent convection in a square cross-section of fluid saturated porous material heated from below.
Abstract: A pseudo-spectral numerical scheme is used to study two-dimensional, single-cell, time-dependent convection in a square cross-section of fluid saturated porous material heated from below. With increasing Rayleigh number R convection evolves from steady S to chaotic NP through the sequence of bifurcations S→P(1)→QP2→P(2)→NP, where P(1) and P(2) are simply periodic regimes and QP2 is a quasi-periodic state with two basic frequencies. The transitions (from onset of convection to chaos) occur at Rayleigh numbers of 4π2, 380–400, 500–520, 560–570, and 850–1000. In the first simply periodic regime the fundamental frequency f1 varies as . The chaotic states are characterized by spectral peaks with at least 3 fundamental frequencies superimposed on a broadband background noise. The time dependence of these states arises from the random generation of tongue-like disturbances within the horizontal thermal boundary layers. Transition to the chaotic regime is accompanied by the growth of spectral components that destroy the centre-symmetry of convection in the other states. Over-truncation can lead to spurious transitions and bifurcation sequences; in general it produces overly complex flows.


Journal ArticleDOI
TL;DR: In this article, the authors examined the ionospheric convection signature at high latitudes during periods of prolonged northward interplanetary magnetic field (IMF) and showed that a four-cell convection pattern can frequently be observed in a region that is displaced to the sunward side of the dawn-dusk meridian regardless of season.
Abstract: Observations of the ionospheric convection signature at high latitudes are examined during periods of prolonged northward interplanetary magnetic field (IMF). The data from Dynamics Explorer 2 show that a four-cell convection pattern can frequently be observed in a region that is displaced to the sunward side of the dawn-dusk meridian regardless of season. In the eclipsed ionosphere, extremely structured or turbulent flow exists with no identifiable connection to a more coherent pattern that may simultaneously exist in the dayside region. The two highest-latitude convection cells that form part of the coherent dayside pattern show a dependence on the y component of the IMF. This dependence is such that a clockwise circulating cell displaced toward dawn dominates the high-latitude region when B(Y) is positive. Anti-clockwise circulation displaced toward dusk dominates the highest latitudes when B(Y) is negative. Examination of the simultaneously observed energetic particle environment suggests that both open and closed field lines may be associated with the high-latitude convection cells. On occasions these entire cells can exist on open field lines. The existence of closed field lines in regions of sunward flow is also apparent in the data.

Journal ArticleDOI
TL;DR: In this article, it is shown that even in the absence of curvature of the surfaces bounding the fluid annulus in the axial direction, a mean flow is generated by Reynolds stresses.
Abstract: The nonlinear equations describing convection in the form of thermal Rossby waves in a rotating annulus are solved both by an analytical perturbation theory and by a numerical method. It is shown that even in the absence of curvature of the surfaces bounding the fluid annulus in the axial direction a mean flow is generated by Reynolds stresses. The good agreement between analytical expressions and numerical results indicates that the former are valid over a larger domain of the parameter space than may be expected on the basis of the analysis of convection rolls in a non-rotating layer. This is caused in part by the reduced release of potential energy accompanying the reduced convective heat transport owing to the drift of the convection columns. The effect of curvature causes the replacement of the basic mode of convection by a different mode characterized by a double roll structure. The associated zonal mean flow is typically stronger than in the case without curvature.

Journal ArticleDOI
TL;DR: In this article, the authors measured heat flow on the Bermuda Rise and the surrounding seafloor and found that the heat flow is higher than either the plate or boundary layer models predict, reaching a uniform value of about 50 mW m−2 on 120 m.y old crust.
Abstract: The Bermuda Rise is a broad topographic swell which is apparent in both residual depth and geoid anomaly maps of the western North Atlantic. The magnitudes of the depth and geoid anomalies associated with the Bermuda Rise are similar to the anomalies associated with other swells surrounding recent volcanic islands (e.g., Hawaii), suggesting that despite the lack of recent volcanism on Bermuda, the rise has a similar origin to other midplate swells. Results are reported from 171 new heat flow measurements at seven carefully selected sites on the Bermuda Rise and the surrounding seafloor. Off the Bermuda Rise the basement depths are generally shallower and the heat flow higher than either the plate or boundary layer models predict, with the measured heat flow apparently reaching a uniform value of about 50 mW m−2 on 120 m.y. old crust. On the Bermuda Rise the heat flow is significantly higher (57.4±2.6 mW m−2) than off the swell (49.5±1.7 mW m−2). The magnitude of the anomalous heat flux (8–10 mW m−2) is comparable to that previously found along the older portion of the Hawaiian Swell near Midway. The existence of higher heat flow on both the Hawaiian Swell and Bermuda Rise indicates that these features fundamentally have a thermal origin. The differences in the shape, uplift, and subsidence histories of the Hawaiian Swell and Bermuda Rise can be quantitatively explained by the different absolute velocities of the Pacific and North American plates moving across a distributed heat source in the underlying mantle. Two-dimensional numerical convection models indicate that the observed depth, geoid, and heat flow anomalies are consistent with simple convection models in which the lower part of the thermally defined plate acts as the upper thermal boundary layer of the convection.


Journal ArticleDOI
TL;DR: In this paper, the onset of convection in a layer of viscoelastic liquid heated from below is investigated, and it is shown that the nature of the convective solution depends strongly on the particular constitutive relation used to characterize the viscousity.
Abstract: The onset of convection in a layer of viscoelastic liquid heated from below is investigated. It is shown that the nature of the convective solution depends strongly on the particular constitutive relation used to characterize the viscoelasticity. For certain models and certain parameter ranges the convection is supercritical and stable, while for other models and parameter ranges it can be subcritical and unstable. It is suggested that observations of convective behavior can provide a test for constitutive relations proposed for a particular liquid. A Fourier representation of the solution to the nonlinear problem is developed which is shown to admit aperiodic, or chaotic, solutions in a specific truncation that generalizes the classical Lorenz system for the Newtonian Benard problem.

Journal ArticleDOI
TL;DR: In this article, the results of two earlier papers on convection in the mixed layer and on the solar heating profile are introduced into a one-dimensional model in order to investigate the following consequences of the daily cycle of solar heating in the upper ocean:
Abstract: The results of two earlier papers on convection in the mixed layer and on the solar heating profile are here introduced into a one-dimensional model in order to investigate the following consequences of the daily cycle of solar heating in the upper ocean: 1. the daytime convection depth becomes less than the turbocline depth; 2. the convective power supply to turbulence in the mixed layer is reduced; 3. the mixed layer below the convection layer becomes stably stratified; 4. the depth of the turbocline is reduced, leaving a diurnal thermocline between it and the top of the seasonal thermocline; 5. the heat content and potential energy of the diurnal and seasonal thermoclines are increased, slowing down the subsequent nocturnal descent of the turbocline. These diurnal changes are illustrated by integrating a one-dimensional model forced by the astronomical cycle of solar heating and seasonal variation of surface meteorology derived from Bunker's climatology. The model is integrated for 18 months to show the seasonal modulation of the diurnal cycle. Nocturnal convection plays a dominant role. The convection depth closely follows the thermal compensation depth during the day when they are less than the turbocline depth. Integrating the model with a 24-hour time step leads to large errors in the seasonal variation of mixed layer temperature and depth, and in the source term of isopycnic potential vorticity. The errors are reduced by using two time steps per day, one for the daytime when convection is quenched, the other for the night when it is active. A novel parametrization based on tuning the daily equivalent solar elevation to surface temperature further reduces the error. This parametrization is used to investigate the sensitivity of the seasonal cycles of mixed layer depth and temperature to: (1) seasonality in the surface fluxes; (2) systematic changes in the net annual solar heating; (3) random changes in the seasonal cycles of solar heating induced (i) monthly and (ii) daily. The sensitivity to uncertainty in seawater turbidity is investigated in the same way. The profile of isopycnic potential vorticity subducted into the thermocline depends on the vernal correlation of mixed layer depth and density, so gyre circulation is sensitive to solar heating in spring.