Showing papers on "Buoyancy published in 1978"

The Simulation of Three-Dimensional Convective Storm Dynamics

Abstract: A new three-dimensional cloud model has been developed for investigating the dynamic character of convective storms. This model solves the compressible equations of motion using a splitting procedure which provides numerical efficiency by treating the sound wave modes separately. For the subgrid turbulence processes, a time-dependent turbulence energy equation is solved which depends on local buoyancy, shear and dissipation. First-order closure is applied to nearly conservative variables with eddy coefficients based on the computed turbulence energy. Open lateral boundaries are incorporated in the model that respond to internal forcing and permit gravity waves to propagate out of the integration domain with little apparent reflection. Microphysical processes are included in the model using a Kessler-type parameterization. Simulations conducted for an unsheared environment reveal that the updraft temperatures follow a moist adiabatic lapse rate and that the convection is dissipated by water loadin...

The diffusive interface in double-diffusive convection

Abstract: A model of the diffusive interface in double-diffusive convection at high Rayleigh number is proposed. The interface is assumed to have a double structure: two marginally stable boundary layers from which blobs or thermals arise on the outer edges of the interface, separated by a diffusive core across which all transport takes place by molecular diffusion. The model is time-independent and comparison is made with unsteady ‘run-down’ experiments on the assumption that the experiments run down through a sequence of equilibrium states each of which can be considered separately. The model predicts a constant ratio of the buoyancy fluxes of the two components at a value equal to the square root of the ratio of their molecular diffusivities, and individual fluxes in reasonable agreement with the available experimental data. Some time-dependent features of the model are also examined.

On the Theory of Turbulence in the Buoyancy Subrange of Stably Stratified Flows

Abstract: A theoretical investigation is made of turbulence in the buoyancy subrange of stably stratified sheer flows. This theory is based on a new calculation of the buoyancy flux spectrum B (k). In the Lumley-Shur theory, it was assumed that B (k) had a universal form which could be determined by a simple dimensional consideration. That assumption is shown to be incorrect. One new result of the present calculation is that B (k) has a fairly sharp transition at a wavenumber kB = 0.8½ωB/vm, where ωB is the Brunt-Vaisala frequency and vm the root-mean-square velocity in the equilibrium range. Physically, this transition is “interpreted” as an emission of incoherent gravity waves fed by the kinetic energy of vertically fluctuating air particles. When k kB, the gravity waves are strongly damped and consequently contain very little energy. The transition of the energy spectrum E(k) at kB is foun...

Buoyancy-induced flows in water under conditions in which density extrema may arise

Abstract: The temperature dependence of the density of both pure and saline water, even to very high salinity and pressure levels, decreases at decreasing temperature toward an extremum. The nature of this variation precludes approximating the buoyancy-force density difference linearly with a temperature difference. This peculiar density variation of water has very significant effects, even at environmental temperature levels. A new equation has appeared which relates density to temperature, salinity and pressure with very high accuracy. Its form is especially suited to the analysis of convective motions. We consider here vertical boundary-layer flows. Analysis of flows arising from thermal buoyancy and from combined buoyancy effects shows the simplicity of the formulation. Relatively few new parameters arise. Extensive calculations for thermally buoyant flows show the large magnitude of the effects of the complicated density variation on transport. Buoyancy-force reversals and convective inversions are predicted. The latter are in close agreement with past experiments. A new Grashof number arises which is an accurate indication of the actual local flow vigour. The effects of specific temperature conditions are given in detail. The appreciable effect of the Prandtl number is calculated. Transport parameters are given for salinities and pressures up to 40 p.p.t. and 1000 bars, respectively.

The influence of buoyancy on turbulent transport

Abstract: Turbulent transport of fluctuating turbulent energy, turbulent momentum flux, temperature variance, turbulent heat flux, etc. in the upper part of the atmospheric boundary layer is usually dominated by buoyant transport. This transport is responsible for the erosion of the overlying stably stratified region, resulting in progressive thickening of the mixed layer. It is easy to show that a classical gradient transport model for the transport will not work, because it transports energy in the wrong direction. On the other hand, application of the eddy-damped quasi-Gaussian approximation to the equations for the third moments results in a transport model which predicts realistic inversion rise rates and heat-flux profiles. This is also a gradient transport model, but like molecular transport in solutions, a flux of one quantity depends on gradients of all relevant quantities. Transport coefficients are modified by the heat flux, so that the vertical transport is severely reduced near the inversion base. A simple Lagrangian model of transport of an indelible scalar in a stratified flow indicates that the form of the modified transport coefficients results from a marked anisotropic change in the Lagrangian time scale in stratification.

A theory of mixing in a stably stratified fluid

Abstract: A theory is developed for turbulence in a stably stratified fluid, for example in the experiments of Rouse & Dodu and of Turner where there is no shear and the turbulence is induced by a source of energy near the lower boundary of the fluid. A growing mixed layer of thickness D appears in the lower portion of the fluid and is separated from the non-turbulent fluid above, in which the buoyancy gradient is given, by an interfacial layer of thickness h. The lower mixed layer has a very weak buoyancy gradient and the large buoyancy difference across the interfacial layer is Δb.As indicated by the experiments of Thompson & Turner and Hopfinger & Toly, and derived by the author in a recent paper, if u is the root-mean-square horizontal velocity and l is the integral length scale, the eddy viscosity ul is a constant in a homogeneous fluid agitated by a grid. When there is stratification, the theory indicates that the fluid motion is unaffected by buoyancy forces in the mixed layer, so that ul should again be constant in the lower portions of the mixed layer. Since l is proportional to distance, we may conveniently suppose that the source of the disturbances is at a level z = 0 where u is infinite in accordance with uz = K. Thus we may take K to be a fundamental parameter characterizing the turbulent energy source. Then z is distance above the plane of the virtual energy source. If the non-turbulent fluid has uniform buoyancy, DΔb = U2 may be shown to be constant. In general, whether constant or not, U may be taken to be a fundamental parameter expressing the stability. The quantity is the most fundamental of the several Richardson numbers that have been introduced in this problem because, with its use, ‘constants’ of proportionality do not depend on the molecular coefficients of viscosity or diffusion (for high Reynolds number turbulence) or on the geometry of the grid.The theory contains a number of results: .h ∼ D, as observed in several experiments.

Power converter and method

Abstract: A method of and apparatus for increasing the power output of an impeller which is mounted in a stream of free flowing fluid, such as water or air. A portion of the free flowing fluid is received by the impeller and some of the portion leaves the impeller and is caused re-enter the free stream at an angle of intersection of not less than 35° but less than 75°. When designed for operation under water, buoyancy chambers are sized and positioned to negate gravitational stresses and distortions when submerged to thereby reduce cost and improve performance.

The relation between the flux ratio and energy ratio in convectively mixed layers

Abstract: Two alternative formulations of the problem of entrainment at the top of a convecting surface layer are in current use. One expresses the mixing in terms of the ratio of the buoyancy flux at the top of the convecting layer to that at the ground, and the other (which is the more fundamental) compares the energy used for entrainment with that produced by the destabilizing flux at the ground. Several authors have proposed similar methods of calculating the latter and relating the two ratios, but we believe these authors are in error because of a fallacious assumption about the nature of the mixing in the practically uniform layer. The present note attempts to resolve this difficulty by using a simple model which considers explicitly the separate contributions of the environment and the surface flux to the density of the mixed layer. We suggest that the physically relevant energy ratio is the increase in potential energy due to the redistribution of the initial density profile compared with the potential energy made available by heating from below.

Free and forced convection flow in a rotating channel bounded below by a permeable bed

Abstract: The steady flow in a parallel plate channel rotating with an angular velocity Ω and bounded below by a permeable bed is analysed under the effect of buoyancy force. On the porous bed the boundary condition of Beavers and Joseph is applied and an exact solution of the governing equations is found. The solution in dimensionless form contains four parameters: The permeability parameterσ 2, the Grashof numberG, the rotation parameterK 2 and a dimensionless constantα. The effects of these parameters, specially,σ 2, G andK 2, on the slip velocities and velocity distributions are studied. For largeK 2, there arise thin boundary layers on the walls of the channel.

Magnetic instabilities of a rotating gas

Abstract: We explore two types of instability which may develop when a highly conducting gas rotates rapidly in the presence of a radial gravitational force and an azimuthal magnetic field. Beyond a critical radius (equal to twice the isothermal scale height) a decrease of magnetic flux (per unit mass) outwards leads to the appearance of eastward-propagating waves by the mechanism of ‘magnetic buoyancy’. Within the critical radius an increase of magnetic flux outwards leads to westward-propagating waves by a totally different mechanism. Provided that the effects of Ohmic dissipation are not too large, either instability may set in for quite modest magnetic flux gradients, even when the magnetic energy of the system is very much smaller than the rotational energy.

Three dimensional free convection flow and heat transfer along a porous vertical plate

Abstract: The free convection flow along a vertical porous plate with transverse sinusoidal suction velocity distribution is investigated. Due to this type of suction velocity at the plate the flow becomes three dimensional one. For the asymptotic flow condition, the wall shear stress in the direction of main flow for different values of buoyancy parameter G is obtained. For G=0, the skin friction in the direction of free stream and the rate of heat transfer from the plate to the fluid are given. It is found that these results differ from those obtained by Gersten and Gross.

Wave Instability of Mixed Convection Flow Along a Vertical Flat Plate

Abstract: An analysis is performed to investigate the linear wave instability of laminar mixed convection flow over an isothermal vertical flat plate, in which the buoyancy force arises solely from the temperature gradients in the fluid. In the stability analysis, the main flow and thermal fields are treated as nonparallel, and are obtained by the local nonsimilarity solution method The eigenvalue problem consisting of the linearized system of coupled differential equations for the velocity and temperature disturbances are solved by a direct Runge-Kutta numerical integration scheme along with a filtering technique to remove the “parasitic errors” inherent in the numerical integration of the disturbance equations. Neutral stability curves and critical Reynolds numbers are presented for a range of buoyancy parameters covering both assisting and opposing flow situations for two representative Prandtl numbers of 0.7 and 7. It is found that the flow becomes more stable as the buoyancy force increases for assist...

Convection due to surface-tension gradients

Abstract: The use of dimensionless parameters to study fluid motions that could occur in a reduced-gravity environment is discussed. The significance of the Marangoni instability is considered, and the use of dimensionless parameters to investigate problems such as thermo and diffusocapillary flows is described. Characteristics of fluid flow in space are described, and the relation and interaction of motions due to capillarity and buoyancy is examined.

Low-Level Turbulence Structure in the Vicinity of a Hurricane

Abstract: Turbulent low-level properties, as determined from aircraft measurements on 17 September 1975, are presented for a peripheral portion of Hurricane Eloise. Application of the Deardorff (1972b) planetary boundary layer parameterization scheme to the mean data indicates that the shear production of turbulence is far greater than that due to buoyancy. it is inferred from an examination of the terms contributing to the energy budget for the upper mixed-layer levels that the vertical shear production of turbulence principally occurs in the surface layer. The surface stress calculated from Deardorff's approach is almost identical to that observed from the momentum flux profile. This profile also shows that the top of the mixed layer is delineated by a vanishing stress, in agreement with previous undisturbed trade wind environment observations.

The scale of solar granulation

Abstract: We derive the observed scale of granulation as a consequence of a physical model. At scales smaller than granulation, horizontal radiative transport reduces temperature fluctuations and the resultant buoyancy forces in the surface layers. At scales only slightly larger than granulation, the dynamical pressure required to drive horizontal motions changes the opacity sufficiently to reduce the apparent contrast. This raises the possibility that the dark center of an exploding granule may actually be hot below the surface. We also estimate the maximum possible horizontal extent of a surface driven convective flow as 4/5 times granular scale.

Shear flow beneath oceanic plates: Local nonsimilarity boundary layers for olivine rheology

Abstract: The principle of local similarity, which has been used to model the two-dimensional boundary layers in the oceanic upper mantle, permits calculation of the temperature, velocity, and stress fields with essentially analytic techniques. Finite difference numerical methods are hard pressed to resolve the detail required by the large variation of viscosity between the lithosphere and the asthenosphere. In this paper the local similarity approximation has been justified by quantitatively evaluating the effect of nonsimilarity due to viscous heating, nonlinear temperature- and pressure-dependent rheology, buoyancy, adiabatic cooling, etc. Nonsimilar effects produce only small modifications of the locally similar boundary layers; important geophysical observables such as surface heat flux and ocean floor topography are given to better than 10 percent by the locally similar solution. A posteriori evaluations of the terms neglected in the boundary layer simplification of the complete equations have been conducted on the locally similar temperature and velocity profiles close to the spreading ridge. The boundary layer models are valid to depths of 100 km at 3 m.y. and 10 km at 0.3 m.y.

Electromagnetically and thermally driven flow phenomena in electroslag welding

Abstract: Through the statement of Maxwell's equations, the turbulent Navier-Stokes equations, and the convective heat balance equation, a mathematical model has been proposed for the Electroslag Welding Process. In the formulation, allowance has been made for both electromagnetic and buoyancy forces for driving the slag and the metal flow. The principal finding of the work is that convection in the molten slag region has a marked effect on the heat transfer process. For a rectangular geometry, using plate electrodes, the flow field is driven by buoyancy forces, the circulating flow is less intense, and the thermal efficiency of the process is improved. In contrast, for wire electrodes (approximated by a cylindrical geometry) the flow is driven by electromagnetic forces and a substantial part of the thermal energy is dissipated to the plates.

Transition of the axisymmetric starting plume cap

Abstract: The beginning of a continuous buoyancy (heat) injection into a stationary fluid results in a cap of buoyant fluid followed by a steady plume. This cap undergoes a transition in which a breakup is observed at a height from the source which increases with decreasing buoyancy injection rates. Sequences of cine film frames are presented illustrating this transition. A numerical criterion for the transition was found, namely, that the product of the power injected times the time at which transition occurs is a constant (19 cal). This can be related to an effective Rayleigh or Reynolds number, but the transition mechanism remains unknown. A critical effective Rayleigh number for the thermal may be estimated from these results to be 105 which in this case represents an injected heat of 10 cal.

Buoyancy control for ocean characteristic measurement system

Abstract: A system for measuring ocean characteristics. The system includes a sensor assembly and an associated means to control the system buoyancy to achieve cyclic ascent and descent at controlled speeds, either along a mooring line or free-drifting. Buoyancy control is provided by a pump assembly including two rolling diaphragm-sealed, low friction displacement pistons driven by a high torque d.c. motor operated at low speed. There are four functional groups of data gathering instrumentation. The first group measures horizontal water transport, and includes sensors for current (flow velocity), system azimuth, system tilt, and vertical velocity. The second group provides a determination of salinity, and includes sensors for conductivity, temperature and pressure. The third group monitors conditions within the system, and includes sensors for internal temperature and humidity. The fourth group monitors conditions utilized in the buoyancy control, and includes sensors for pressure (depth and depth rate) and piston position. A programmed microprocessor configuration provides overall operational control for the system.

Method for submerging an equipment of negative buoyancy

Abstract: The equipment is connected through a line to an auxiliary buoyant element to form an assembly of positive buoyancy, the equipment to be submerged and the auxiliary element being at first held in spaced relationship. The equipment is thereafter dropped into water, the length of the connecting line being so limited that the equipment then becomes suspended in water under the auxiliary element without reaching the water bottom. The location of the assembly is then optionally adjusted, and its buoyancy is reduced to a negative value.

Floating island for extracting or processing gas

Abstract: A floating island for the extraction of gas from the sea having a plurality of buoyancy units positioned on a base plate with columns extending upward therefrom, a height approximately the wave height expected. A platform containing gas liquefaction apparatus is positioned on the top of the columns. The buoyancy units are selected so that when the island is free floating, the columns project more than half way from the water.

Diffusion flame in free convection

Abstract: This US Bureau of Mines report on experimental and theoretical studies of diffusion flames in free convection (1) explores the cross-coupling between buoyancy-induced flows and the combustion process as it relates to the size, structure, and radiative balance of flames, (2) presents new data for the size-dependent radiance oscillations of diffusion flames and for the flame, and (3) compares both amplitude and freqency of the measured oscillations with the theoretical predictions that are based on a new view of the structure of diffusion flames. This new view is at variance with the traditional one, which assumes uniform reaction in the diffusive mixing zone. It recognizes the significance of the role played by convective buoyancy and its duality in both aiding and impeding flame propagation. Buoyancy quenches propagation at low burning velocities, introducing a real discontinuity in the combustion rate. A flammable volume is thus defined as that bound between lean- and rich-limit contours. However, in the flow disturbances generated by combustion waves that consume that volume, buoyancy aids propagation by promoting the convective mixing of a new flammable volume. The measured radiance oscillations are manifestations of these propagation and remixing cycles.

Characteristics of a front formed by cooling of the sea surface and inflow of the fresh water

Abstract: Two numerical studies (Endoh, 1977;Harashima et al., 1978) have been proposed on a front formed by a coupling effect of cooling of the sea surface and inflow of the fresh water in a vertical two-dimensional plane without the rotation of the earth. It is, however, not easy to interpret their numerical results. A simple interpretation will be proposed by an analytical study in this paper. It is found that local convection due to the density inversion, which is expressed by the convective adjustment of the vertical diffusion coefficient in the actual numerical calculations, plays an important role on the front formation. The characteristics of the front is also clarified in the case of steady state. Namely, simple functional dependences are obtained of the position and the width of the front, the horizontal and the vertical velocities and the distribution of the buoyancy and the salinity in the neighborhood of the front on the horizontal coordinate, the cooling rate, the eddy coefficients of diffusion and viscosity, the water depth and the vertically averaged horizontal fluxes of buoyancy and salinity.