Showing papers on "Buoyancy published in 1975"

Entrainment by a plume or jet at a density interface

Abstract: The rate of entrainment through the end of a plume or jet which impinges on a density interface has been determined in the laboratory, where the interface was produced by layers of fresh and salt water and the plume by a salt-water source. Observations of the impingement area indicated that entrainment was confined to a region about the size of the plume cross-section. It was thus concluded that the entrainment flux into the plume must be a function of the local width, velocity and buoyancy difference, and these can be combined into a single para- meter, the Froude number. Measurements of the volume flux showed it to be proportional to the cube of the Froude number. The flux of buoyancy from the salt-to fresh-water volumes is consequently proportional to the Froude number. In the second part of the study the density distribution in the initially fresh layer was derived and is verified by the experiments. This distribution has direct applications in the analysis of convective motions in the atmosphere and the ocean.

A study of the entrainment and turbulence in a plane bouyant jet

Abstract: The entrainment and mixing processes in a two-dimensional vertical turbulent buoyant (heated) jet in its transition state from a pure jet to a pure plume have been studied. The ambient fluid is of uniform density and non-flowing except for the flow induced by the jet. Density variations are assumed small. The equations of motion integrated across the jet have been carefully examined and it has been found that the kinematic buoyancy flux of a heated plume and the kinematic momentum flux of a pure jet are not in general conserved. It has been proven that the flow in a two-dimensional pure jet is not self-preserving. A systematic set of experiments was carried out to examine turbulent buoyant jet behavior for a wide range of initial Richardson numbers (or densimetric Froude numbers). Values of the Richardson number, which describes the relative importance of buoyancy in a jet, extended from the value appropriate for a pure jet (zero) to that appropriate for a plume (approximately 0.6). The buoyant jet temperature and velocity fields were measured using calibrated fast response thermistors and a laser Doppler velocimeter respectively. The velocity and temperature data obtained were recorded magnetically in digital form and subsequently processed to extract both mean and fluctuating values of temperature and velocity. The structure of the mean flow (including the spreading rate of the mean velocity and temperature profiles, velocity and temperature distribution along jet axis, and the heat flux profile), the turbulence structure (including the profile of turbulence intensity and turbulent heat transfer, probability density distribution of temperature and velocity, skewness and flatness factor of temperature fluctuations) and the large scale motions (intermittency, profile of maximum and minimum temperature, frequency of crossing of hot/cold, cold/hot interface) of a buoyant jet were investigated as a function of the jet Richardson number. It was determined that the turbulent heat transfer and the turbulent intensity increase with increasing the Richardson number. The spreading rate of the transverse mean velocity and temperature profiles were found to be independent of the Richardson number. The turbulent buoyancy flux in a fully developed buoyant jet has been found to be a significant fraction (38%) of the axial buoyancy flux.

The onset of transient convective instability

Abstract: The stability of a horizontal fluid layer when the thermal (or concentration) gradient is not uniform is examined by means of linear stability analysis. Both buoyancy and surface-tension effects are considered, and the analogous problem for a porous medium is also treated. Attention is focused on the situation where the critical Rayleigh number (or Marangoni number) is less than that for a linear thermal gradient, and the convection is not (in general) maintained. The case of constant-flux boundary conditions is examined because then a simple application of the Galerkin method gives useful results and general basic temperature profiles are readily treated. Numerical results are obtained for special cases, and some general conclusions about the destabilizing effects, with respect to disturbances of infinitely long wavelength, of various basic temperature profiles are presented. If the basic temperature gradient (considered positive, for a fluid which expands on heating, if the temperature decreases upwards) is nowhere negative, then the profile which leads to the smallest critical Rayleigh (or Marangoni) number is one in which the temperature changes stepwise (at the level at which the velocity, if motion were to occur, would be vertical) but is otherwise uniform. If, as well as being non-negative, the temperature gradient is a monotonic function of the depth, then the most unstable temperature profile is one for which the temperature gradient is a step function of the depth.

Bouyancy Effects on Forced Convection Along a Vertical Cylinder

Abstract: The effects of buoyancy forces on the longitudinal forced convective flow and heat transfer along an isothermal vertical cylinder are studied analytically. This problem does not admit similarity solutions, the nonsimilarity arising both from the transverse curvature ξ = (4/r0 ) (νx/u∞)1/2 of the cylindrical surface and from the buoyancy effect expressible as Ω = Grx /Rex2 where Grx and Rex are, respectively, the Grashof and Reynolds numbers. The governing equations are solved by the local nonsimilarity method in which all the nonsimilar terms are retained in the conservation equations and only in the derived subsidiary equations are terms selectively neglected according to the two-equation or three-equation model. Numerical results for the velocity and temperature profiles, wall shear stress, and surface heat transfer for the case of assisting flow are presented for gases having a Prandtl number of 0.7 over a wide range of values of ξ from 0 (i.e., a flat plate) to 4.0 and Ω from 0 (i.e., pure forced convection) to 2.0. It is found that the wall shear and surface heat transfer rate increase with increasing buoyancy force and increasing curvature of the surface.

Turbulent entrainment across stable density step structures

Abstract: This paper is a summary of a research on the properties of the turbulent entrainment across stable density-stratified layers, a phenomenon commonly observed in geophysical fluid dynamics. A turbulent environment is created by oscillating grids in quasi-homogeneous layers of slightly different density separated by thin sheets of fluid containing a strong density gradient. The buoyancy flux across thin stable layers is found to be a function of the Richardson and Prandtl numbers. Theoretical and experimental studies are made, leading to a determination of the order of magnitude of the four terms expressing the balance of energy in physical space. It is shown that the turbulent energy flux is of the same order of magnitude as the viscous dissipation of kinetic energy in the quasi-homogeneous layers where the slight density gradient is not altogether negligible because a small but measurable fraction of the turbulent energy flux goes into maintaining the buoyancy flux. Data taken in the stable layer show the simultaneous existence of large internal waves and patchy turbulence. Some properties of these waves as functions of the Richardson number are determined. DOI: 10.1111/j.2153-3490.1975.tb01677.x

Pressure- and buoyancy-driven thermal convection in a rectangular enclosure

Abstract: Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Semi-submersible vessels

Abstract: An apparatus for damping vertical movement of a semi-submersible vessel having a small waterplane area, whose buoyancy is provided substantially completely by submerged pontoon means and which includes at least one submerged damper plate having valves or similar flow controllers therein for providing substantially greater resistance to upward movement of the plate than downward movement. The damper plate is supported deep beneath the semi-submersible vessel by flexible, tensioned support elements such as chains or cables, at a depth beneath the water surface in the semi-submerged condition of the vessel, at which depth the amplitude of subsurface wave motion is less than the maximum heave amplitude which would be experienced by the semi-submersible vessel alone under identical sea conditions. The area of the damper plate is several times larger than the waterplane area of the vessel. An upward only-damping action is achieved due to the entrainment of large apparent masses of relatively still water by the damper plate.

A note on helicity

Abstract: Theoretical work on the generation of magnetic fields by fluid motions, by the so-called “hydromagnetic dynamo” process, has called attention to the importance of the role of helicity H (defined as the scalar product of the velocity and vorticity vectors), implying that the discovery of general relationships between the helicity and other properties of the fluid should facilitate the future study of specific dynamo models. It is shown in the present note that H in a rapidly-rotating Roussinesq fluid satisfies where t denotes time, u is the Eulerian flow velocity relative to a frame which rotates with angular velocity ω, [pbar] + p′ is the density of the fluid and [pbar] the mean density, and g is the acceleration due to gravitational and centrifugal effects. The first term is proportional to the speed of vertical motion and is not in general zero when the kinetic energy of the fluid is produced by buoyancy forces; the second is proportional to the adjective term in the equation of heat transfer, ...

X-ray bright spots on the sun and the nonequilibrium of a twisted flux rope in a stratified atmosphere

Abstract: The calculations are concerned with the hydrostatic equilibrium of a magnetic flux tube whose two ends are anchored at some level in a stratified atmosphere. It is shown that no hydrostatic equilibrium exists if the whole flux tube is twisted more than a modest amount, equivalent to a 45degree pitch over only one scale height. When the total twisting exceeds this small amount, the tube is subject to negative tension (compression) and buckles, spirals, and/or lengthens into a contorted form which causes rapid dissipation and reconnection of the magnetic field. The rapid dissipation continues until the excess azimuthal field is consumed and equilibrium is again possible. It is suggested that the magnetic flux tubes in the Sun generally have more than the allowed twisting, so that, when they rise up through the surface, as a consequence of their buoyancy, they are subject to rapid dissipation, causing the phenomenon observed as the X-ray bright spot. (AIP)

Turbulent Sediment Transport Over a Flat Bottom Using Momentum Balance

Abstract: The turbulent flow of a sediment-fluid mixture over a flat bottom is studied using momentum balance. The in-the-small forces included are gravity, buoyancy, and a linear drag. A turbulent average is applied and mixing length theory is used for the resulting Reynolds stresses. Assuming small concentrations and small still water settling velocity, the resulting velocity profile is logarithmic; the sediment concentration profile is relatively constant near the bottom, and drops off rapidly above a certain level predicted by the theory. Numerical and asymptotic results are discussed.

The Energy Budget in a Clear Air Turbulence Zone as Observed by Aircraft

Abstract: High sample rate aircraft data in a zone of moderate turbulence are analyzed to determine a turbulent energy budget. Combination of the Reynolds stress, buoyancy, and frictional dissipation terms produces a good balance. A further look at the Reynolds stress component shows the relation of the turbulent zone growth and decay with the synoptic situation. The need is demonstrated for including turbulent mixing processes in modeling fronts.

Circulations and density distributions in a deep, strongly stratified, two-layer estuary

Abstract: The paper discusses a theoretical model of statistically steady flow in a strongly stratified estuary. A halocline is assumed to be present and the lower layer is taken to be deep and non-turbulent. The outflowing upper fluid mixes with the salty lower fluid and the flux of the brackish water increases with distance from the head of the estuary. The mixing is assumed to be similar to that in laboratory models of mixing across density interfaces.Two equations of mass conservation are used, one for the steady-state mass flux across a vertical section from top to bottom of the channel and one for the mass flux into a section of the upper fluid. A buoyancy conservation equation is used for the buoyancy flux across a vertical section. A final equation is obtained by integrating the horizontal equation of motion across a section of the upper fluid. The flow in this layer is assumed to be opposed by a frictional force proportional to the square of the velocity averaged over the layer. The pressure-gradient force arising from the slope of the free surface is solved for in terms of the thickness of the upper layer, the buoyancy difference across the interface, the slope of the interface and the horizontal density gradient in the upper layer. The derivation shows that the horizontal pressure-gradient force vanishes in the lower layer.The mathematical problem reduces to two ordinary differential equations for the flux in the upper layer and its thickness. Attention is confined to the solution for subcritical flow, in which the interface falls with distance from the head, reaching a maximum depth at a certain section of the estuary. Beyond this the interface rises. At the mouth, where, by definition, the width of the estuary increases rapidly, it is shown that there must be a transition from subcritical to supercritical flow. This condition, applied to the solution for uniform width, determines a remaining unknown related to the depth of the halocline at the head of the estuary and the complete solution is obtained as a function of the freshwater influx per unit width, the r.m.s. turbulent velocity, the estuary length and the buoyancy of sea water.The solution is complicated but has reasonable behaviour for variations of the given parameters of the problem. A basic feature for values of the constants appropriate to fjord-type estuaries is the dominance of friction, omitted in an earlier, incomplete investigation by Stommel. This is also revealed by the large drop in the free surface over the length of the estuary.A comparison with two estuaries, Oslofjord and Knight Inlet, British Columbia, indicates that the former is very different from the model of this paper but that the latter may have a similar nature.

The influence of shear on mixing across density interfaces

Abstract: This paper discusses critically observations of mixing processes across density interfaces in laboratory experiments and inferences that have been made and can be made from these observations. Fluxes of heat or salt and entrainment velocities have been found to depend on negative powers of an overall Richardson number Ri* based on the buoyancy jump across the interface, the depth of the homogeneous layer and the intensity of the turbulence near the source. When the Reynolds and Peclet numbers are large, the fluxes or entrainment velocities appear to be proportional to the minus one and minus three-halves powers of Ri* for flows with and without mean shear respectively, and this difference has caused speculation about the accuracy of the experimental data and about the reasons for the two laws if the difference is real. In the present discussion, we accept the accuracy of the two laws and attribute the higher entrainment rate for shear flows to the decrease of r.m.s. velocities near the interface with increasing Ri* in the case of zero shear. A plausible argument yields the unifying result that the entrainment rates in both cases are proportional to Ri−1, where Ri is a Richardson number based on the buoyancy jump and velocities and lengths characteristic of the turbulence near the interface. It is suggested that the behaviour inferred by Turner is based on an erroneous interpretation of experimental data.In the course of the discussion, it is shown that the drag coefficient in flow of a stratified fluid over a rough surface is independent of the Richardson number (or density jump across the interface or inversion) and depends only on the ratio of the roughness length to the depth of the homogeneous layer. This has obvious implications for problems of parameterizing the momentum flux near the ground in the atmosphere.

Controlled buoyancy underwater riser system

Abstract: An underwater riser system in which the primary riser is surrounded by lengths of jacket pipe which form annular buoyancy chambers, there being a pressure fluid supply connected to the buoyancy chambers via valve means including at least a pressure differential valve which controls the amount of water displaced from the chamber by the pressure fluid. Advantageously, the valve means for each chamber also includes remotely controlled means by which the amount of buoyancy provided by the chamber can be varied at will, e.g., from a positive buoyancy to a buoyancy less than the operating weight of the portion of the riser system with which that chamber is associated. In best embodiments, the lengths of jacket pipe are interconnected into a continuous structural unit by connectors each having a female connector member secured to the upper end of the lower length of jacket pipe and a male member secured to the lower end of the upper length of jacket pipe, the female member having an annular bulkhead which closes the space between the jacket and primary riser pipe and on which the valve means is mounted.

Fire spread over liquid fuels: Liquid phase parameters

Abstract: Fire spread over liquid fuels at sub-flash temperatures is known to be controlled mainly by flows induced in the liquid. The liquid flows are driven by surface tension and buoyancy forces, and depend upon Prandtl number, fuel depth and flame speed. The effect of these parameters has been obtained from numerical solutions of the equations governing the liquid phase and results are reported and summarized in the present paper. The induced surface velocities are found to depend principally upon surface tension and layer depth, and therefore emerge as a property of a liquid fuel layer. The surface velocity is hypothesized as rate-determining, and is found to be in good agreement with experimental flame spread rates for hydrocarbon and alcohol fuels reported by Glassman, Akita, and others.

Some experiments on the motion of an isolated laminar thermal

Abstract: A novel technique for injecting buoyancy (heat) into a liquid is described and demonstrated. When buoyancy was injected for a short time a laminar vortex ring formed. Its vertical displacement was found to be only approximately proportional to the square root of time (measured from an apparent initial time). Approximate geometrical similarity was also observed although the Reynolds number decreased from 28 to about 14.

Solar energy system utilizing buoyancy as a conversion force

Abstract: A closed cycle energy conversion system adaptable for use with, inter alia, solar collectors and other sources of available heat for increasing the temperature of a circulating fluid to a super heated condition and employing a substantially vertically positioned gas expander column comprising an endless arrangement of cups journaled for movement in a closed path within a liquid medium in the column for trapping the super heated fluid when flashed into a gas inside a succession of the cups inverted at the bottom of the column and displacing at least a part of the liquid in the cups, thereby providing a buoyancy force on the cups causing them to rise in the column exerting a rotating force on the endless arrangement of cups. The trapped gas is released at the top of the liquid in the column to be condensed, pressurized and recirculated to solar collectors and/or other sources of heat for reuse in the system.

An asymptotic solution for slightly buoyant laminar plumes

Abstract: When the buoyancy forces are small compared with the inertia forces, heated plumes in laminar flows which are uniform at upstream infinity approximately satisfy a linearized version of the Boussinesq equations, here called the Oseen–Boussinesq equations. An analytic solution is constructed for arbitrary Prandtl number and arbitrary direction of the unperturbed flow in the case of a plume produced by a point source. The two-dimensional case of the plume from a line source is considered briefly. A Stokes-type paradox occurs: it is found that a line-source solution that vanishes at infinity does not exist.

Buoyancy control apparatus for divers

Abstract: A buoyancy control system for carrying by a diver has a fluid-tight reservoir comprised of a plurality of parallel longitudinally extending passageways, into which water and compressed gas can be selectively admitted through respective inlet valves to displace gas and water respectively in the reservoir through respective outlet valves. The relative amounts of water and gas in the reservoir can therefore be adjusted to provide a required degree of buoyancy for the diver.

Development of the region of a turbulized liquid in a stratified medium

Abstract: The article discusses the plane unsteady-state problem of the development of a region of turbulent pulsations in an incompressible stratified liquid. At the initial moment of time, the energy of the turbulence is given inside a region of finite dimensions. A semiempirical system of equations describing this process is proposed. The article gives the data from numerical calculations, illustrating the original expansion of the region as a result of turbulent diffusion, its subsequent compression along a vertical (“collapse”) under the action of the forces of buoyancy, and the internal waves generated by the collapse.

Hydromagnetic edge waves in a rotating stratified fluid

Abstract: The properties of edge waves confined by the interaction of buoyancy and Coriolis forces to the vicinity of a rigid plane boundary in a rotating, stratified, electrically conducting fluid pervaded by a magnetic field are established in some simple cases. The background shear is taken to be zero, the basic Alfven velocity V and Brunt–Vaisala frequency N are assumed uniform, and all dissipative effects are taken to be vanishingly small. It is shown that waves trapped against the bounding wall can occur only if V is parallel to the wall. When the basic rotation vector Ω is also parallel to the wall, the hydromagnetic edge waves have a higher frequency and smaller spatial extent perpendicular to the wall than their non-hydromagnetic counterparts, but more complex behaviour is found when Ω possesses a component normal to the wall. There are conditions under which edge waves may exist even when the basic density stratification is top-heavy (i.e. when N 2

Methods and apparatus for applying buoyant forces to offshore tower legs and providing and enclosing buoyancy chambers

Abstract: Improvements in buoyancy structures independently comprising each of A radiating, circumferentially extending buoyancy cell network encircling an offshore jacket leg, and A double-walled buoyancy chamber wall fabricated from a shell and overlapping pipe segments bonded thereto. An offshore platform jacket assembly is disclosed in which a plurality of jacket legs are anchored by piling members to the bed of a body of water. A buoyancy unit is disposed at a lower portion of the jacket in association with at least one of the jacket legs. Each buoyancy unit comprises a chamber disposed around its respective leg. Each chamber is divided into a plurality of circumferentially displaced, radiating cells and these cells are disposed inwardly of a periphery defined by a series of piling guides spaced around the leg. A plurality of generally upright divider fins extend radially outwardly from the leg to divide the chamber into the radiating cells which are arranged about the leg for the reception of a buoyant medium. The fins are operably connected to the piling guides to transmit forces in a generally uniform manner between the leg and the piling guides. In one preferred embodiment, the buoyancy cells are of less than water-tight construction and are filled with a buoyancy-generating foam. In another preferred embodiment of the invention, the buoyancy cells are of water-tight construction and are reinforced by a double-wall construction which includes overlapping pipe segments, welded to the interior periphery of a chamber-defining shell situated around the tower leg. A double-walled buoyancy chamber including a shell wall and an edge overlapping network of pipe segments bonded thereto.

Submerged Buoyant Jets in Quiscent Fluids

Abstract: An integral-type analysis is developed for submerged buoyant jets discharged horizontally into quiescent homogeneous fluids. Equations for conservation of volume flux, buoyancy flux, and kinematic conditions are combined with three self-similarity assumptions and one entrainment assumption. The entrainment velocity is assumed to consist of two components: one is related to the initial jet momentum, the second to the buoyancy force, so that the constant entrainment coefficients obtained from studies of pure jets and pure plumes can be utilized. A closed-form solution is obtained which yields polynomials describing the trajectories of both round and slot jets and linear and parabolic relations for the dilution for round and slot jets, respectively. These relations compare favorably with experimental and numerical results reported by other investigators.

Method and apparatus for moving an object on the bottom of a body of water

Abstract: A method for moving an object on the bottom of a body of water comprising producing a positive buoyancy in the region of one of the supports of the object to lift the support from the bottom of the body of water and then turning the object in the desired direction around another of the supports which remains at rest on the bottom of the body of water. Upon completion of the turning movement of the object, the raised support is lowered by producing a negative buoyancy in the region of such support. The positive and negative buoyancy is produced by means of gas and water pumped into containers mounted in the region of the supports.

A developing boundary layer over an evaporating surface

Abstract: The problem of air flow over a sudden change in surface temperature and humidity has been solved using mixing-length theory The method is similar to that used by P A Taylor (1970) with some modifications The form of the mixing length suggested by Blackadar is used and this allows calculation farther downwind A vapor diffusion equation is included in the set of conservation equations and a vapor buoyancy term is included in the stability length The vapor buoyancy is found to enhance significantly the turbulent diffusion but to a lesser degree than does the thermal buoyancy