Stratified Fluid Layer Research Articles

Natural convection heat transfer in an inclined rectangular enclosure with two stratified fluid layers. 2nd report. Experimental study of heat transfer in boundary layer type flow.

Natural convection heat transfer of fluids with two-layer stratification in an inclined rectangular enclosure was studied. The experiments were carried out for stratified fluids such as spindle oil-pure water for the Rayleigh numbers in the range of RawI (spindle oil)=8.1X106-3.5X107 and RawII (pure water)=3.8X107-1.6X108, and an aspect ratio H/W=2. The velocity and the temperature fields and the heat transfer coefficient were investigated at several inclination angles of the enclosure. It was clear for the inclined enclosure that the configuration of each fluid region, varying with the inclination angle, significantly effects the heat transfer coefficient.

Concentrated solutions for internal wave equations

We consider the propagation of internal gravity waves in a stratified fluid layer with a current. Formal asymptotic solutions concentrated in the horizontal plane are constructed for the linearized system of equations in the Boussinesq approximation. The complex space-time ray method is used.

Internal wave structure in a three-layer fluid with a stratified middle layer

The behavior of internal waves in a vertically bounded channel differs considerably from the wave motion in an infinite stratified fluid. In [1] the phase structure of the internal waves in an exponentially stratified layer of fluid between rigid horizontal planes was experimentally and theoretically investigated. A characteristic feature of such a channel is the boundedness of the phase and group velocities of each mode. Below, the case of an exponentially stratified channel between layers of homogeneous unbounded fluid is considered.

Convection coefficients for stably stratified layers

The physics of heat transfer across stably stratified fluid layers adjacent to horizontal surfaces are examined. Different assumptions are found to lead to widely varying values for the convection coefficient, and this raises some doubt about the applicability of the present recommended values for horizontal building surfaces.

Time-dependent thermal convection in a stably stratified fluid layer heated from below

Time-dependent thermal convection resulting when a stably stratified fluid layer is heated from below is analyzed as an initial-value problem of a linear model. The effect of stratification on its development and structure is investigated. The convection is found to develop in three stages. Initially the given disturbance induces oscillatory motion with the corresponding Brunt–Väisälä frequency. In the second stage the stratification works to form secondary cells above the primary cell. This multiple cell pattern, however, changes slowly but periodically with time. Finally, the convection grows with an exponential growth rate, retaining a similar cell pattern. The vertical scale of the primary cell decreases with the stratification level, while the horizontal scale remains constant. The onset time of the manifest convection is predicted to be delayed as the stratification shifts from neutral to stable conditions. Attaining a maximum, it then becomes slightly earlier. Experimental results supporting the model predictions are also presented.

Asymptotic behaviour of the solution of a problem in the theory of waves on the surface of a thin layer of stratified fluid

Asymptotic behaviour of the solution of a problem in the theory of waves on the surface of a thin layer of stratified fluid

N-Soliton Solution of the Higher Order Wave Equation for a Fluid of Finite Depth

Exact N -soliton solution of the higher order wave equation for a stratified fluid layer of finite depth is obtained by employing Hirota's bilinear transformation method. The solution reduces to the N -soliton solution of the higher order Korteweg-de Vries equation in the shallow water limit and to that of the higher order Benjamin-One equation in the deep water limit. The asymptotic form of the solution for large time is derived.

Baroclinic instabilities in Jupiter's zonal flow

The baroclinic stability of Jupiter's zonal flow is investigated using a model consisting of two continuously stratified fluid layers. The upper layer, containing a zonal shear flow and representing the Jovian cloudy regions above p ∼ 5 bars, is the same as Eady's (1949) model for the Earth. The lower layer has a relatively large but finite depth with a quiescent basic state, representing the deep Jovian fluid bulk below p ∼ 5 bars. Due to the presence of the lower layer, the linearized non-dimensional growth rates are drastically reduced from the O(1) growth rates of the original Early model. Only very long wavelengths relative to the upper fluid's radius of deformation L 1 are unstable. Eddy transports of heat are also reduced relative to estimates based on scaling arguments alone. Since the hydrostatic approximation for the lower-layer perturbation breaks down at great depths, a second model is presented in which energy propagates downward in an infinitely deep lower fluid obeying the full linearized fluid equations. In this model, the growth rates are again very small, but now all wavelengths are unstable with maximum growth rates occurring for wavelengths O(1) relative to L 1. These results illustrate the importance for the upper-layer meteorology of the interface boundary condition with the lower fluid, which is radically different from the rigid lower boundary of the Earth's troposphere.

Thermoconvective waves in a compressible fluid

The conditions for the propagation of one-dimensional thermoconvective waves are shown to contradict the stability criterion for a vertically unbounded fluid. This leads to the problem of two-dimensional wave propagation in a stratified fluid layer confined between horizontal walls. The eigenvalue-problem is solved by a two-parameter expansion that is singular with respect to one of the parameters. The results show that the horizontal walls do not prevent the existence of weakly damped thermoconvective waves provided that the Rayleigh-number is large. Finally the interaction of thermoconvective waves and sound waves is investigated, and the amplitudes of the various wave modes are determined.

Propagating Thermal Modes in a Fluid under Thermal Constraint

In a stably stratified fluid layer there is a transition beyond which an oscillatory behavior appears. Using forced-Rayleigh-scattering spectroscopy, we found experimental evidence for the existence of propagating modes in agreement with the theoretical predictions.

A theoretical and experimental study of thermal disturbances propagating in a fluid layer heated from below

A theoretical and experimental study is presented of the longitudinal propagation of disturbances in an unstably stratified fluid layer, especially those generated by periodic temperature fluctuations at a side boundary. The most important characteristics of the waves at both supercritical Rayleigh numbers, in the presence of steady roll-like cells, and subcritical Rayleigh numbers are determined.

Thermal instability of a viscosity stratified fluid layer heated from below

T HE stability of a fluid layer, under Boussinesq's approximation with viscosity n ( z ) heated from below between two parallel planes (at z = 0 and 1) is investigated under linear theory by the normal mode technique. The theoretical foundations for the correct interpretation of the problem of the onset of thermal instability in horizontal layers of fluid heated from below were laid by Rayleigh in a fundamental paper. He proved that the principle of the exchange of stabilities is valid for this problem for the case of two nondeformable free boundaries. The proof for the general case is due to Pellew and South well. 2 They also proved the existence of a variational principle. Many authors, after that, have discussed the stability of a fluid layer heated from below. All the authors have considered the viscosity to be constant. For the nonheatconducting, density, and viscosity stratified fluid, Chandrasekhar, 7 Hide, and Fan have made an analytical treatment of its stability. Banerjee and Kalthia 10 obtained some bounds for the growth rate of arbitrary small disturbances, and a sufficient condition for the stability. Chandra has modified their results, by relaxing the condition on the sign of D^. In this Note, the viscosity of the fluid is taken to be stratified in the vertical direction. It is proved that the transition from stability to instability must occur via the stationary state, and the solution of the characteristic value problem at the marginal state can be expressed in terms of variational principles. Critical Rayleigh number is obtained from the first-order solution to the eigenvalue problem. Consider a steady thermally stratified viscous fluid layer between two horizontal boundaries at z = 0 and d, which are maintained at constant temperatures T0 and Tj, respectively. Following the usual procedure of linearization of perturbation equations, assuming the functional dependence of the perturbed quantities on time and space coordinates of the form

Intrusions and double-diffusive convection

A STRATIFIED fluid layer in which two components contribute to the vertical density distribution need not be stable even though the net density decreases upwards. If one of the components is unstably distributed, then molecular diffusion can release its potential energy—a phenomenon known as double-diffusion convection1. Considerable progress has been made over the past 10 years in the study of double-diffusive convection in situations where the properties vary in one direction (vertically) only. In the ocean, horizontal advection is nearly always important and its neglect in the previous laboratory experiments makes it difficult to apply the results in a wider context. A first step in the study of two-dimensional effects in double-diffusive convection was made by Turner and Chen2, and here I follow up one of their suggestions in detail in the hope that it may help to understand the layering which occurs when an outflow intrudes into an ambient fluid with the same density but different component concentrations3.

Stability of plane-parallel convective fluid flow in a horizontal layer relative to spatial perturbations

The stability of stationary plane-parallel convective flow between horizontal planes along which a constant temperature gradient is given, is investigated relative to spatial perturbations. It is shown that the flow crisis is caused by spiral perturbations in a broad range of Prandtl number values (P > 0.24). Spiral perturbations are developed in unstably stratified fluid layers adjoining the upper and lower layer boundaries, and are of Rayleigh nature.

Lateral squeezing of horizontally stratified viscous layers

A fluid mechanics model for the slow deformations of layered geophysical materials is adopted. The problem consists of the slow viscous flow of two horizantally stratified fluid layers of different viscosities as being laterally squeezed between two frictionless planes. For solution a perturbation scheme is applied and the resulting approximation equations are solved numerically. The interface and free surface shapes, and the streamline patterns within the fluid layers are given.

On Cellular Cloud Patterns. Part 3: Applicability of the Mathematical and Laboratory Models

Abstract A nonlinear mathematical model of an unstably stratified layer of fluid with an imposed uniform vertical mass flux γ through porous boundaries has shown that, for Rayleigh number R near its critical value Rc for | γ | ≤ 1, and for Prandtl number Pr > 1.1, open cells are the only stable flow if γ 0; and roll convection is the only stable flow if γ = 0. Laboratory experiments have verified these results and have shown that their range of validity can be extended to | γ | ≈ 2, and R several times Rc. Here these results are applied to the region of sinking air behind cold fronts of mid-latitude cyclones over the oceans. The quasi-geostrophic omega equation is used to compute vertical velocities. An equivalent potential temperature gradient is determined from upper air soundings. Good agreement is found between regions of large-scale descending motion and occurrence of open cells, and between regions of large-scale ascending motion and occurrence of cl...

Intermittent convection: confirmation of a model for mass transfer into stratified fluid layers

A series of nonsteady mass transfer experiments has been performed with sulfur dioxide being absorbed into deep water layers. For this system the layer is subject to density-driven instabilities, and the rate of absorption is controlled by the resulting convective motion. The time course of the mass transfer rate was monitored from the initiation of absorption up to times approaching total saturation of the layer, a period several times greater than that corresponding to onset of first motion. These rate data were used to reveal features of the convective motion. The mass transfer results are shown to be consistent with an intermittent convection model based on the concept of a periodically erupting boundary layer, a model first proposed by Howard [14]. Interestingly, the predicted mass transfer behavior has features of conventional surface renewal theory, but with the additional facet that the renewal rate is directly relatable to the instability of the boundary layer. The combined effects of buoyancy and mechanically induced convection were explored in one series of experiments. In addition, we have resolved some inconsistencies which have appeared in recent publications concerning the stability criterion for the SO 2/water system.

Natural convection boundary layer flow over horizontal and slightly inclined surfaces

Laminar natural convection boundary-layer flow above horizontal and slightly inclined surfaces is considered. The effect of a small surface inclination on flow and transport is studied as a perturbation of flow over a horizontal surface. Solutions of the higher approximations have been numerically determined for the velocity, pressure and temperature fields for a Prandtl number of 0.7. These distributions are also given for the perfectly horizontal surface, for a wide range of Prandtl number. Both the surface conditions of uniform temperature and heat flux are considered. A Mach-Zehnder interferometer was used to study the nature of the laminar boundary-layer. The temperature distributions and heat transfer parameters were measured for the first time in such a flow, in air at atmospheric pressure. Present results may have a direct application to micro-meteorological and technological problems, and should clarify many aspects of natural convection flows which arise above horizontal and inclined planes through the initial impetus of unstably stratified fluid layers near the surface.

Thermal Instability of Nonhomogeneous Fluids

The present paper is an attempt to investigate theoretically the stability of a continuously stratified layer of an inviscid fluid, statically confined between two horizontal boundaries and heated or cooled uniformly underside. The basic stratification is assumed to be of the exponential type (ρ=ρ0ēδ1z, δ1=constant) depending only on the vertical coordinate (z) while the fluid extends indefinitely in the horizontal directions. The stability problem is shown to depend on a single nondimensional number N(z) and it is established that the configuration is stable or unstable according as N(z) is negative or positive everywhere in the flow domain respectively. The character of the basic stratification in the presence of a uniform temperature gradient is also discussed. Some other results include a circle theorem concerning the growth rate of an arbitrary oscillatory mode and the characterization of the neutral modes and the marginal state.