bluuebunny/crossref_metadata_2025_split huggingface dataset:
Two-dimensional effects in double-diffusive convection
Authors: Turner J. S. , Chen C. F. 
Published: March 2006

The limitations of existing one-dimensional experiments on double-diffusive convection are discussed, and a variety of new two-dimensional phenomena are described. We have used the sugar-salt system and shadowgraph photography to make exploratory studies of motions which can arise in a fluid with two smooth, opposing, vertical concentration gradients, with and without horizontal gradients. Many different effects have been observed, the most important of which are the following, (a) In the ‘finger’ case, local disturbances can propagate rapidly as wave motions, which cause a simultaneous breakdown to convection over large horizontal distances. (b) Layers formed in the’ diffusive’ sense overturn locally to produce fingers, but propagate more slowly, as convective rather than wave motions, (c) A series of layers, separated by diffusive interfaces, can become unstable, in the sense that successive layers merge in time as their densities become equal, (d) The presence of horizontally separated sources of water of similar density but differentT,Scharacteristics can lead to the development of strong vertical gradients and extensive quasi-horizontal layering.Most of our results are qualitative, but it is hoped that they will stimulate further quantitive work on each of the new processes described. It is already clear that much more needs to be done before the mechanism of formation of layers observed in the ocean can be regarded as properly understood.
Hydromechanics of low-Reynolds-number flow. Part 1. Rotation of axisymmetric prolate bodies
Authors: Chwang Allen T. , Wu T. Yao-Tsu 
Published: March 2006

The present series of studies is concerned with low-Reynolds-number flow in general; the main objective is to develop an effective method of solution for arbitrary body shapes. In this first part, consideration is given to the viscous flow generated by pure rotation of an axisymmetric body having an arbitrary prolate form, the inertia forces being assumed to have a negligible effect on the flow. The method of solution explored here is based on a spatial distribution of singular torques, called rotlehs, by which the rotational motion of a given body can be represented.Exact solutions are determined in closed form for a number of body shapes, including the dumbbell profile, elongated rods and some prolate forms. In the special case of prolate spheroids, the present exact solution agrees with that of Jeffery (1922), this being one of very few cases where previous exact solutions are available for comparison. The velocity field and the total torque are derived, and their salient features discussed for several representative and limiting cases. The moment coefficient CM = M/(8πμω0ab2) (M being the torque of an axisymmetric body of length 2a and maximum radius b rotating at angular velocity ω0 about its axis in a fluid of viscosity μ) of various body shapes so far investigated is found to lie between $\frac{2}{3}$ and 1, usually very near unity for not extremely slender bodies.For slender bodies, an asymptotic relationship is found between the nose curvature and the rotlet strength near the end of its axial distribution. It is also found that the theory, when applied to slender bodies, remains valid at higher Reynolds numbers than was originally intended, so long as they are small compared with the (large) aspect ratio of the body, before the inertia effects become significant.
Finite-amplitude thermal convection in a spherical shell
Authors: Young Richard E. 
Published: March 2006

The properties of finite-amplitude thermal convection for a Boussinesq fluid contained in a spherical shell are investigated. All nonlinear terms are retained in the equations, and both axisymmetric and non-axisymmetric solutions are studied. The velocity is expanded in terms of poloidal and toroidal vectors. Spherical surface harmonics resolve the horizontal structure of the flow, but finite differences are used in the vertical. With a few modifications, the transform method developed by Orszag (1970) is used to calculate the nonlinear terms, while Green's function techniques are applied to the poloidal equation and diffusion terms.Axisymmetric solutions become unstable to non-axisymmetric perturbations at values of the Rayleigh number that depend on Prandtl number and shell thickness. However, even when stable, axisymmetric solutions are not a preferred solution to the full equations; steady non-axisymmetric solutions are obtained for the same parameter values. Initial conditions determine the characteristics of the finite-amplitude solutions, including, in the cases of non-axisymmetry, whether or not a steady state is achieved. Transitions in horizontal flow structure can occur, accompanied by a transition in functional dependence of heat flux on Rayleigh number. The dominant modes in the solutions are usually the modes most unstable to the onset of convection, but not always.
The inviscid nonlinear instability of parallel shear flows
Authors: Robinson J. L. 
Published: March 2006

In this paper we assume the existence of a nonlinear boundary layer centred on the critical point, and explore its effect on the development of unstable parallel shear flows. A velocity matching condition derived in a qualitative discussion suggests a growth of harmonics which differs from that predicted by previous theories; however, the prediction is in excellent agreement with experimental data. A hyperbolic-tangent velocity profile, subjected to perturbations with wavenumbers and frequencies close to marginal values, is then chosen as a mathematical model of the nonlinear development, both temporal and spatial instability growth being considered.A singularity in the analysis which has been treated in previous theories by the introduction of viscosity is dealt with in the present work by the introduction of a growth boundary layer. The asymptotics are non-uniform and the time-dependent solution does not resemble the steady viscous solutions, even as the growth rate tends to zero. The theory suggests that the instability will develop as a series of temporally growing spiral vortices, a description differing from that of a cat's-eye pattern predicted by existing theories, but in accord with experimental and field observations.
Kelvin wave propagation along an irregular coastline
Authors: Mysak L. A. , Tang C. L. 
Published: March 2006

We discuss the theory of Kelvin wave propagation along an infinitely long coast-line which is straight except for small deviations which are treated as a stationary random function of distance along the coast. An operator expansion technique is used to derive the dispersion relation for the coherent Kelvin wave field. For the subinertial case σ = ω/f < 1 (ω = wave frequency, f = Coriolis parameter), it is shown that the wave speed is always decreased by the coastal irregularities. Moreover, while the coherent wave amplitude is unaltered, the energy flux along the coast is decreased by the irregularities. For the case σ > 1, however, we show that in the direction of propagation the wave is attenuated (with the energy being scattered into the random Poincaré and Kelvin wave modes) and that the wave speed is again decreased. Applications of the theory are made to the California coast and North Siberian coast to determine the decrease in phase velocity due to small coastal irregularities. For the California coast the percentage decrease is only about 1%. For the Siberian coast, however, the percentage decrease is about 25% for the K1 tide, and a minimum of 25% for the M2 tide. The attenuation of a Kelvin wave, however, appears to be due to very large scale irregularities. An estimate of the actual attenuation rate is not possible, though, because of the relatively short extent of coastal contours available for spectral analysis.Although attention in this paper has been focused on Kelvin wave propagation, the method developed could readily be used to study the behaviour of other classes of waves trapped against a randomly perturbed boundary.
Investigation of turbulent convection under a rotational constraint
Authors: Chan Shu-Kwan 
Published: March 2006

Turbulent convection for a rotating layer of fluid heated from below is studied in this paper. The boundaries of the fluid layer are taken to be free. The underlying principle, used is the Malkus hypothesis that the flow tends to transport the maximum amount of heat possible, subject to certain constraints. By taking the Prandtl number to be infinite, a linear differential constraint and an integral constraint are used. The variational problem that follows then depends on two dimensionless parameters, the Taylor number T and the Rayleigh number R.Asymptotic analysis for the turbulent regime shows that the flow arranges itself so as to tend to offset the stabilizing effect of the rotational constraint, at least in so far as the heat flux is concerned. The dimensionless heat flux, or the Nusselt number, has in general different dependence on T and R, depending on the particular region in the parameter space. For T [les ] O(R), the flow is essentially non-rotating. For O(R) [les ]T [les ] O(R4/3), the flow will always have finitely many horizontal wavenumbers, though the total number of modes increases as T increases in this region. For O(R4/3) [les ] T [les ] O (R3/2), the Nusselt number has a functional dependence proportional to R3/T2, having essentially infinitely many horizontal modes as both R and T increase indefinitely in this region. The last expression is particularly interesting, as it agrees qualitatively with results in finite-amplitude laminar convection. It is also linearly dependent on the layer thickness, as one might expect from dimensional argument. It is suggested that, in the context of the maximum principle, the result in this region of the parameter space may be applicable as well to the same fluid layer with rigid boundaries through the existence of an Ekman layer that is thinner than the thermal layer.
The stability of unsteady cylinder flows
Authors: Hall P. 
Published: March 2006

First, the linear stability of the flow between two concentric cylinders when the outer one is a t rest and the inner has angular velocity Ω{1+ εcosωt} is considered. In the limit in which ε and ω tend to zero it is found that the critical Taylor number a t which instability first occurs is decreased by an amount of order ε2from its unmodulated value, the stabilizing effect a t order ε2ω2being slight. The limit in which ω tends to infinity with ε arbitrary is then studied. In this case it is found that the critical Taylor number is decreased by an amount of order ε2ω−3from its unmodulated value.Second, the effect of taking nonlinear terms into account is investigated. It is found that equilibrium perturbations of small but finite amplitude can exist under slightly supercritical conditions in both the high and low frequency limits. Some comparisons with experimental results are made, but these indicate that further theoretical work is needed for a broad band of values of ω. In appendix B it is shown how this can be done by an alternative formulation of the problem.
Stability characteristics of a single-phase free convection loop
Authors: Creveling H. F. , De Paz J. F. , Baladi J. Y. , Schoenhals R. J. 
Published: March 2006

Stability characteristics of a single-phase free convection loop are presented. In the experiments, water was placed inside a toroidal glass loop oriented in a vertical plane. The lower half of the loop was heated and the upper half was cooled. At low heat-transfer rates and also a t high heat-transfer rates the free convection flow was observed to be steady. For the intermediate range, however, the flow was found to be highly oscillatory. Stability predictions are also developed. The comparison between theory and experiment yields favourable agreement.Observations of unstable behaviour have been reported previously for single-phase fluids in the vicinity of the thermodynamic critical point. In these situations it has been assumed that the unusual behaviour of the fluid properties in the near-critical region necessarily constitutes the underlying cause of such instabilities. In contrast t o this view, analyses by Keller (1966) and Welander (1967) indicate that instabilities can occur for ordinary fluids as well. Results of the present study confirm this contention, since instabilities were clearly observed for water at atmospheric pressure and moderate temperatures.
The nonlinear calculation of Taylor-vortex flow between eccentric rotating cylinders
Authors: Diprima R. C. , Stuart J. T. 
Published: March 2006

This paper is concerned with the nonlinear stability of the flow between two long eccentric rotating cylinders. The problem, which is of interest in lubrication technology, is an extension both of the authors’ earlier work on the linear eccentric case and of still earlier work by Davey and others on the nonlinear concentric analysis of Taylor-vortex development. There are four parameters which are assumed small in the analysis; they are the mean clearance ratio, the eccentricity, the amount by which the Taylor number exceeds its critical value; and the Taylor-vortex amplitude. Following the earlier work mentioned above, relation-ships are specified between these parameters in order to develop a satisfactory perturbation scheme. Thus a non-local solution is obtained to the nonlinear stability problem, in which the whole flow field is taken into account.Of some importance in the analysis is the fact that it is necessary to allow for the development of a pressure field substantially bigger than that associated with Taylor vortices in the concentric case, owing to the Reynolds lubrication effect in a viscous fluid moving through a converging passage. I n order to achieve this mathematically, it is necessary to solve the continuity equation to a higher order than is necessary for the momentum equations.It is found that the angular position for maximum vortex activity, which is 90° downstream of the maximum gap in the linear case, can taken on any value between 0 and 90°, depending on the value of the supercritical Taylor number. For a particular experiment of Vohr (1968) acceptable agreement is obtained for this angle (50°), though the ‘small’ parameters are somewhat outside the expected range of perturbation theory. Formulae are obtained for the torque and forces acting on the inner cylinder.
Starting vortex, separation bubbles and stall: a numerical study of laminar unsteady flow around an airfoil
Authors: Mehta Unmeel B. , Lavan Zalman 
Published: March 2006

The stalling characteristics of an airfoil in laminar viscous incompressible fluid are investigated. The governing equations in terms of the vorticity and stream function are solved using an implicit finite-difference scheme and point successive relaxation procedure. The development of the impulsively started flow, the initial generation of circulation, and the behaviour of the forces at large times are studied.Following the impulsive start, the lift is at first very large and then it rapidly drops. The subsequent growth of circulation and lift is associated with the starting vortex. After incipient separation, the lift increases owing to enlargement of the separation bubble and intensification of the flow rotation in it. The extension of this bubble beyond the trailing edge causes it to rupture and brings about the stalling characteristics of the airfoil. Subsequently, new bubbles are formed near the upper surface of the airfoil and are swept away. The behaviour of the lift acting on the airfoil is explained in terms of the strength and sense of these bubbles. The lift increases when attached clockwise bubbles grow and when counterclockwise bubbles are swept away and vice versa.
Finite amplitude analysis of a flow-structure interaction problem
Authors: Hilaire A. O. St , Vaidya P. G. 
Published: March 2006

The interaction between a vibrating structure and an unsteady potential flow-field disturbance induced by the motion of the structure itself is investigated, and is shown to be a significant source of both nonlinear excitation and nonlinear dissipation. An approximate analysis, based on small nonlinear disturbance theory, is presented of the forces that influence the characteristic behaviour of self-excited harmonium reeds vibrating at finite amplitudes. It is demonstrated that the ideas brought forth by this example can be generalized to apply to other flow-induced vibrating systems, regardless of the excitation mechanism, provided that certain basic assumptions about the flow can be made. For the case of the harmonium reed, it is shown that, taken by itself, an account of the feedback forces arising from induced higher-order unsteady disturbances in the surrounding potential flow field is sufficient for predicting the net nonlinear dissipative force that eventually causes the reed to reach and maintain a finite limiting amplitude. In particular, it is demonstrated that the nonlinear energy drain from the motion of the reed is a consequence of the net effect of the higher-harmonic disturbances that are generated near the structure.A result of the analysis is the development of a functional dependence of the interactive forces on the system geometry and the flow velocity. One of the advantages of obtaining a functional expression is the ability to carry out parametric studies in the context of vibration and noise control.
Some remarks on the initiation of inertial Taylor columns
Authors: Huppert Herbert E. 
Published: March 2006

The quasi-geostrophic flow over an obstacle placed on the lower of two horizontal planes in rapid rotation about the vertical z axis is considered. The flow field is calculated in the limit of vanishing viscosity after assuming the flow far upstream of the obstacle to be uniform, of magnitude V. The effects that occur in homogeneous flow are compared with those that occur in stratified flow.If the flow is homogeneous, there is a region of closed streamlines if
\[
h_0R^{-1} > \min_r\left[r\left/\int_0^r xh(x)dx\right. \right],
\]
where the obstacle is assumed to be cylindrically symmetric and given by z = Hh0h(r/L), H is the distance between the planes and R is the Rossby number V/(fL). For any obstacle the right-hand side of (1) is greater than zero and hence h0 must be positive for a closed-streamline region to occur. It is argued, and illustrated by a particular example, that because (1) involves an integral of h(x) a representative flow pattern can be obtained for obstacles of less than critical height by considering the special case of a flat-topped obstacle, as is done by Ingersoll (1969).If the flow is stratified with constant Brunt-Väisälä frequency N, the condition for the existence of closed streamlines is shown to be
\[
h_0R^{-1} > \min_r \left[B\int_0^{\infty}\int_0^{\infty}xt\cot h(Bt)h(x)J_0(tx)J_1(tr)\,dt\,dx \right]^{-1},
\]
where B = NH/fL. In contrast to the homogeneous situation, the right-hand side of (2) can be zero and is so if the obstacle is somewhere vertical. Such obstacles will produce a closed-streamline region no matter now small their height and will hence not lead to patterns representative of smooth obstacles. This is because a stratified column of fluid cannot be stretched or compressed over an infinitesimal distance. Instead, the column bends markedly and the fluid flows around the obstacle. The critical conditions (1) and (2) for a number of specific obstacles are calculated and discussed.
On the gravitationally forced motions of a compressible fluid within a horizontally rotating cylinder
Authors: Gans Roger F. 
Published: March 2006

The effect of gravity acting perpendicularly to the stratification induced by rotation in a compressible fluid is investigated. The γ = 1 approximation used by Gans (1974) in an investigation of the free modes of a rotating gas is used to find an inviscid solution. The boundary layers are calculated, and their suctions are shown to lead to a resonance. The amplitude of the resonance mode is calculated and seen to be of the same order as the simple inviscid solution, so that a corrected solution can be obtained.The stability of the system is discussed in a simple fashion. It seems likely that a turbulent core will form in a cylinder. The interaction of such a core with the remainder of the fluid is beyond the scope of this paper. Finally a procedure by which a zonal flow field can be found is given.
Numerical models of hydromagnetic dynamos
Authors: Jepps S. A. 
Published: March 2006

The magnetic induction equation is solved numerically in a sphere for a variety of prescribed fluid flows. The models considered are the so-called ‘αω dynamos’, in which both small-scale turbulence and large-scale shearing play a significant role. Solutions are obtained by marching the finite–difference equations forward in time from some initial field. For a critical value of the magnetic Reynolds numberRmsolutions which neither grow nor decay are found.Further calculations are performed with a ‘cut-off effect’ in which an attempt is made to simulate the effect of the Lorentz forces on the turbulence. For supercritical values of R, the magnetic field now stabilizes a t a finite value instead of increasing indefinitely. The form of the final field is compared with that produced at criticalRmin the absence of the cut-off effect.
Parametric instability of internal gravity waves
Authors: McEwan A. D. , Robinson R. M. 
Published: March 2006

A continuously stratified fluid, when subjected to a weak periodic horizontal acceleration, is shown to be susceptible to a form of parametric instability whose time dependence is described, in its simplest form, by the Mathieu equation. Such an acceleration could be imposed by a large-scale internal wave field. The growth rates of small-scale unstable modes may readily be determined as functions of the forcing-acceleration amplitude and frequency. If any such mode has a natural frequency near to half the forcing frequency, the forcing amplitude required for instability may be limited in smallness only by internal viscous dissipation. Greater amplitudes are required when boundaries constrain the form of the modes, but for a given bounding geometry the most unstable mode and its critical forcing amplitude can be defined.An experiment designed to isolate the instability precisely confirms theoretical predictions, and evidence is given from previous experiments which suggest that its appearance can be the penultimate stage before the traumatic distortion of continuous stratifications under internal wave action.A preliminary calculation, using the Garrett & Munk (197%) oceanic internal wave spectrum, indicates that parametric instability could occur in the ocean at scales down to that of the finest observed microstructure, and may therefore have a significant role to play in its formation.