摘要:

The evolution of the withdrawal through a line sink of an initially quiescent, linearly stratified fluid in a semi‐infinite, horizontal duct is investigated. It is shown that due to the shear present in the withdrawal layer the previously suggested mechanism for the control of the higher mode shear fronts, which assumes that the velocity of the fronts is balanced by the oncoming flow, cannot occur. An alternative mechanism for the control of this flow is proposed based on solutions for the vertical structure of linear, long, internal waves in horizontal shear. This results in a model for unsteady selective withdrawal in agreement with steady‐state solutions. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868773

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

A one‐dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self‐similar pinching solutions that yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Furthermore, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one‐dimensional model gives a consistent terminal state, with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inertial forces in the momentum equations to derive an evolution system modeling the breakup of Navier–Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868540

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The oscillations of an axially symmetric liquid drop in an acoustic standing wave field in air have been studied using the boundary integral method. The interaction between the drop oscillation and sound field has been included in this analysis. Our computations focus on the frequency shift of small‐amplitude oscillations of an acoustically deformed drop typical of a drop levitated in air. In the presence or absence of gravity, the trend and the magnitude of the frequency shift have been given in terms of drop size, drop deformation, and the strength of the sound field. Our calculations are compared with experiments performed on the United States Microgravity Laboratory (USML‐1) and with ground‐based measurements, and are found to be in good agreement within the accuracy of the experimental data. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868541

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The onset of convection in binary fluid mixtures in a rotating vertical cylinder is considered. Parameter values and boundary conditions relevant to experiments on3He–4He mixtures with negative separation ratio are used. The eigenfunctions take the form of rigidly precessing spirals. The azimuthal wavenumber of the first unstable mode as the Rayleigh number increases is calculated as a function of the rotation rate and the separation ratio, as are the critical Rayleigh numbers and precession frequencies. Depending on the parameters the spirals may take the form of spatially extended body modes which fill the container, or of wall modes confined to its boundary. The former typically precess in the retrograde direction, while the latter are prograde. Under appropriate circumstances the binary system with a negative separation ratio becomes unstable for lower Rayleigh numbers than a pure fluid. This property of the system is enhanced by the wall modes. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868542

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The multiplicity features and the secondary flow structure of the fully developed, laminar flow of a Newtonian fluid in a straight pipe that is rotating about an axis perpendicular to the pipe axis are examined. The governing equations of motion are solved numerically using the control volume method and the SIMPLE algorithm. The solution structure is governed by two dynamical parameters, Ekman number, Ek=&ngr;/D2&OHgr; and Rossby number, Ro=U/D&OHgr;, whereDis the pipe diameter, &ngr; is kinematic viscosity, &OHgr; is rotational speed, andUis velocity scale. Results are presented for a fixed Ekman number of Ek=0.01 and a range of Rossby numbers between 0 to 20. The primary solution branch begins as a unique solution at low Rossby numbers. Its secondary flow structure consists of two‐cells. At higher values of Ro a hitherto unknown solution with a four‐cell flow structure appears, which coexists with the two‐cell flow structure over a range of Ro up to 20. Transient, two‐dimensional simulations were carried out to determine the stability of the solutions to two‐dimensional perturbations. The two‐cell flow structure is stable to both symmetric and asymmetric perturbations. Four‐cell flow structure is stable to symmetric perturbations and unstable to asymmetric perturbations, where it breaks down to a two‐cell flow structure. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868543

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

In this paper our most recent research results on natural convection in a closed cylinder, where our interest focuses on pattern structure dependence on aspect ratio and on temperature‐dependent viscosity, are summarized. The main results are (a) the experiments on the onset pattern and conditions for pure Rayleigh convection in circular cylinders compare favorably with linearized stability results of Hardinetal. [Int. J. Num. Methods Fluids10, 79 (1990)], as well as three‐dimensional nonlinear calculations made by us; and (b) experiments and nonlinear calculations indicate a variation of the patterns at and near the codimension two points when large temperature differences are introduced, so as to cause a substantial change in viscosity. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868544

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The spread and mixing of a fluid jet into an ambient stream occurs at a rate which deserves further study to improve efficient mixing. Mixing enhancement techniques, such as introduction of periodic disturbances into the jet flow, are used to increase mixing between a jet and the surrounding fluid. Pulsations were generated by the periodic closing and opening of a jet flow. The dynamics and trajectories of vortex rings, formed by the pulsation of the jet in a uniform crossflow, are studied. In particular, the effects of pulsation on the development of vortex rings and their penetration in a crossflow were investigated. Detailed measurements were made using flow visualization techniques including laser‐induced fluorescence and hot‐film anemometry. Vortex rings generated in a crossflow at one specific frequency (1 Hz) were measured using a hot‐film probe. Measurements indicated that vortex rings were fully‐formed at a distance of three times the jet exit diameter. To simulate the dynamics of vortex rings in crossflows, a numerical experiment was performed based on a Lagrangian, grid‐free, three‐dimensional vortex element method. At low frequencies, the fluid in the vortex rings penetrated into the crossflow to a height much greater than that for either high frequency pulsation or for a steady jet. At low frequencies, interaction between sequentially generated vortex rings was negligible; therefore, each ring behaved as a single discrete vortex ring. The vortex rings moved into the flow occasionally tilting up to about 30°, depending on the ring’s strength. Numerical simulation indicated that the tilting of the ring was due to the combined effects of viscosity and the crossflow. It is postulated that the increased penetration combined with the discretization of a jet into vortex rings results in a more efficient mixing rate. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868545

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

A simplified Lagrangian closure for the Navier–Stokes equation is used to study the production of intermittency in the inertial range of three‐dimensional turbulence. This is done using localized wave packets following the fluid rather than a standard Fourier basis. In this formulation, the equation for the energy transfer acquires a noise term coming from the fluctuations in the energy content of the different wave packets. Assuming smallness of the intermittency correction to scaling allows the adoption of a quasi‐Gaussian approximation for the velocity field, provided a cutoff on small scales is imposed and a finite region of space is considered. In these approximations, the amplitude of the local energy transfer fluctuations can be calculated self‐consistently in the model. Definite predictions on anomalous scaling are obtained in terms of the modified structure functions: ⟨⟨E(l,a)⟩qR⟩, where ⟨E(l,a,r,t)⟩Ris the part of the turbulent energy coming from Fourier components in a band (a−1)karoundk∼l−1, spatially averaged over a volume of sizeR∼l/(a−1) aroundr. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868546

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Linear stability theory is used to study the effect of cross‐flow on Go¨rtler instability in incompressible boundary layers. The results cover a wide range of sweep angle, pressure gradient, and wall curvature parameters. It is shown that the cross‐flow stabilizes Go¨rtler disturbances by reducing the maximum growth rate and shrinking the unstable band of spanwise wave numbers. On the other hand, the effect of concave wall curvature on cross‐flow instability is destabilizing. Calculations show that the changeover from Go¨rtler to cross‐flow instabilities is a function of Go¨rtler number, pressure gradient, and sweep angle. The results demonstrate that Go¨rtler instability may still be relevant in the transition process on swept wings even at large angles of sweep if the pressure gradient is sufficiently small. The influence of pressure gradient and sweep can be combined by defining a cross‐flow Reynolds number. Thus, the changeover from Go¨rtler to cross‐flow instability takes place at some critical cross‐flow Reynolds number whose value increases with Go¨rtler number. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868547

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

A method for studying natural oscillations of fluids and plasmas in the neighborhood of two‐dimensional elliptical flows is presented. The method uses scaling combined with the Fourier transformation to reduce the spectral stability problem for such flows to a spectral problem for an ordinary differential operator. This reduction is used to obtain a complete description of the spectrum for fluid flows and a qualitative description of the spectrum (including bounds for the complex part of the spectrum) for plasma flows. It is shown that a steady planar fluid flow with elliptical streamlines is spectrally unstable. It is also shown that all planar magnetized plasma flows with elliptical streamlines are spectrally unstable, except for the case when the magnitudes of the fluid velocity and the Alfve´n velocity are exactly equal to each other. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868481

出版商:AIP    

年代:1995

数据来源: AIP