摘要:

Stability properties of a thin liquid film subject to internal heat generation are studied within the framework of the long-wave theory. A strongly nonlinear evolution equation for the film interface is derived, studied, and solved numerically. Linear stability analysis is performed by a further reduction of the evolution equation. Internal heat generation is found to stabilize the film interface. The film is linearly stable if the intensity of internal heat generation is sufficiently strong. Within the range of linear instability the nonlinear evolution of the film results in the film rupture. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869577

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Consider a cylindrical container of circular section filled with a viscous fluid. We consider flow in such a cylinder driven by the motion of flat belts across the partially open end walls of the container. The flow field is determined by the use of a vector eigenfunction expansion. The critical points that are exhibited in the plane of symmetry include elliptic points, foci, and saddles. As the parameters are varied one can have bifurcations in which one type of critical point bifurcates to a collection of others. An example of a limiting surface is also demonstrated. Since the flow fields considered have little symmetry, the three-dimensional streamlines are for the most part not closed. As a consequence the flow fields tend to globalize structures that would otherwise have been isolated. This feature can have important consequences for mixing. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869581

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The expression of the hydrodynamic force experienced by a spherical bubble having a variable radius and moving in a viscous incompressible liquid is derived analytically in two different asymptotic situations. The solution is obtained by rewriting the initial problem in a frame of reference where the bubble has a fixed radius and where the relevant dimensionless parameters are conserved. It is shown that when the assumption of unsteady creeping motion is valid, the bubble radius variation combined with a constant rise velocity produces a nonzero history force. This contribution can have a significant effect on the bubble motion, especially for a collapsing bubble. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869582

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

It is well known that thermocapillary convection arises in liquid bridges when the support discs are heated differentially and uniformly. Upon increasing the temperature difference, the convective flow shows a transition from an axisymmetric to an oscillatory regime. This phenomenon has been investigated both experimentally and theoretically, but prior experimental results exhibit some discrepancies with respect to the predictions of stability analyses. The present paper discusses experimental results obtained under microgravity conditions, comparing them with previous experimental observations made on ground and in space and with recent theoretical models of the instability. The results agree with the description of oscillations in terms of superposition of hydrothermal waves. Finally, a possible mechanism for a “pulsating” instability is proposed, together with a new scaling law for the oscillation frequencies at onset; this law, which correlates the critical frequency to the fluid properties, the geometrical parameters and the critical temperature difference, agrees with all the available experimental data. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869583

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Wick action is the transport of water and any species it may contain through a concrete element from a face in contact with water to a drying face. Analytical models are presented for chloride transport in concrete due to wick action. Two cases are considered for convection-controlled systems: (1) No precipitation of chloride salt at a wet-dry interface, and (2) precipitation of chloride salt at the interface. For both cases, a constant concentration of chloride salt is assumed for the face of the concrete in contact with salt solution, while at the interface continuity of fluxes is assumed for Case 1, and a constant chloride saturation level for Case 2. Perturbation techniques are used to solve the transient problems for the two cases investigated. The perturbation solution is compared with experimental and numerical results and good agreement is found when chloride binding is accounted for. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869584

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Transport of passive scalars in a chain of vortices in a shear layer is studied using a model motivated by the quasigeostrophic equation, and a discrete map model. Surrounding the vortices there is a stochastic layer where particles alternate chaotically between being trapped in the vortices, and moving following the shear flow. Transport in the stochastic layer is asymmetric: Mixing between the vortices and the up-stream flow is, in general, different from mixing between the vortices and the down-stream flow. We use the Melnikov method to study this asymmetry, and to construct a generalized separatrix map model for asymmetric transport. The statistics of the passive scalar is non-Gaussian. In particular, there is anomalous advection, and anomalous (non-Brownian) diffusion. Thus, transport in this system cannot be described by an advection-diffusion equation with an effective diffusivity. The probability density function (PDF) of particle displacements&dgr;x,P(&dgr;x,t),is asymmetric and broader than Gaussian. At large times,Prelaxes to a self-similar limit distribution of the formt−&ggr;/2f(X/t&ggr;/2),whereX≡&dgr;x−⟨&dgr;x⟩,fis a scaling function, and &ggr; is the anomalous diffusion exponent. As a result, the moments scale as⟨Xn⟩∼tn&ggr;/2.We present a systematic study of the dependence of the mean, the variance, the skewness, and the flatness, on the parameters controlling the asymmetry of the flow. The PDFs of the duration of flight (motion following the shear flow) events, and vortex trapping events, exhibit algebraic decay. In some cases, the flights correspond to Le´vy flights. The results of the model are compared with recent experiments on chaotic advection and Le´vy flights in a rotating annulus. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869585

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

A comparison is made between experimental, numerical and analytical results for the two-dimensional flow on a square domain. The experiments concern the flow at the interface of a two-layer stratified fluid, evoked by either stirring the fluid with a rake, or by injecting additional fluid at the interface. Two numerical simulations were performed with initial conditions and boundary conditions that correspond approximately with those met in the experiments. The analytical results concern the calculation of the lowest modes of a decaying Stokes flow on a square domain. At late times, the experimental and numerical flows resemble the fundamental mode of the Stokes flow. The damping of small-scale structures by viscous diffusion plays an important role even if the initial Reynolds number is high. In particular, viscous diffusion is likely to be responsible for the appearance of an almost linear relationship between vorticity and stream function in the experiments and the simulations. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869586

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

A derivation of an expression for the self-induced velocity of a helical vortex filament with moderate and small pitch is presented for the cases of an infinite space as well as a space bounded by a cylindrical tube. This result supplements the known Kelvin’s formula for helix with large pitch in an infinite space. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869587

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

An analytical solution is derived for the two-dimensional, laminar, compressible, planar free jet. The solution assumes constant pressure, specific heats, and unity Prandtl number and accounts for the effects of heat conduction and viscous dissipation in a self-consistent fashion. Exact closed-form expressions are provided for the streamwise and transverse velocities, temperature, vorticity, and dilatation. Temporal instability analyses of these high Reynolds number mean flows indicate that jet-to-ambient temperature ratio exerts a far greater effect on instability growth rates than compressibility. Relative to isothermal conditions, a hot jet flowing into cold ambient fluid is an order of magnitude more unstable and is unstable over a far greater range of wavenumbers. For this hot jet both symmetric and antisymmetric modes are equally amplified whereas isothermal jets have relatively stronger amplification of their antisymmetric modes. A cold jet issuing into a hot fluid is very stable relative to isothermal conditions. Increasing compressibility suppresses instability growth rates for all temperature ratios. All modes found were two-dimensional. Comparison of the instability analysis and the mean vorticity transport equation indicates that the relative instability growth rates of these jets is qualitatively predicted by the mean inertial vorticity generation term,−&ohgr;&thgr;. Jets exhibiting the greatest mean vorticity generation rate inside of the jet half-thickness are the most unstable.

ISSN:1070-6631    

DOI:10.1063/1.869599

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The subharmonic nonlinear route to transition in a wall jet with respect to the Craik resonant–triad instability is considered theoretically. The general technique based on linear stability theory, allowing one to reveal the resonant triads in a parametric space, was developed and successfully implemented for both the boundary layer and the wall jet. The analysis showed that only resonant interaction between inner instability modes occurring in the vicinity of the wall is prospective for an experimental observation. The detailed calculations were performed for the particular case of the resonant triad consisting of components which all become neutral at the same downstream location. At a sufficiently large initial amplitude of the two-dimensional (2D) Tollmien–Schlichting wave imposed on the basic flow, the rapid emergence of its 3D subharmonics occurs within a few wavelengths of the fundamental. It follows from the present results that a wall jet is very sensitive to the three-dimensional wavy perturbations propagating in a narrow band of wave angles around &thgr;=58°. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869588

出版商:AIP    

年代:1998

数据来源: AIP