摘要:

We report on stabilizing the unstable no-motion state in a moderate aspect ratio one-dimensional Rayleigh–Be´nard convection experiment. A linear proportional control algorithm uses shadowgraphic convection images to determine heat flux perturbations which are applied to the lower boundary by a network of local heaters. We show that simple linear control stabilizes the otherwise unstable no-motion (conduction) state over a substantial range of supercritical Rayleigh numbers. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869335

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A model is proposed to predict the depth of penetration of the air bubbles entrained by a round water jet impacting into a flat, liquid pool. This depth is shown to be determined only by the initial jet momentum and by the non-monotonic nature of the bubble terminal velocities as a function of their size. The model is shown to be in excellent agreement with measurements of the depth and width of penetration of the bubbles performed over a wide range of jet diameters, velocities, and plunging angles. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869336

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

An experimental investigation is made into the active control of the near-wall region of a turbulent boundary layer using a linear feed-forward control algorithm. A wall-based detection scheme is described which effectively detects coherent structures and predicts downstream flow behavior. A simple demonstration, using three wall-based sensors and a single actuator, achieves a maximum of 31&percent; reduction inurmsand 17&percent; reduction inprms.©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869337

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We present a diffuse-interface treatment of the internal gravity waves which have been observed experimentally by Berg &etal; in xenon near its thermodynamic critical point. The results are compared with theoretical predictions by Berg &etal; that were obtained using separate models above and below the critical temperatureTc.The diffuse-interface model applies both above and belowTc,and is formulated by using the density as an order parameter. The diffuse interface is represented as a transition zone of rapid but smooth density variation in the model, and density gradients appear in a capillary tensor, or Korteweg stress term, in the momentum equation. We obtain static density profiles, compute internal wave frequencies and compare with the experimental data and theoretical results of Berg &etal; both above and below the critical temperature. The results reveal a singularity in the diffuse-interface model in the limit of incompressible perturbations.

ISSN:1070-6631    

DOI:10.1063/1.869309

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The stability problem for the axisymmetric equilibrium states of an isorotating liquid bridge between equidimensional circular disks in a constant axial gravity field is considered. In particular, we examine the stability of bridges satisfying two constraints that are typical for the floating zone method used for materials purification and single crystal growth. First we consider the constraint that the relative volume of the bridge,V,is equal to 1. Here,Vis the ratio of the actual bridge volume to that of a cylinder pinned to the edges of disks. For this case, the critical values of the slenderness (&Lgr;) (ratio of the disk separation to the diameter) and of the free surface slopes(&bgr;1,&bgr;2)at both disks have been determined for a wide range of the Bond(B)and Weber(W)numbers. The second constraint is that the surface slope&bgr;1at one of the disks is prescribed. The chosen values are 90° and 75° and correspond to extremes in growth angle values encountered in floating zone crystal growth. For this case, the dependencies of critical &Lgr; andVvaluesBandWhave been calculated. In addition, both axial gravity directions are considered separately and the values of the slope angle,&bgr;2,at the other disk are also analyzed for critical states. The solution of the stability problem for any liquid bridge is discussed in detail using the case forB=W=0.1as an example. In particular, the relationship between the general boundary of the stability region and the stability of bridges subject to the constraints outlined above is examined. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869475

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The bifurcation of the solutions of the nonlinear equilibrium problem of a weightless liquid bridge with a free surface pinned to the edges of two coaxial equidimensional circular disks is examined. The bifurcation is studied in the neighborhood of the stability boundary for axisymmetric equilibrium states with emphasis on the boundary segment corresponding to nonaxisymmetric critical perturbations. The first approximations for the shapes of the bifurcated equilibrium surfaces are obtained. The stability of the bifurcated states is then determined from the bifurcation structure. Along the maximum volume stability limit, depending on values of the system parameters, loss of stability with respect to nonaxisymmetric perturbations results in either a jump or a continuous transition to stable nonaxisymmetric shapes. The value of the slenderness at which a change in the type of transition occurs is found to be&Lgr;s=0.4946.Experimental investigation based on a neutral buoyancy technique agrees with this prediction. It shows that, for&Lgr;<&Lgr;s,the jump is finite and that a critical bridge undergoes a finite deformation to a stable nonaxisymmetric state. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869310

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Two-dimensional overstable convection in a rotating layer is studied for large Taylor numbers. In this regime, the leading order nonlinearity arises from the distortion of the horizontally averaged temperature profile. Fully nonlinear solutions in the form of traveling and standing waves are obtained via an asymptotic expansion in the Taylor number. The formulation leads to a nonlinear eigenvalue problem for the vertical structure and frequency of each solution type and allows the computation of the Nusselt number and frequency as functions of the applied Rayleigh number. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869311

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The effect of slight viscosity on a near-critical axisymmetric incompressible swirling flow in a straight pipe is studied. We demonstrate the singular behavior of a regular-expansion solution in terms of the slight viscosity around the critical swirl. This singularity infers that large-amplitude disturbances may be induced by the small viscosity when the incoming flow to the pipe has a swirl level around the critical swirl. It also provides a theoretical understanding of Hall’s boundary layer separation analogy to the vortex breakdown phenomenon. In order to understand the nature of flows in this swirl range, we develop a small-disturbance analysis. It shows that a small but finite viscosity breaks the transcritical bifurcation of solutions of the Euler equations at the critical swirl into two branches of solutions of the Navier–Stokes equations. These branches fold at limit points near the critical swirl with a finite gap between the two branches. This means that no near-columnar equilibrium state can exist for an incoming flow with swirl close to the critical level and the flow must develop large disturbances in this swirl range. Beyond this range, two equilibrium states may exist under the same inlet/outlet conditions. When the flow Reynolds number is decreased this special behavior uniformly changes into a branch of a single equilibrium state for each incoming swirl. We also derive a weakly nonlinear approach to study the effect of slight viscosity on standing waves in a long pipe. This special behavior of viscous solutions shows good agreement with the numerical simulations of the axisymmetric Navier–Stokes equations by Beran and Culick and provides a theoretical understanding of these computations. The relevance of the results to the axisymmetric vortex breakdown in a pipe is also discussed. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869312

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A circular jet of perfectly conductive inviscid liquid in a uniform longitudinal magnetic field can be absolutely or convectively unstable for different values of the flow parameters. Higher intensity of the field always reduces the domain of absolute instability. For both cases of absolute and convective instability, the corresponding jet of large but finite length is globally unstable if suitable boundary conditions hold at its beginning and end. The unstable global mode is based on a pair of waves that propagate in opposite directions and reflect from one into the other at the flow boundaries. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869308

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We study numerically the simplest model of two incompressible, immiscible fluids shearing past one another. The fluids are two-dimensional, inviscid, irrotational, density matched, and separated by a sharp interface under a surface tension. The nonlinear growth and evolution of this interface is governed by only the competing effects of the Kelvin–Helmholtz instability and the dispersion due to surface tension. We have developed new and highly accurate numerical methods designed to treat the difficulties associated with the presence of surface tension. This allows us to accurately simulate the evolution of the interface over much longer times than has been done previously. A surprisingly rich variety of behavior is found. For small Weber numbers, where there are no unstable length-scales, the flow is dispersively dominated and oscillatory behavior is observed. For intermediate Weber numbers, where there are only a few unstable length-scales, the interface forms elongating and interpenetrating fingers of fluid. At larger Weber numbers, where there are many unstable scales, the interface rolls-up into a “Kelvin-Helmholtz” spiral with its late evolution terminated by the collision of the interface with itself, forming at that instant bubbles of fluid at the core of the spiral. Using locally refined grids, this singular event (a “topological” or “pinching” singularity) is studied carefully. Our computations suggest at least a partial conformance to a local self-similar scaling. For fixed initial data, the pinching singularity times decrease as the surface tension is reduced, apparently towards the singularity time associated with the zero surface tension problem, as studied by Moore and others. Simulations from more complicated, multi-modal initial data show the evolution as a combination of these fingers, spirals, and pinches. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869313

出版商:AIP    

年代:1997

数据来源: AIP