摘要:

The stability of an inviscid two‐dimensional bubble subject to two‐dimensional disturbances is considered and the bubbles are found to be linearly stable for all Weber numbers, for which a steady solution is known. Certain aspects of the nonlinear initial value problem are also studied. An initial condition that consists of a superposition of a suitable symmetric eigenmode (of the linear stability operator) on a steady state is found to result in pinching of the bubble neck as it tends to oscillate about the steady state. An estimate of the threshold amplitude of such a disturbance needed to cause breakup of a large aspect ratio bubble is obtained. The presence of gravity appears to inhibit this pinching process. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868518

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The laminar flow in a twisted square duct is studied numerically to analyze the formation and reorganization of Dean roll cells under abrupt curvature change. The flow geometry consists of four 90° bends, the curvature plane of each making a 90° angle with that of its neighbor. Straight ducts are inserted between successive bends. The flow geometry studied here is a basic element of a twisted duct flow in which chaotic advection has been observed [Jones, Thomas, and Aref, J. Fluid Mech.209, 335 (1989)]. Steady incompressible full Navier–Stokes equations have been solved by an approximate factorization technique. Vector plots of the secondary flow (Dean roll cells) show upstream diffusion of curvature effects. The upstream propagation is weak, however, and the Dean roll cells adopt the rotation protocol of the bend immediately at its entrance. Farther downstream, roll cells continue to develop and reach an axially invariant state before leaving the bend. A passive tracer was also introduced at the center of the entrance to the twisted duct. Tracer distribution was followed in the downstream direction and was visualized every 30°. Comparison of the secondary flow velocity vector plots and the corresponding tracer patterns shows that the tracer distribution lags behind the velocity field in adjusting to changes in curvature. Tracer patterns show strong stretching and folding, which lead to mixing enhancement. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868759

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

In this paper the linear stability analysis of the interface between two Newtonian liquids with temperature‐dependent viscosity in plane Poiseuille flow is presented. A piecewise linear temperature profile is considered. The linearized equations describing the evolution of small, two‐dimensional disturbances are derived and the stability problem is formulated as an eigenvalue problem for a set of ordinary differential equations. The continuous eigenvalue problem is solved numerically by a pseudospectral method based on Chebyshev polynomial expansions. The method leads to a generalized matrix eigenvalue problem, which is solved by the QZ algorithm. Results on the onset of instability are presented in the form of stability maps for a range of thickness ratios, disturbance wave numbers, imposed temperature differences, constant‐temperature viscosity ratios, thermal conductivity ratios, and Reynolds numbers. Increasing the imposed temperature difference, constant‐temperature viscosity ratio, or Reynolds number can have a stabilizing or destabilizing effect, depending on the flow configuration (thickness ratio) and disturbance wavelength. Increasing the thermal conductivity ratio has a destabilizing effect on the interface for all configurations and disturbance wavelengths. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868519

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

This paper studies the translational instability of an oscillating bubble. It is shown that when a spherical bubble undergoing volume oscillation becomes unstable, giving rise to shape oscillations of two neighboring modes, the translational mode is intimately coupled with the two shape modes and this results in translational instability of the bubble. The main contribution is twofold. First, the integral relations for motions of bubbles in an infinite perfect liquid are not relied on, hence result is applicable to liquids with weak viscous effect. Second, the method of deriving the amplitude equations, which is similar to that of normal form calculations for ordinary differential equations, has not been applied to partial differential equations before. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868520

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

This paper is concerned with the propagation of linear plane waves in incompressible, two‐dimensional weakly nonparallel shear flows for large Reynolds numbers. Waves are analyzed for arbitrary complex frequency &ohgr; and local wave numberkwhen nonparallel effects are assumed to be due to weak viscous diffusion. The inviscid approximation is shown to correctly describe, at leading order, the cross‐stream variations of local plane waves at all stations where they are locally amplified in a frame of reference moving at the local phase speed@FRe&ohgr;/@FRek, i.e., at stations where the temporal growth rate &sgr;≡@FFm&ohgr;−@FFmk@FRe&ohgr;/@FRekremains positive. This result also holds as long as the local phase speed lies outside the range of values reached by the basic velocity profile. By contrast, the inviscid approximation fails to represent cross‐stream variations in the critical layers when waves are locally neutral (&sgr;=0), and in large viscous regions when they become damped (&sgr;<0). Uniformly valid WKBJ approximations are derived in these regions and the results are applied to the description of forced spatial waves and self‐excited global modes. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868521

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The electrohydrodynamic stability of a plane layer of nonpolar liquid is analyzed under certain basic assumptions. The liquid is supposed to be perfectly insulating, the space charge resulting from a unipolar injection of charge. The injection is considered to be nonautonomous, that is, following a field dependent law. The regions of linear stability under stationary conditions have been computed both in terms of nondimensional parameters and directly measurable variables, such as the applied voltage and the gap spacing between the electrodes. The results have shown that the onset of instability is strongly dependent on an injection strength parameter and can be approximated by the linear criterion corresponding to autonomous injection, provided that the injected charge is given by the injection law. Experiments have also been performed to determine the instability threshold under transient conditions. An interpretation of these experiments has been done by generalizing an approximated theoretical study for autonomous injection to the case of a nonautonomous injection. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868522

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The Benjamin–Davis–Acrivos–Ono equation is generalized to account for finite, large amplitude solitary waves in a sheared deep fluid. It is shown how fine structure of stratification and weak noncritical shear in such geophysical flows do affect length (shape), wave (phase) velocity, and even stability of finite amplitude solitary waves. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868523

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Vortex rings are seen to form when dyed water drops strike a water surface and their formation and structure depend on height of fall and surface tension. The assumption that a vortex sheet envelopes the penetrating drop, frequently stated without explanation in the literature, does not explain these factors and this paper shows why it is incorrect. Alternative mechanisms have been proposed in the literature but none explains adequately the vorticity generation or the restriction of vortex ring formation to low Weber numbers. This paper proposes a mechanism based on the generation of vorticity on relaxation of surface stresses at coalescence. The condition that the surface viscous stress be continuous across the water‐air interface leads to a boundary condition on vorticity and the total amount of vorticity generated depends on the quantity which can be diffused into the fluid interior from the boundary during coalescence. At low values of Weber number this condition appears to be sufficient to generate enough vorticity to allow flow separation at the surface, such separation being a necessary condition for vortex sheet roll‐up and ring production. The existence of a critical Weber number above which vortex rings do not form is the result of a balance between the rate at which the ring of contact moves outward associated with on the one hand, the action of surface tension forces and, on the other, the rate of surface destruction due to the coming together of surfaces. If surface destruction dominates then the fluid elements to which the surface viscous stress boundary condition applies will become part of the fluid interior before diffusion has carried significant vorticity away from the surface. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868524

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Single‐component velocity field measurements, mean and fluctuating wall shear stress measurements, and photographic flow visualizations have been made of a magnetohydrodynamic (MHD) body‐force modified turbulent boundary layer. The turbulent boundary layer flowed over a flat plate in salt water at zero pressure gradient; the MHD force was created by the interaction of a permanent magnetic field and an applied electric field from a magnet/electrode array integral to the surface of the plate. A MHD force, when applied to an electroconducting fluid and acting in a streamwise direction, can generate a near‐wall jet, decreasing the boundary layer thickness and suppressing the intensity of the turbulent fluctuations across the boundary layer. At very high interactions, the force causes an increase in mean wall shear and in turbulence; in the zero free‐stream velocity limit, the force acts as a pump. An increase in local skin friction, however, is offset by a grain in thrust due to the force. At moderate interactions, mean quantities are unaffected, but fluctuating wall shear stress and turbulence intensity are suppressed by up to 30% of their unperturbed values across the lower part of the boundary layer. At very low interactions, effects are seen only near the wall. An interaction parameter is derived that characterizes these regimes. The effects likely occur because the MHD force pumps high momentum fluid along the wall, disrupting the liftup of shear‐generated wall vorticity. This jet effect is associated with increased convection of turbulent kinetic energy by the mean flow. With the force directed axial upstream, turbulence amplification is seen, along with a reduced mean velocity. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868525

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Using a method developed by Foias and Temam [J. Funct. Anal.87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier–Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868526

出版商:AIP    

年代:1995

数据来源: AIP