摘要:

Exact solutions are presented for a steady stream of bubbles in a Hele–Shaw cell when the effect of surface tension is neglected. These solutions form a three‐parameter family. For specified area and distance between bubbles, the speed of the bubble remains arbitrary when surface tension is neglected. However, numerical and analytical evidence indicates that this arbitrariness is removed by the effect of surface tension. The branch of solutions that corresponds to the McLean–Saffman finger solution were primarily studied. A dramatic increase was observed in bubble speeds when the distance between bubbles is on the order of a bubble diameter, which may have relevance to experiments done by Maxworthy [J. Fluid Mech.173, 95 (1986)].

ISSN:0899-8213    

DOI:10.1063/1.858146

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

In a thin layer of an aqueous solution of sucrose, convection due to evaporation takes place, after a chaotic regime, as a unique toroidal roll occupying the whole container. When a mask drilled with holes is placed just above the upper surface of the fluid layer, there is cellular convection imposed by the distribution of holes. Immersed solid particles preferentially settle at the bottom of the cell walls, where the fluid is rising. This is explained by the combined effects of diffusion and convection, when the latter is dominant (large Pe´clet number).

ISSN:0899-8213    

DOI:10.1063/1.858147

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Numerical solutions of the Navier–Stokes equations governing shear flow in a trapezoidal enclosure have been obtained at fine grid resolutions using an efficient multigrid calculation procedure. The effects of flow Reynolds number and wall boundary conditions are studied in detail. Interesting flow patterns are observed to develop, especially at high Reynolds numbers. To the author’s knowledge, such a flow development has not been reported previously.

ISSN:0899-8213    

DOI:10.1063/1.858207

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The effect of suction on controlling the three‐dimensional secondary instability is investigated for a boundary layer with a pressure gradient in the presence of a small but finite‐amplitude Tollmien–Schlichting wave. The focus is on the principal parametric resonance responsible for the strong growth of subharmonics in a low disturbance environment. Calculations are presented for the effect of suction on the onset and amplification of the secondary instability in Blasius and Falkner–Skan flows, as well as its effect on controlling the production of the vortical structure.

ISSN:0899-8213    

DOI:10.1063/1.858148

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The effect of a solid‐body rotation, characterized by an angular velocity &OHgr;, on a two‐dimensional mixing layer (in a plane perpendicular to &OHgr;) of relative vorticity &ohgr;2D, upon which is superposed a small three‐dimensional turbulent perturbation, is considered. Using the Kelvin theorem in the frame rotating with &OHgr;, and with the aid of arguments based on the straining of absolute vortex filaments by the basic velocity, it is shown that the rotation is always stabilizing (with respect to the nonrotating case) in the cyclonic case. In the anticyclonic case, a slight rotation is destabilizing. At a local Rossby numberR0=‖&ohgr;2D‖/2‖&OHgr;‖ of the order of 1, the anticyclonic rotation disrupts catastrophically the coherent structures of the mixing layer. Anticyclonic rotation becomes stabilizing again forR0<0.5. Also presented are three‐dimensional numerical simulations which support the theory, and agree qualitatively with experimental results. The consequences for oceanic and atmospheric vortices are briefly discussed.

ISSN:0899-8213    

DOI:10.1063/1.858149

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

A stability analysis based on Arnol’d–Lyapunov arguments in a gauge‐variable formalism is applied to a generalized form of propagating modons. The method was previously applied to the special case of Stern’s modon in a quiescent background flow. The analysis presented here shows that propagating‐modon solutions in the shallow‐water equations are stable to small‐amplitude perturbations, regardless of the sign of their translational speed, as long as this is much smaller in magnitude than the solid‐rotation speed of the Earth. Sufficient conditions for stability are that the given flow be quasigeostrophic, i.e., that the Rossby number be small, and that the associated Froude number be one order of magnitude smaller than the Rossby number.

ISSN:0899-8213    

DOI:10.1063/1.858096

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity–scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.

ISSN:0899-8213    

DOI:10.1063/1.858097

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The formation of a thermocline generated by the interaction between a stabilizing buoyancy flux and shear‐free turbulence was studied using a numerical model. The time evolutions of the vertical distributions of the buoyancy and turbulent kinetic energy were calculated and were used to evaluate the depth of the thermocline and the time required for its formation. The numerical results are compared with the results of previous laboratory experiments. The mechanisms responsible for the formation of the thermocline are discussed in view of the numerical results.

ISSN:0899-8213    

DOI:10.1063/1.858098

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The one‐dimensional transonic flow of an inviscid fluid, which at large values of the specific heats exhibits both positive (&Ggr;¯>0) and negative (&Ggr;¯<0) nonlinearity regions {&Ggr;¯=(1/&rgr;)[∂(&rgr;a)/∂&rgr;]s} and which remains in a single phase, is studied. By assuming that &Ggr;¯ changes its sign in the small neighborhood of the throat of the nozzle where transonic flow exists and introducing a new scaling of the independent variables, an approximate first‐order partial differential equation (PDE) with a nonconvex flux function is derived. It governs both the steady transonic flows and the upstream moving waves near sonic point. The existence of continuous and discontinuous steady transonic flows when the throat area is either a maximum or a minimum is shown. The existence of standing sonic discontinuities and rarefaction shocks in the transonic flow are noted for the first time. Unlike in the classical gas flows, there are two sonic points and continuous transonic flows are possible only through one of them. The numerical evolution of those transonic waves that have both positive and negative nonlinearity in the same pulse is studied and some comments are made on the local stability of the particular steady flows.

ISSN:0899-8213    

DOI:10.1063/1.858099

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The objective of this paper is to study weakly nonlinear waves on a viscous magnetic fluid flow down an inclined plane under the influence of gravity and a constant magnetic field parallel to the plane. An approximate evolution equation is derived and a critical Reynolds number for the stability of three‐dimensional long waves obtained. It is found that the component of the applied magnetic field aligned with the flow has a stabilizing effect but that the transverse component, however, has a destabilizing effect on the long waves. Stability regions of two‐dimensional long waves at the critical Reynolds number and numerical results for the solution of a nonlinear ill‐posed problem are presented. Several progressive‐wave solutions are also given.

ISSN:0899-8213    

DOI:10.1063/1.858100

出版商:AIP    

年代:1991

数据来源: AIP