摘要:

We compare the quasi-stationary state obtained from a numerical integration of the two-dimensional Navier-Stokes equation, performed by Matthaeus &etal; [Phys. Rev. Lett.66, 2731 (1991)] with predictions of a mean field theory based on inviscid dynamics. We find that over a relatively short initial period, the theory does not apply, whereas at later stages its prediction for the quasi-stationary state is very good. We relate the failure and success of the inviscid theory to the relevance of viscous effects in the dynamics. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869393

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

When a hot solid particle is submerged into an ambient fluid near a free liquid-gas interface, a non-uniform temperature field around the particle produces surface tension gradients at the interface and generates thermocapillary flow in the surrounding fluid. This flow sets the particle itself in motion towards or away from the interface. In the first part of the paper, the interaction between a hot spherical solid particle and a plane undeformable liquid-gas interface is studied. The velocity of the thermocapillary induced motion of the solid particle is proportional to the surface tension gradient at the liquid-gas interface, and is calculated in the approximation of the Stokes flow and a zero Peclet number as a function of the separation distance between the particle and the interface. The asymptotic cases of both small and large separation distances are studied. In the second part of the paper, the interaction between a hot solid sphere and a gas bubble submerged into an ambient fluid is studied in the limiting case when the separation distance between them tends to zero. The velocity of a pairwise migration of a particle and a bubble in contact is calculated as a function of their radius ratio. The asymptotic values of the individual velocities of a solid particle and a gas bubble in near contact are also computed. The relative velocity of their motion towards each other is found to be proportional to the separation distance between them. In the third part of the paper, we investigate the effect of gravity on the thermocapillary driven motion of a solid particle for the two cases. It is shown that due to the thermocapillary interaction, a particle can move against the buoyancy forces. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869394

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

There are very few explicit solutions of the free-surface Euler equations in the presence of gravity. These include Stokes’ corner flow, Richardson’s flow, and Joukovski’s flow. In this paper, it is shown how these solutions appear as particular solutions of a more general family of solutions of the free-surface Euler equations in the presence of gravity, which can only be computed numerically. The numerical method is based on series truncation. The physical relevance of these solutions is discussed as well. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869395

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We consider a flow of colliding spheres that interacts with a flat, frictional wall and calculate the flux of fluctuation energy in two limits. In the first limit, all spheres slide upon contact with the wall. Here, we refine the calculations of Jenkins [J. Appl. Mech.59, 120 (1992)] and show that a correlation between two orthogonal components of the fluctuation velocity of the point of contact of the grains with the wall provides a substantial correction to the flux originally predicted. In the other limit, the granular material is agitated but the mean velocity of the contact points with respect to the wall is zero and Jenkins’ earlier calculation is improved by distinguishing between those contacts that slide in a collision and those that stick. The new expressions for the flux agree well with the computer simulations of Louge [Phys. Fluids6, 2253 (1994)]. Finally, we extend the expression for zero mean sliding to incorporate small sliding and obtain an approximate expression for the flux between the two limits. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869396

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

An analysis is carried out of the viscous-inviscid interaction due to the thermal expansion of the gas in the laminar boundary layer over a flat plate whose temperature presents a step elevation above the ambient temperature at a finite distance of its leading edge. Numerical solution of the triple-deck problem for infinitely large Reynolds numbers shows that the boundary layer separates for a critical value of the ratio of plate-to-gas temperature, dependent on the Prandtl number and the temperature sensitivity of the gas viscosity (which is assumed to increase as a power of the temperature). As the temperature ratio increases above this value, the separation point continuously shifts upstream of the temperature step whereas reattachment occurs shortly downstream of the step, leading to a triangle shaped recirculation bubble. An asymptotic description is given of the flow with incipient separation. For very large values of the temperature ratio a neatly defined interface develops between the cold and hot parts of the flow and the closure of the bubble becomes very abrupt, with the fluid recirculating near its rear section in a characteristic manner that depends on the combined effects of the large decrease of density and increase of viscosity due to the strong heating. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869397

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A reduced equation set in two space dimensions capable of describing three-dimensional Langmuir circulation in a layer of unstratified water is derived. The reduced description is valid for circulations having large horizontal scales compared to vertical scales, and should be useful for pattern formation studies when this condition is met. Windrow patterns on the surface are found from numerical simulations of the reduced equation set, guided by secondary instability theory. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869398

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

By using a previously developed technique [A. Lifschitz, Phys. Fluids A7, 1626 (1995)], it is shown that the spectrum of linear hyperbolic flows in the plane occupies a strip in the complex plane along the real axis which is independent of the geometry of the basic flow and that all the points in this strip are simple eigenvalues. The relevance of this result to the stability theory is explained. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869399

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Numerical simulations of the effects of buoyancy on the stability and morphology of Taylor–Couette flow have been conducted. The three-dimensional equations of motion are discretized using a hybrid Chebyshev collocation/Fourier spectral method. The problem geometry consists of an air-filled vertical annulus with radius ratio,&eegr;=ri/ro=0.5(whereriandroare the inner and outer radii, respectively), and aspect ratio,&Ggr;=L/(ro−ri)=10(whereLis the height of the annulus). The flow is generated by combined heating and rotation of the inner cylinder. Results for various values of the Reynolds number,Re, and Grashof number,Gr, show several bifurcations of the system. The most notable change in flow structure with increasing rotational effects is the onset of spiral flow in certain parameter ranges. Compared to existing analytical and experimental results, the current numerical results show good agreement. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869400

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The linear stability of boundary-layer flow of fluid with temperature-dependent viscosity over a heated or cooled flat-plate is investigated. Decomposition of the disturbance into normal temporal modes leads to a sixth-order “modified” eigenvalue problem. Making the additional ad hoc assumption of parallel flow leads to a simpler sixth-order “parallel” eigenvalue problem which, unlike the modified problem, reduces to the classical Orr–Sommerfeld problem in the isothermal case. Two viscosity models are considered, and for both models numerically-calculated stability results for both the modified and parallel eigenvalue problems are obtained. For both viscosity models it is, perhaps surprisingly, found that for both eigenvalue problems a non-uniform decrease in viscosity across the layer stabilizes the flow while a non-uniform increase in viscosity across the layer destabilizes the flow. Results for the two eigenvalue problems are shown to be quantitatively similar with, however, the parallel problem always over-predicting the critical Reynolds number in comparison to the modified problem. Finally, we discuss the physical interpretation of our results in terms of velocity–profile shape and thin-layer effects. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869401

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

In this paper an extensive investigation is done of the linear stability of a film falling down a vertical rotating cylinder. Two cases are considered: flow in the outside and flow in the inside of the cylinder. To this end, a system of differential equations which describe the instability is solved numerically with the Runge–Kutta fourth and sixth order methods. We show that in different circumstances the azimuthal disturbances become the most unstable when the rotation is taken into account. Moreover, a splitting of the azimuthal modes appears due to the Coriolis force. In the case of flow in the inside there is a threshold in the centrifugal force above which the flow is linearly stable. Besides, new results for the nonrotating case are also obtained. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869402

出版商:AIP    

年代:1997

数据来源: AIP