摘要:

This paper reports a linear temporal instability analysis of an incompressible plane gas sheet in a quiescent viscous liquid medium of infinite expanse. Results indicate that there exist two unstable modes of disturbance waves, sinuous and varicose, and surface tension always reduces, while the relative velocity between the gas and liquid phases and the gas density always enhance instability development. For both unstable modes, the presence of liquid viscosity increases the instability limit, which is however independent of the absolute value of viscosity. It is also shown that the sinuous mode becomes stable when the gas Weber number, defined as the ratio of aerodynamic forces to surface tension forces, is less than the critical value of one. At slightly larger gas Weber numbers, liquid viscosity exhibits dual effects—it may enhance or suppress the growth of unstable disturbances, depending on specific flow conditions. However, for sinuous mode at high Weber numbers and varicose mode at any Weber numbers, liquid viscosity always reduces disturbance growth rates and dominant wave numbers. Unlike the case for plane liquid sheets, varicose mode controls the instability process for all Weber number ranges and for both inviscid and viscous liquids, and only at high Weber numbers, do varicose and sinuous modes become almost equally important. It is further found that the wave propagation velocity for both unstable modes is much smaller than the gas velocity at the mode of maximum instability, implying that the disturbance waves appear almost stationary rather than travelling‐wave type, in contrast with the plane liquid sheet results. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868819

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

This study is concerned with the experimental and numerical analysis of thermohaline natural convection in an aqueous solution, driven by melting of a block of pure ice into the liquid mixture. Experimentally, the flow structure evolution and the heat transfer characteristics are studied for a binary H2O–Na2CO3mixture in the domain of negative buoyancy ratios and for a wide range of solutal and thermal Rayleigh numbers. The observations are analyzed with the help of the classical results about cell formation in a stratified fluid due to sideways heating. The comparison with the numerical results shows that the mechanisms that define the flow structure are essentially due to thermohaline convection and not to the melting process. Finally, the fusion kinetics is analyzed, and the melting rate is correlated to the governing parameters of natural convection in the liquid. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868820

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Depending upon the relative sizes of the parameters of the problem, rotating flow of a vertically confined fluid past an asymmetric object—in this case a circular cylinder with top sliced at an angle—may induce flow inside the Taylor column, driven by the viscous stresses in the column wall. The motion is along the constant‐depth contours, which are not closed in such a situation. We show from theoretical considerations that so long as the angle of the slice is bigger than the one‐quarter power of the Ekman number,E, such an interior motion in the column does occur. In general, the motion consists of two eddies over the obstacle. A series of case study laboratory experiments is presented in support of the analysis, to show the effect of the slice orientation and magnitude on the flow over such a bump, and to illustrate the nature of the flows which are generated when inertial effects are dominant. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868821

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Two‐dimensional solitary waves generated by a submerged body moving near the critical speed in a shallow water channel are studied numerically. The incompressible Navier–Stokes equations in a curvilinear free‐surface‐fitted coordinate system are solved by the finite difference method. The present numerical results are compared with the existing experimental data, and with the numerical solutions of two inviscid‐flow models, i.e. the general Boussinesq equation and the forced Korteweg‐de Vries equation. It is found that the viscous effect in the boundary layer around the body and on the bottom of the channel plays an important role in the generation of solitary waves on the free surface. Hence the Navier–Stokes solutions have a better agreement with the experimental data than those obtained from two inviscid‐flow models. The effect of the submergence depth of the body on the waves generated is also investigated. It reveals that waves are insensitive to the submergence depth of the body, except for a small region quite close to the bottom of the water channel. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868822

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherentlyunsteady. Here we show that for a vortex convected by a uniform shear flow, there is asteadysolution when the speed of the vortexcvis sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (cv→∞) and numerically at more moderate speeds. This solution may provide a useful base state about which to investigate the stability of a boundary layer induced by external disturbances. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868823

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

In this paper we explore essentially nonlinear disturbances produced in an incompressible boundary layer by a roughness on the wall. The scale of the stationary roughness is supposed to be large enough so that generated waves are governed by the forced Benjamin–Davis–Acrivos (fBDA) equation. The disturbance patterns for a wide range of roughness sizes are analyzed revealing the remarkable phenomenon of bifurcations. A very specific oscillation motion over the obstacle is found. It appears to be the basic mechanism causing the periodic generation of solitary waves upstream and downstream. The general structure of disturbances in space at different values of time is discussed. The asymptotic analysis of the solution, when the intensity of the external agencyQbecomes a small parameter, is given. The quadratic term of an expansion based on this parameter is responsible for the redistribution of solution mass between regions located ahead and behind the obstacle, inevitably leading to the gradual growth of nonlinear effects. According to the asymptotic consideration, the timeTc*determining the onset of the nonlinear stage of disturbance development isO(Q−3), this estimation correlates well with numerical results. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868824

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

In this paper, Galerkin projections on eigenfunctions as obtained by proper orthogonal decomposition of numerically computed flow fields are used to derive dynamical models for different regions of a transitional boundary layer. The regions investigated cover the stages of the transition process from the evolution of low‐amplitude Tollmien‐Schlichting waves up to the final stages of transition, right at the onset of turbulence. In a first part of the paper, the possibilities and limitations of the approach chosen are investigated in detail, and in a second part the application of the techniques developed before is demonstrated for the case of a spatially evolving boundary layer that is inhomogeneous in all spatial directions. The focus of this work is mainly on how characteristic properties of the dynamics change as transition evolves in the streamwise direction. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868825

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

It is pointed out that, for microscale Reynolds numbers less than about 1000, the passive scalar spectrum in turbulentshearflowsis less steep than anticipated and that the Obukhov–Corrsin constant can be defined only if the microscale Reynolds number exceeds this value. In flows where the large‐scale velocity field is essentially isotropic (as in grid turbulence), the expected 5/3 scaling is observed even at modest Reynolds numbers. All known data on the Obukhov–Corrsin constant are collected. The support for the notion of a ‘‘universal’’ constant is shown to be reasonable. Its value is about 0.4. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868826

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Using results of direct numerical simulations of isotropic turbulence the subgrid‐scale energy transfer in the physical space is calculated exactly employing a spectral decomposition of the velocity field into large (resolved) and small (unresolved) scales. Comparisons with large‐scale quantities reveal large qualitative correlations between regions of subgrid transfer and the boundaries of regions of large vorticity production. This suggests a novel analysis of the nonlinear term, where it is decomposed into four components determined by four combinations of the resolved and unresolved velocity and vorticity fields. It is found that there is a 90% vector‐correlation between the subgrid transfer and the component of the full transfer associated with the resolved velocity and unresolved vorticity, but that 90% of the total subgrid energy production is determined by the component associated with the unresolved velocity and resolved vorticity. These results suggest subgrid‐scale models that have higher correlation values with the exact subgrid scale terms than a number of other physical quantities that are traditionally considered to govern the dynamics of the large scales of turbulence. The distinguishing feature of the new models is that they emphasize the nonlinear dynamics of the smallest resolved scales in the modeling procedures. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868827

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The dispersion of a passive tracer in a quasi‐two‐dimensional turbulent flow and the geometry of corresponding isoconcentration lines are investigated experimentally. The flow consists in an array of 900 vortices, forced in a thin layer and driven in a turbulent regime. Both the instantaneous velocity field and the concentration field are measured. A remarkable regime of anomalous diffusion—characterized by a dispersive front moving liket0.32±0.04—is observed. Examining the trajectories of individual neutral particles, we reveal the presence of ‘‘traps’’ that control most of the characteristics of this hypodiffusive regime. The fractal dimension of isoconcentration profiles and the exponents of the structure functions of both the velocity and the concentration fields are established. The corresponding values are consistent with mathematical inequalities, recently discovered, but show some disagreements with recent conjectured equalities proposed by Constantinetal. [Nonlinearity7, 1045 (1994)]. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868828

出版商:AIP    

年代:1996

数据来源: AIP