摘要:

A surface distribution of point forces has been used to calculate the Stokes flow drag on a thin flat ring moving either parallel to or perpendicular to the axis of rotational symmetry. The results for motion parallel to the axis are confirmed by experiment. The drag is found to depend primarily upon the outside diameter of the ring and to be relatively insensitive to the inside diameter, in contrast to measurements at high Reynolds number. When the inside diameter is zero, the results agree with the known exact solutions for the circular disk.

ISSN:0031-9171    

DOI:10.1063/1.863843

出版商:AIP    

年代:1982

数据来源: AIP

摘要:

The sudden expansion of a laminar flow in a two‐dimensional channel is examined theoretically in the limit of large Reynolds numberR. Previous investigators found, from experiment and from numerical solutions of the equations of motion, that a region of closed streamlines is formed whose streamwise length is linearly related toRforR= O(102). It is desired to determine if the steady solutions to the Navier–Stokes equations continue to exhibit this relationship indefinitely for increasingR. Since solutions are sought for which the longitudinal length scale isO(R) and that in the tranvserse direction isO(1), the equations of motion reduce to the boundary‐layer equations asR→∞. These equations are solved numerically using a finite difference technique for selected values of &lgr;, the ratio of the upstream channel half‐width to the step height. Steady solutions are found for all values of &lgr; when the inlet velocity profile is parabolic. However, a uniform inlet velocity profile yields steady solutions with anO(R) wake length only for &lgr;⩽&lgr;c= 1.54. Analogous results apply in the axisymmetric case for which &lgr;cis found to be equal 3.67.

ISSN:0031-9171    

DOI:10.1063/1.863844

出版商:AIP    

年代:1982

数据来源: AIP

摘要:

The stability of two‐dimensional convection rolls in a horizontal fluid layer heated from below with rigid boundaries is investigated theoretically for the case when a vertical magnetic field permeates the layer. It is assumed that the magnetic diffusivity is large compared with the thermal and viscous diffusivities of the fluid. Low Prandtl numbers are emphasized in order to make the analysis directly applicable to experiments on convection in mercury and liquid sodium. The theory predicts that the onset of the oscillatory instability of convection rolls is delayed by the effects of the magnetic field and that the parameter range over which steady rolls are stable increases with the magnetic field strength. In the parameter regime investigated, there does not seem to exist a new mode of instability introduced by magnetic forces. It is also found that the magnetic field tends to increase the efficiency of the convective heat transport thereby conpensating in part for the delay in the onset of convection caused by the stabilizing effect on the Lorentz force.

ISSN:0031-9171    

DOI:10.1063/1.863845

出版商:AIP    

年代:1982

数据来源: AIP

摘要:

Boundary conditions are derived for the envelope function of convective rolls approaching a rigid sidewall at an arbitrary orientation. This generalizes previous results for parallel and perpendicular rolls. It provides the first step in a study of the convective pattern to be expected close to onset in Rayleigh–Benard cells of any cross section, and allows consideration of more complicated patterns in rectangular or circular cross sections.

ISSN:0031-9171    

DOI:10.1063/1.863835

出版商:AIP    

年代:1982

数据来源: AIP

摘要:

A formula for the viscous decay of a long internal solitary wave, propagating into a quiescent fluid in a two‐layer model was derived. The result is analogous to Keulegan’s (1948) formula for the viscous decay of long surface waves. The requirement of quiescent fluid ahead of the wave is important, as indicated by a comparison with experiments.

ISSN:0031-9171    

DOI:10.1063/1.863846

出版商:AIP    

年代:1982

数据来源: AIP

摘要:

The phenomenon of three‐dimensional capillary gravity waves on deep water is considered. The solution is obtained by bifurcation from a two‐dimensional wave into three‐dimensional waves composed of the two‐dimensional wave plus a pair of oblique waves. The streamwise period of the three‐dimensional waves is doubled, and there is another period in the spanwise direction. The speed and the stability of the three‐dimensional waves are discussed.

ISSN:0031-9171    

DOI:10.1063/1.863847

出版商:AIP    

年代:1982

数据来源: AIP

摘要:

A quadrant analysis technique based on instantaneous productsuv,u&Vthgr;, andv&Vthgr; (u,vare the longitudinal and normal velocity fluctuations, &Vthgr; is the temperature fluctuation) is used to obtain averages, in ejection and sweep quadrants, associated with coherent structures contributing significantly to Reynolds stress and heat flux in a turbulent boundary layer. Conditional averages ofu,v, &Vthgr; and productsuv,u&Vthgr;, andv&Vthgr; in ejection and sweep quandrants indicate only partial qualitative agreement with those obtained by other conditional sampling techniques, with detection based on the internal front characterized by rapid changes in velocity and temperature. Although the frequency of occurrence of ejections is nearly equal to that of sweeps, only a small percentage of the total number of ejections is followed by sweeps, whereas the percentage of ejections following sweeps is negligible.

ISSN:0031-9171    

DOI:10.1063/1.863848

出版商:AIP    

年代:1982

数据来源: AIP

摘要:

A simple model of temperature, based on conditional averages associated with the coherent temperature fronts, yields a distribution of the temperature derivative skewness in reasonable agreement with measurements.

ISSN:0031-9171    

DOI:10.1063/1.863849

出版商:AIP    

年代:1982

数据来源: AIP

摘要:

The flow of gas–particle mixtures through an axially symmetric nozzle is analyzed. The particle behavior is considered under the condition where the velocity and temperature lags are small. Particular attention is paid to the particle streamlines, and the problem is solved only for the particle streamlines in the first approximation. It is rigorously proved that, when the impingement of the particles on the nozzle wall occurs in the supersonic region, there is an upper limiting point (line) in the wall region where the particles can impinge. The location of this point (line) does not depend on the particle size, but only on the nozzle geometry and the equilibrium reservoir conditions.

ISSN:0031-9171    

DOI:10.1063/1.863850

出版商:AIP    

年代:1982

数据来源: AIP

摘要:

A path integral equation formalism is developed to obtain the frequency spectrum of nonlinear mappings exhibiting chaotic behavior. The one‐dimensional map,xn+1=f(xn), wherefis nonlinear andnis a discrete time variable, is analyzed in detail. This map is introduced as a paradigm of systems whose exact behavior is exceedingly complex, and therefore irretrievable, but which nevertheless possess smooth, well‐behaved solutions in the presence of small sources of external noise. A Boltzmann integral equation is derived for the probability distriburtion functionp(x,n). This equation is linear and is therefore amenable to spectral analysis. The nonlinear dynamics inf(x) appear as transition probability matrix elements, and the presence of noise appears simply as an overall multiplicative scattering amplitude. This formalism is used to investigate the band structure of the logistic equation and to analyze the effects of external noise on both the invariant measure and the frequency spectrum ofxnfor several values of &lgr;∈[0,1].

ISSN:0031-9171    

DOI:10.1063/1.863851

出版商:AIP    

年代:1982

数据来源: AIP