摘要:

The flow field induced in a cylindrical container by the rotation of the container and/or the end wall(s) about the axis of symmetry is highly vortical. If the container and the end walls are rotated at different angular velocities, a meridional flow develops due to the tilting and stretching of the axial vorticity created by the rotation of the bounding surfaces. In the present study, the flow field induced by the differential rotation of the container and one end wall while the other end wall remains fixed is numerically studied for a range of Reynolds numbers and ratios of the container to the end wall rotation rate. It is shown that the production of azimuthal vorticity by the tilting and stretching of axial vorticity causes the container side wall boundary layer to separate for a range of Reynolds numbers and ratios of the container to the end wall rotation rate. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868917

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Experimental results are presented concerning the evolution of instabilities generated by the interaction between low‐level broad‐band acoustic waves and small two‐dimensional roughness elements. Streamwise perturbation velocity spectra are measured and it is found that on the smooth plate, naturally‐occurring Tollmien‐Schlicting (T‐S) waves grow in a manner consistent with a resonant subharmonic wave interaction. However, in the presence of small two‐dimensional roughness elements, a strong primary T‐S mode is forced by an interaction with the background acoustic field. This leads to aK‐type of nonlinear interaction characterized by the generation of harmonics (up to six harmonics are observed) at the expense of the subharmonic. The scaling of the T‐S waves and their harmonics with the number and amplitude of the wall roughness is also considered. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868918

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Instability of fluid flow has long been linked with the eigenvalues of the Orr‐Sommerfeld equation. Recently, it has been shown that even though all eigenvalues may be stable, it is still possible to have disturbance growth. This is because the Orr‐Sommerfeld operator is non‐normal. We identify which eigenmodes are important in two‐dimensional disturbance growth. We find a relationship between maximum growth and growth caused by the adjoint of the leading eigenmode for both plane Poiseuille flow and plane Couette flow. The work points to a connection between the occurrence of the first degeneracy of the Orr‐Sommerfeld operator and the first appearance of disturbance growth. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868919

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The stability of buoyant‐thermocapillary‐driven flows in a fluid layer subjected to a horizontal temperature gradient is analyzed. Our purpose is the modelization of recent experimental results obtained for a fluid of Prandtl number Pr=7, by Daviaud and Vince [Phys. Rev. E48, 4432 (1993)], who observed a transition between traveling waves and stationary rolls when the height of fluid is increased. Our model takes into account several effects that were examined separately in previous studies. The relative importance of buoyancy and thermocapillarity is controlled by the ratioWof Marangoni number to Rayleigh number. The fluid layer is bounded below by a rigid plane whose temperature varies linearly along the direction of the thermal gradient. A Biot number is introduced to describe heat transfer at the top free surface. Our stability analysis establishes the existence of a transition between stationary and oscillatory modes whenWexceeds a valueW0which is a function of the Biot number. Moreover, two types of oscillatory modes have been identified which differ by the range of variation of their critical parameters (wave number, frequency, angle of propagation) versusW. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868920

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The effect of symmetries on instabilitites in rotating hydrodynamic and magnetohydrodynamic flows is considered. Examples are described in which models of such flows or special cases have O(2) symmetry instead of the expected SO(2) symmetry. This change in symmetry has a profound effect on the nature of any instabilities and on their subsequent evolution. Both primary and secondary instabilities in systems with O(2) symmetry are discussed, and the effects of restoring SO(2) symmetry are analyzed. Implications of the results for convection in a rotating annulus, magnetohydrodynamic instabilities in accretion disks and a two‐layer baroclinic instability model are described. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868921

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The effects of viscosity on centre‐modes of instability/stability are considered, with particular emphasis on the trailing line vortex. These effects are shown to be particularly significant when the axial wavenumber is withinO(Re−1/(2+&lgr;)) of the critical (inviscid) value, whereReis the Reynolds number, and &lgr; is a (positive) parameter defined explicitly in the paper. Also examined are the critical (singular) layers that arise within the flow, which are shown to have thicknessO(Re−2&lgr;/3(4+2&lgr;)). A number of numerical results are presented, and these show that viscosity seems to generally play a stabilising role on the stability of the flow. In the Appendix, wavenumbers somewhat closer to the critical inviscid value are examined, and the effects of viscosity are shown to substantially permeate outside of the critical layers, and lead to a system similar to that discussed by Stewartson, Ng and Brown [Philos. Trans. R. Soc. London Ser. A324, 473 (1988)] in the context of swirling Poiseuille flow. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868922

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Just above the liquid‐vapor critical point, a fluid’s large compressibility causes a stable stratification in which the density varies by as much as 10% in 1 cm. This stratification supports internal gravity waves which we observed with an oscillator immersed in a near‐critical xenon sample. We found the number and frequencies of the observable modes depended on the sample cell’s orientation, with only two modes seen in the horizontal cell. The frequencies of the two modes had different temperature dependences: with decreasing temperature, the higher frequency increased monotonically from 0.7 to 2.8 Hz, but the lower frequency varied nonmonotonically, with a maximum of 1.0 Hz at 20 mK above the critical temperature. These temperature dependences continued to 20 mK below the critical temperature, where the xenon was separated into liquid and vapor phases. We calculated these two frequencies by solving the eigenvalue problem of internal waves in a box containing a stratified fluid. The fluid’s density profile was obtained from xenon’s equation of state. The calculated and measured frequencies agree to within 15%. Analytical calculations based on simple approximations of the density profile provide insight into the observed temperature dependences. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868923

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Detailed quantitative measurements of three‐dimensional subharmonic waves have been obtained with a scanning laser anemometer in the near‐wake region of a circular cylinder. A spatial decomposition technique has been used to separate the secondary three‐dimensional flow from the primary Strouhal vortex flow. The appearance of subharmonic frequencies in the spectrum of the secondary instability field at Reynolds numbers of 300 and above provides experimental evidence consistent with the scenario of a period‐doubling route to turbulence. The basic flow structure of the secondary field responsible for producing the subharmonics is shown to be pairs of counter‐rotating streamwise vortices, which alternate the direction of rotation every Strouhal period. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868924

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A local peak in the atmospheric wind or stability profile supports ducted (vertically trapped) modes. If the duct is rather high in the atmosphere it cannot be directly excited by the major atmospheric sources such as convection, but an internal gravity wave radiating out of such sources transfers energy to the duct via nonlinear processes related to the resonance triad interaction. The amplitude of such a transfer is computed. The modal excitations remain after the internal wave has left the region, and while each passing wave adds only a small amount of activity to the duct such contributions are cumulative and drive the modal activity up to a level where it is limited by local dissipation. This suggests the possibility of monitoring the mean flux of internal waves through the region by measuring activity within elevated ducts, a procedure that offers several advantages over monitoring the wave flux directly. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868925

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

There is evidence from previous analytical work based on a model equation and from numerical computations that gravity–capillary solitary waves in a liquid layer are nonlocal—they feature oscillatory tails of constant amplitude—when the Bond number &tgr; is less than 1/3. Here, the full gravity–capillary wave problem is examined and these tails are calculated asymptotically in the weakly nonlinear regime. For given values of &tgr; (0<&tgr;<1/3) and Froude numberFslightly greater than 1, there exists a one‐parameter family of weakly nonlocal solitary waves characterized by the phase shift of the tails relative to the main peak. The tail amplitude depends on the phase shift and is exponentially small with respect to the wave peak amplitude. Predictions of the asymptotic theory are confirmed by numerical computations using a spectral method. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868926

出版商:AIP    

年代:1996

数据来源: AIP