摘要:

The Lagrangian flow around a Kida vortex [J. Phys. Soc. Jpn.50, 3517 (1981)], an elliptical two‐dimensional vortex patch embedded in a uniform and constant background shear, is described by a nonintegrable two‐degree‐of‐freedom Hamiltonian. For small values of shear, there exist large chaotic zones surrounding the vortex, often much larger than the vortex itself and extremely close to its boundary. Motion within the vortex is integrable. Implications for two‐dimensional turbulence are discussed.

ISSN:0899-8213    

DOI:10.1063/1.857814

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The Karhunen–Loe`ve procedure is applied to the analysis of digitally imaged two‐dimensional gas concentration fields obtained for a seeded axisymmetric jet. Large scale structures observed in the transitional region of a low Reynolds number jet are characterized in terms of anoptimalbasis. The essential features are captured by retaining roughly 30 parameters in the expansion. By retaining more terms smaller scales of the flow can be resolved.

ISSN:0899-8213    

DOI:10.1063/1.857815

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Steady thermocapillary flow is examined in a square two‐dimensional cavity with a single free surface and differentially heated side walls. The numerical solutions are obtained with a finite difference method applied to a streamfunction‐temperature formulation. This work investigates the Prandtl number dependence, structure, and stability of high Marangoni number flow. It is found that the character of thermocapillary flow is highly sensitive to the value of the Prandtl number over a range of Marangoni numbers exceeding 1×105for 1≤Pr≤50, the magnitude of the flow showing nonmonotonic dependence on the Marangoni number for Pr≤∼10. A complete structural analogy is observed between flow in a cavity driven by a moving lid and thermocapillary flow in the boundary layer limit, and it is found that all the solutions, spanning a wide range of Marangoni and Prandtl numbers, are linearly stable to a restricted class of disturbances.

ISSN:0899-8213    

DOI:10.1063/1.857763

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The spin‐up from rest of (i) a homogeneous and (ii) a linearly stratified fluid in a rectangular container has been examined in the laboratory. In the spin‐up process leading to the ultimate state of rigid‐body rotation, three main stages can be discerned, these being (1) the starting flow, characterized by zero absolute vorticity, (2) flow separation due to cyclonic vorticity generation at the lateral tank walls, and (3) a subsequent organization of the flow into a regular array of alternately cyclonic and anticyclonic cells. During the final stage the flow in these cells gradually decays due to the spin‐down/spin‐up mechanism provided by the Ekman boundary layer present at the bottom of each cell. Experiments have been performed with free‐surface and rigid‐lid upper boundary conditions, and the organization of the flow in these cases was observed to be essentially different. In particular, it was noted that the central cell in the free‐surface case is always cyclonic. A model for this behavior is advanced, in terms of the tendency of cyclonic vortices to move toward the rotation axis in the free‐surface configuration.

ISSN:0899-8213    

DOI:10.1063/1.857764

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

A cylindrical container, filled with a homogeneous suspension of heavy particles in a fluid, is instantaneously set into rapid rotation around its axis of symmetry. The subsequent mixture motion is investigated within the framework of an averaged continuum approach, by asymptotic and numerical solutions of the ‘‘mixture’’ and ‘‘two‐fluid’’ models, respectively. The resulting velocity field is similar to that of a homogeneous fluid [J. Fluid Mech.20, 383 (1964)], where three regions can be distinguished: a nonrotating, shrinking, core (I); the embedding, spinning but still undeveloped domain (III); and the Ekman layers (II), which transport fluid from region I into region III. This flow field induces a novel and peculiar solution for the volume fraction &agr;, whose details are governed by &lgr; (=ratio of separation to spin‐up time intervals). The results indicate that the initial &agr;(0) prevails in regions I and II, but considerable separation takes place in domain III—provided that &lgr; is not large. Therefore, during the spin‐up process, [&agr;/&agr;(0)] decays substantially not only with time, but also with the axial distance from the endplates (Ekman layers) and with radial distance from region I. Moreover, if &lgr;≪1, [&agr;/&agr;(0)]≪1 is expected in region III.

ISSN:0899-8213    

DOI:10.1063/1.857765

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Fluctuating flow with mass transfer induced by a rotating disk electrode with a time‐periodic angular velocity &OHgr;0[1+&agr; cos(p&tgr;)]bis analyzed by solving numerically the time‐dependent von Ka´rma´n self‐similar form of the Navier–Stokes and convective diffusion equations when the electrochemical reaction at the disk electrode is mass transfer limited. Results are presented for the full frequency range for several values of the waveform parameterband &agr;<1. At the intermediate frequencyp=1.24 (with &agr;=0.9,b=1), the time‐periodic flow undergoes a transition from a quasisteady von Ka´rma´n flow to a double boundary layer structure. The transition, which is characterized by an abrupt shift from phase lead (p<1.24) to phase lag (p>1.24) in the far‐field angular velocity, is discussed in terms of a viscous wave confined to the Stokes layer by axial inflow. The numerical results forb=1 are compared to the low‐ and high‐frequency asymptotic theories of Chawla and Verma [Proc. R. Soc. London Ser. A386, 163 (1983)], and it is shown that terms ofO(p−5/2) neglected by Chawla and Verma are required in the high‐frequency expansion to describe the flow in the far field. Electrochemical measurements of the fluctuating mass transfer limited flux induced by the modulating disk electrode are in excellent agreement with the numerical results. The low‐frequency calculations show that a judicious choice ofbresults in the cancellation of all harmonics other than the fundamental near the disk surface for certain field variables. The implications for electrochemical studies are discussed.

ISSN:0899-8213    

DOI:10.1063/1.857766

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

In this paper a concept of dilatation dissipation &egr;dfor high Reynolds number compressible turbulence is introduced. The concept is predicated on the existence of shocklike structures embedded within energetic turbulent eddies. A parametric expression for &egr;dis found that contains calculable parameters of a turbulent field: turbulence energy and length scale, rms (turbulent) Mach number, and the kurtosis of the fluctuating velocity. The dilatation dissipation is incorporated in a second‐order closure model for compressible mixing layers and model predictions of mean and turbulence quantities are presented and, where possible, compared with experiments. It is shown that the model is capable of predicting the reduction of layer growth rates as a function of the convective Mach numberMcin accordance with Papamoschou–Roshko experiments; the computations are also shown to compare well with available measurements of Reynolds stresses atMc=0.5–0.86. Finally, the physical implications of the new model and results obtained are discussed and compared with other existing explanations of the Mach number effect on mixing layer dynamics.

ISSN:0899-8213    

DOI:10.1063/1.857767

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Recent laboratory and field observations suggest that the effects of nonlinearity and dispersion may be significant for the evolution of Kelvin waves in rotating channels. Here, it is shown that a pair of Kelvin wave modes may interact with a third Poincare´ mode to form a resonant triad. The evolution of the triad is governed by the well‐known three‐wave interaction equations. The implications of this instability for naturally occurring Kelvin waves are discussed.

ISSN:0899-8213    

DOI:10.1063/1.857768

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The wave field resulting from a surface pressure or a bottom topography in a horizontally unbounded domain is studied. Upstream‐advancing waves successively generated by various forcing disturbances moving with near‐resonant speeds are found by numerically solving a forced Kadomtsev–Petviashvili (fKP) equation, which shows in its simplest form the interplay of a basic linear wave operator, longitudinal and transverse dispersion, nonlinearity, and forcing. Curved solitary waves are found as a slowly varying similarity solution of the Kadomtsev–Petviashvili (KP) equation, and are favorably compared with the upstream‐advancing waves numerically obtained.

ISSN:0899-8213    

DOI:10.1063/1.857769

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The scattering of a capillary–gravity wave by a surface‐piercing obstacle depends on the condition applied at the contact line between the fluid and the obstacle. A model for this condition that incorporates the effect of dynamic contact‐angle variation is used to determine the wave field close to the obstacle and at large distances from it. The solutions depend on the ratio between the wavelength of the incident wave and the radius of the obstacle, which is taken to be a circular cylinder, and on the relative size of the capillary and gravitational restoring forces. A third parameter is a constant of proportionality in the edge condition. Extreme values of this parameter relate to the special cases of orthogonal contact and of a fixed contact line. The strength of the scattered wave and the angular variation of its amplitude at large distances are calculated for a range of values of the parameters. The amplitude of the surface elevation on the boundary of the cylinder is also determined.

ISSN:0899-8213    

DOI:10.1063/1.857770

出版商:AIP    

年代:1990

数据来源: AIP