摘要:

The Richtmyer–Meshkov instability of a two‐liquid system is investigated experimentally. These experiments utilize a novel technique that circumvents many of the experimental difficulties that have previously limited the study of Richtmyer–Meshkov instability. The instability is generated by vertically accelerating a tank containing two stratified liquids by bouncing it off of a fixed coil spring. A controlled two‐dimensional sinusoidal initial shape is given to the interface by oscillating the container in the horizontal direction to produce standing waves. The motion of the interface is recorded during the experiments using standard video photography. Instability growth rates are measured and compared with existing linear theory. Disagreement between measured growth rates and the theory are accredited to the finite bounce length. When the linear stability theory is modified to account for an acceleration pulse of finite duration, much better agreement is attained. Late time growth curves of many different experiments seem to collapse to a single curve when correlated with the circulation deposited by the impulsive acceleration. A theory based on modeling the late time evolution of the instability using a row of vortices is developed. The growth curve given by this model has similar shape to those measured, but underestimates the late‐time growth rate. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868794

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A Lagrangian for strongly nonlinear unsteady water waves (including overturning waves) is obtained. It is shown that the system of quadratic equations for the Stokes coefficients, which determine the shape of a steady wave (discovered by Longuet‐Higgins 100 years after Stokes derived his system of cubic equations) directly follows from the canonical system of Lagrange equations. Applications to the investigation of the stability of water waves and to the construction of numerical schemes are pointed out. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868795

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Wave disturbances caused by the uniform translatory motion of a submerged body on or beneath the free surface of a viscous fluid are investigated analytically. The submerged body is idealized as an Oseenlet or an Oseen doublet, and exact solutions in closed integral forms are obtained. Based on these exact solutions, asymptotic representations of the wave amplitude for large Reynolds numbers based on the deep‐water wavelength at large distances downstream of the body are derived. The results obtained show explicitly the effect of the laminar wake on the amplitude and the phase of the surface waves thus created. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868796

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

It is shown by way of nonlinear numerical simulations of flow restricted to two dimensions that a compact wavepacket of large‐amplitude internal gravity waves incident upon a weakly stratified region in which the buoyancy frequency is less than the frequency of the wavepacket may partially transmit energy into this region through the generation of a wavepacket of lower frequency. In part, the transmission of waves occurs due to the transient nature of the forcing by the incident wavepacket, but if the amplitude of the wavepacket is moderately large, weakly nonlinear effects may act to significantly increase the proportion of the wavepacket that is transmitted. For a range of simulations initialized with wavepackets of different amplitude and vertical extent, the characteristics of the reflected and transmitted waves are analyzed and reflection coefficients are calculated. An explanation for how the nonlinear transmission mechanism operates is given by demonstrating that the wave induced mean‐flow, which is shown to be approximately equal to the horizontal wave pseudomomentum expressed in Eulerian variables, acts to adjust the frequency of the incident waves. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868797

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Some recent results for the force on a translating rigid three‐dimensional body in incompressible flow, in which the integration is over the vorticity field rather than surface pressure, are interpreted from a point of view that distinguishes changes of fluid impulse directly attributable to the vorticity field from those due to its image system in the body. An expression is first derived geometrically for a sphere in inviscid fluid; the flow is taken to consist of discrete vortex loops whose change in impulse, and that of the image system in the sphere, are calculatedviatheir projected areas. As an example, the force on a sphere due to an infinite line vortex is calculated exactly. To generalize the geometrical derivation to bodies of any shape, a reciprocal theorem is proved concerning the impulse of the image system of a dipole. This yields the inviscid form of a result derived mathematically by Howe [J. Fluid Mech.206, 131 (1989)]. Physical interpretations of the various terms in Howe’s expression are offered, and the relationship to a very similar independent result by Chang [Proc. R. Soc. London Ser. A437, 517 (1992)] is discussed. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868798

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Linear theory is used to analyze the stability of two‐dimensional boundary layer flows to stationary Go¨rtler vortices. The basic flow profiles in the boundary layer are described by the Falkner–Skan similarity solutions. We approach the problem both with local linear theory (with the streamwise position held fixed) and with a streamwise marching technique (to represent the evolution of the inlet disturbance). Comparisons of solutions obtained by the two methods are presented: The results are consistent in showing that adverse pressure gradients are destabilizing, as in the case of Tollmien–Schlichting waves. This is at odds with recent findings by Otto and Denier and underscores the sensitivity of the results to initial conditions. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868799

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The stability of the moving contact line is examined for both Newtonian and viscoelastic fluids. Two methods for relieving the contact line singularity are chosen: matching the free surface profile to a precursor film of thicknessb, and introducing slip at the solid substrate. The linear stability of the Newtonian capillary ridge with the precursor film model was first examined by Troianetal. [Europhys. Lett.10, 25 (1989)]. Using energy analysis, we show that in this case the stability of the advancing capillary ridge is governed by rearrangement of fluid in the flow direction, whereby thicker regions develop that advance more rapidly under the influence of a body force. In addition, we solve the Newtonian linear stability problem for the slip model and obtain results very similar to those from the precursor film model. Interestingly, stability results for the two models comparequantitativelywhen the precursor film thicknessbis numerically equal to the slip parameter &agr;. With the slip model, it is possible to examine the effect of contact angle on the stability of the advancing front, which, for small contact angles, was found to be independent of the contact angle. The stability of an Oldroyd‐B fluid was examined via perturbation theory in Weissenberg number. It is found that elastic effects tend to stabilize the capillary ridge for the precursor film model, and this effect is more pronounced as the precursor film thickness is reduced. The perturbation result was examined in detail, indicating that viscoelastic stabilization arises primarily due to changes of momentum transfer in the flow direction, while elasticity has little effect on the response of the fluid to flow in the spanwise direction. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868800

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Laminar vortex shedding behind a circular cylinder and its control using splitter plates attached to the cylinder are simulated. The vortex shedding behind a circular cylinder completely disappears when the length of the splitter plate is larger than a critical length, and this critical length is found to be proportional to the Reynolds number. The Strouhal number of the vortex shedding is rapidly decreasing with the increased plate length until the plate length (l) is nearly the same as the cylinder diameter (d). On the other hand, at 1<l/d<2, the control shows two different behaviors for the Reynolds numbers investigated. The net drag is significantly reduced by the splitter plate, and there exists an optimum length of the plate for minimum drag at a given Reynolds number. From an examination of the instantaneous flow fields, it is found that the Strouhal number modification by the splitter plate is closely related to the size of the primary vortex behind the cylinder and the length of the plate. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868801

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The stability of periodic arrays of Mallier–Maslowe or Kelvin–Stuart vortices is discussed. We derive with the energy‐Casimir stability method the nonlinear stability of this solution in the inviscid case as a function of the solution parameters and of the domain size. We exhibit the maximum size of the domain for which the vortex street is stable. By adapting a numerical time‐stepping code, we calculate the linear stability of the Mallier–Maslowe solution in the presence of viscosity and compensating forcing. Finally, the results are discussed and compared to a recent experiment in fluids performed by Tabelingetal. [Europhy. Lett.3, 459 (1987)]. Electromagnetically driven counter‐rotating vortices are unstable above a critical electric current, and give way to co‐rotating vortices. The importance of the friction at the bottom of the experimental apparatus is also discussed. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868802

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

This article is devoted to the study of the rotating disk flow instability. This inflectional‐type instability, called a cross‐flow instability, exemplary of the transition to turbulence in three‐dimensional boundary layers. We first present the experimental marginal stability curve of unstable waves obtained by hot‐film probe measurements and compare it with the theoretical results available in the literature. The experiment is in accordance with different theoretical determinations of the linear threshold, but we note a difference between experimental and theoretical critical wave‐number values. The unstable wave dynamics is then investigated by means of experimental dispersion curves (linking frequencies to the wave‐number vector components) determined by two‐probe measurements. The results show, in particular, the existence of traveling dispersive waves in the boundary layer of the rotating disk. Finally, we show that the emergence of nonlinear effects occurs very early in the system, far from the transition point. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868803

出版商:AIP    

年代:1996

数据来源: AIP