Six flow modes are distinguished in the flow-focusing experiments of a liquid jet forced by a high-speed air stream. The domains of the modes are identified on the parameter space of the liquid flow rateQland the gas pressure drop Δpg. The disturbance wavelength λ and breakup lengthLof the jet are also measured. A theoretical model considering axisymmetric disturbances is proposed, and a basic velocity profile of hyperbolic-tangent function is utilized. The linear temporal and spatio-temporal instability analyses are carried out using the Chebyshev collocation method. The effects of the flow parameters and the velocity profile on the flow instability are discussed. The temporal instability analysis demonstrates that the interfacial shear causes the instability of short waves and retards the instability of long waves. Moreover, the spatio-temporal instability analysis gives the transition boundary between the absolute and convective instability (AI/CI). The most unstable wavelength predicted by the temporal instability analysis and the AI/CI boundary predicted by the spatio-temporal instability analysis are in good agreement with the experimental results.

The flapping coupling between two filaments is studied theoretically and experimentally in this paper. A temporal linear instability analysis is carried out based on a simplified hydrodynamic model. The dispersion relationship between the eigen-frequency ω and wavenumber k is expressed by a quartic equation. Two special cases of flapping coupling, i.e. two identical filaments having the same length and two filaments having different lengths, are studied in detail. In the case of two identical filaments, the theoretical analysis predicts four coupling modes, i.e. the stretched-straight mode, the antisymmetrical in-phase mode, the symmetrical out-of-phase mode and the indefinite mode. The theory also predicts the existence of an eigenfrequency jump during transition between the in-phase and out-of-phase modes, which has been observed in previous experiments and numerical simulations. In the case of two filaments having different lengths, four modes similar to those in the former case are identified theoretically. The distribution of coupling modes for both the cases is shown in two planes. One is a dimensionless plane of S vs. U, where S is the density ratio of solid filament to fluid and U2 is the ratio of fluid kinetic energy to solid elastic potential energy. The other is a dimensional plane of the half-distance (h) between two filaments vs. the filament length (L). Relevant experiments are carried out in a soap-film tunnel and the stable and unstable modes are observed. Theory and experiment are compared in detail. It should be noted that the model used in our analysis is a very simplified one that can provide intuitional analytical results of the coupling modes as well as their qualitative distributions. The factors neglected in our model, such as vortex shedding, viscous and nonlinear effects, do not allow the model to predict results precisely consistent with the experiments. Moreover, the Strouhal numbers of the flapping filaments are found to be generally around a fixed value in the experiments for both cases, implying that the filaments try to maintain a lower potential energy state.

A theory of three-dimensional incompressible flow separation is presented in terms of the on-wall signatures of the flow. Some long-standing controversial issues are revisited and answers given, such as the inconsistency of the separation criteria based on the topological theory and “open separation,” and whether a separation line is an asymptote or envelope of neighboring skin-friction lines. General criteria for identifying an “open” or “closed” flow separation zone and separation line (including the initial point of the latter), steady and unsteady, are obtained, which apply to a generic smooth curved wall at any Reynolds numbers. The criteria are found to be most clearly given in terms of on-wall signatures of vorticity dynamics. These are then specified to steady boundary layer separation at large Reynolds numbers. A scale analysis under mild assumptions leads to a three-dimensional triple-deck structure near a generic boundary layer separation line. Criteria are presented for “separation watch,” which tells that a boundary-layer may soon break away, and for “separation warning,” which identifies the vorticity characteristics in an already formed boundary-layer separation zone and along a boundary-layer separation line. Flow behavior and its dependence on outer flow conditions are examined qualitatively. A numerical example is given which confirms the predictions of the theory.

The fluid term in the Biot-Gassmann equation plays an important role in reservoir fluid discrimination. The density term imbedded in the fluid term, however, is difficult to estimate because it is less sensitive to seismic amplitude variations. We combined poroelasticity theory, amplitude variation with offset (AVO) inversion, and identification of P- and S-wave moduli to present a stable and physically meaningful method to estimate the fluid term, with no need for density information from prestack seismic data. We used poroelasticity theory to express the fluid term as a function of P- and S-wave moduli. The use of P- and S-wave moduli made the derivation physically meaningful and natural. Then we derived an AVO approximation in terms of these moduli, which can then be directly inverted from seismic data. Furthermore, this practical and robust AVO-inversion technique was developed in a Bayesian framework. The objective was to obtain the maximum a posteriori solution for the P-wave modulus, S-wave modulus, and density. Gaussian and Cauchy distributions were used for the likelihood and a priori probability distributions, respectively. The introduction of a low-frequency constraint and statistical probability information to the objective function rendered the inversion more stable and less sensitive to the initial model. Tests on synthetic data showed that all the parameters can be estimated well when no noise is present and the estimated P- and S-wave moduli were still reasonable with moderate noise and rather smooth initial model parameters. A test on a real data set showed that the estimated fluid term was in good agreement with the results of drilling.

A low-dimensional Galerkin method, initiated by Noack and Eckelmann ͓Physica D 56, 151 ͑1992͔͒, for the prediction of the flow field around a stationary two-dimensional circular cylinder in a uniform stream at low Reynolds number is generalized to the case of a rotating and translating cylinder. The Hopf bifurcation describing the transition from steady to time-periodic solution is investigated. A curve indicating the transitional boundary is given in the two-dimensional parameter plane of Reynolds number Re and rotating parameter ␣. Our results show that rotation may delay the onset of vortex street and decrease the vortex-shedding frequency. © 1996 American Institute of Physics. ͓S1070-6631͑96͒00107-9͔The problem of the flow around a uniformly rotating and translating circular cylinder has been investigated by several researchers due to its engineering importance and academic interest. Badr et al. 1 numerically simulated the steady and unsteady flow past a rotating circular cylinder at low Reynolds numbers Re with rotating parameter ␣, in which Re is based on the cylinder radius R and the incoming velocity U ϱ and ␣ϭR /U ϱ , where represents the angular velocity of the rotating cylinder. Ingham, 2 Ingham and Tang, 3 D'Alessio and Dennis 4 considered numerical solutions of the steadystate N-S equation at subcritical Re. The investigations of the unsteady flow for supercritical Reynolds numbers are relatively fewer than the case of the steady-state flow. Badr et al. 5 numerically studied the time-dependent flow past an impulsively rotating and translating circular cylinder started from rest for ReϾ200, while Coutanceau and Menard 6 gave corresponding experimental results. Chang and Chen 7 investigated the same problem at some higher Re for 0р␣Ͻ2, and suggested there are three modes of vortex shedding existing in wakes depending on Re and ␣.Meanwhile, the research on the bifurcation structure in an open-flow at low Reynolds numbers is of great interest. Provansal et al., 8 Sreenivasan et al., 9 and Schumm et al. 10 experimentally studied the onset of 2-D vortex shedding in the wakes behind a stationary circular cylinder and showed that the transition from the steady to the periodic flow is characterized by a Hopf bifurcation and can be described by the Stuart-Landau equation. Jackson, 11 Zebib 12 and Noack et al. 13,14 numerically investigated the onset of vortex shedding in flow past a stationary circular cylinder by applying the linear stability analysis to an autonomous dynamical system.Following Noack's work, 13 a low-dimensional Galerkin method ͑LDGM͒ is generalized to the case of a 2-D uniformly rotating and translating circular cylinder. Although the LDGM cannot compete with grid-based computational techniques for high accurate simulations of the velocity fields or the resolution of far-wake properties, it is confirmed to be an ideal tool for investigations on global stability and chaos-theoretical analysis. 13,14 In the present Galerkin method, the streamfunction is approximated by a finite ex- BRIEF CO...