Phys. Fluids A (1989-1993) - Physics of Fluids

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Wake mechanics for thrust generation in oscillating foils

M. S. Triantafyllou, G. S. Triantafyllou, and R. Gopalkrishnan

Phys. Fluids A 3, 2835 (1991); http://dx.doi.org/10.1063/1.858173 (3 pages) | Cited 35 times

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Foils oscillating transversely to an oncoming uniform flow produce, under certain conditions, thrust. It is shown through experimental data from flapping foils and data from fish observation that thrust develops through the formation of a reverse von Kármán street whose preferred Strouhal number is between 0.25 and 0.35, and that optimal foil efficiency is achieved within this Strouhal range.

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47.27.W-	Boundary-free shear flow turbulence
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.90.+a	Other topics in fluid dynamics (restricted to new topics in section 47)

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Flapping model of scalar mixing in turbulence

Alan R. Kerstein

Phys. Fluids A 3, 2838 (1991); http://dx.doi.org/10.1063/1.858174 (3 pages) | Cited 6 times

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Motivated by the fluctuating plume model of turbulent mixing downstream of a point source, a flapping model is formulated for application to other configurations. For the scalar mixing layer, simple expressions for single‐point scalar fluctuation statistics are obtained that agree with measurements. For a spatially homogeneous scalar mixing field, the family of probability density functions previously derived using mapping closure is reproduced. It is inferred that single‐point scalar statistics may depend primarily on large‐scale flapping motions in many cases of interest, and thus that multipoint statistics may be the principal indicators of finer‐scale mixing effects.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.27.T-	Turbulent transport processes

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Energy stability of thermocapillary convection in a model of the float‐zone crystal‐growth process. II: Nonaxisymmetric disturbances

G. P. Neitzel, C. C. Law, D. F. Jankowski, and H. D. Mittelmann

Phys. Fluids A 3, 2841 (1991); http://dx.doi.org/10.1063/1.857829 (6 pages) | Cited 22 times

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Energy‐stability theory has been applied to investigate the stability properties of thermocapillary convection in a half‐zone model of the float‐zone crystal‐growth process. An earlier axisymmetric model has been extended to permit nonaxisymmetric disturbances, thus determining sufficient conditions for stability to disturbances of arbitrary amplitude. The results for nonaxisymmetric disturbances are compared with earlier axisymmetric results, with linear‐stability results for a geometry with an infinitely long aspect ratio and with stability boundaries from recent laboratory experiments.

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47.20.Bp	Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
81.10.Aj	Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation

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Convective stability in the Rayleigh–Bénard and directional solidification problems: High‐frequency gravity modulation

A. A. Wheeler, G. B. McFadden, B. T. Murray, and S. R. Coriell

Phys. Fluids A 3, 2847 (1991); http://dx.doi.org/10.1063/1.857830 (12 pages) | Cited 12 times

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The effect of vertical, sinusoidal, time‐dependent gravitational acceleration on the onset of solutal convection during directional solidification is analyzed in the limit of large modulation frequency Ω. When the unmodulated state is unstable, the modulation amplitude required to stabilize the system is determined by the method of averaging, and is O(Ω). Comparison of the results from the averaged equations with numerical solutions of the full linear stability equations (based on Floquet theory) show that the difference is O(Ω^1/2). When the unmodulated state is stable, resonant modes of instability occur at large modulation amplitude. These are analyzed using matched asymptotic expansions to elucidate the boundary‐layer structure for both the Rayleigh–Bénard and directional solidification configurations. The leading‐order term for the modulation amplitude is of O(Ω²); the first‐order correction of O(Ω^3/2) is calculated, and the results are compared with numerical solutions of the full linear stability equations. Based on these analyses, a thorough examination of the dependence of the stability criteria on the unmodulated Rayleigh number, Schmidt number, and distribution coefficient, is carried out.

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47.20.Bp	Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.10.-g	General theory in fluid dynamics
02.60.-x	Numerical approximation and analysis

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Active control of convection

Jonathan Singer and Haim H. Bau

Phys. Fluids A 3, 2859 (1991); http://dx.doi.org/10.1063/1.857831 (7 pages) | Cited 21 times

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It is demonstrated theoretically that active (feedback) control can be used to alter the characteristics of thermal convection in a toroidal, vertical loop heated from below and cooled from above. As the temperature difference between the heated and cooled sections of the loop increases, the flow in the uncontrolled loop changes from no motion to steady, time‐independent motion to temporally oscillatory, chaotic motion. With the use of a feedback controller effecting small perturbations in the boundary conditions, one can maintain the no‐motion state at significantly higher temperature differences than the critical one corresponding to the onset of convection in the uncontrolled system. Alternatively, one can maintain steady, time‐independent flow under conditions in which the flow would otherwise be chaotic. That is, the controller can be used to suppress chaos. Likewise, it is possible to stabilize periodic nonstable orbits that exist in the chaotic regime of the uncontrolled system. Finally, the controller also can be used to induce chaos in otherwise laminar (fully predictable), nonchaotic flow.

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47.52.+j	Chaos in fluid dynamics
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.20.Bp	Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.27.T-	Turbulent transport processes

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Boundary‐layer analysis of the dynamics of axisymmetric capillary bridges

Abhay Borkar and John Tsamopoulos

Phys. Fluids A 3, 2866 (1991); http://dx.doi.org/10.1063/1.857832 (9 pages) | Cited 25 times

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Small‐amplitude oscillations of capillary bridges are examined in the limit of large modified Reynolds number. The contact line between the free surface of the bridge and the upper and lower supporting walls is allowed to undergo a restrained motion by taking its velocity to be proportional to the slope of the free surface there. It is found that the oscillation frequency and damping rate depend on the aspect ratio of the bridge, the mode being excited, the motion of the contact line, and the modified Reynolds number. Very good agreement with other studies is obtained for Re>100.

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47.15.Cb	Laminar boundary layers
47.15.km	Potential flows
47.35.-i	Hydrodynamic waves

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Viscous–inviscid interaction due to the freezing of a liquid flowing on a flat plate

Francisco J. Higuera

Phys. Fluids A 3, 2875 (1991); http://dx.doi.org/10.1063/1.857833 (12 pages)

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The solidification of a liquid flowing along a flat plate whose temperature presents a step reduction from a value above to a value below the melting temperature of the liquid is shown to promote a viscous–inviscid interaction region. The structure of the flow in this region and the growth of the solid phase crust above the plate are described in the limit of high Reynolds numbers using triple‐deck theory. Boundary‐layer separation, which is a regular process in the framework of triple‐deck theory, is shown to occur under appropriate conditions, namely for severe plate temperature reductions leading to thick solid crusts. A simplified approximate method is introduced to deal with these separated flows.

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47.15.Cb	Laminar boundary layers
44.25.+f	Natural convection
47.55.Kf	Particle-laden flows

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A three‐dimensional numerical study of flow separation and reattachment on a blunt plate

D. K. Tafti and S. P. Vanka

Phys. Fluids A 3, 2887 (1991); http://dx.doi.org/10.1063/1.858208 (23 pages) | Cited 16 times

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Three‐dimensional numerical simulation of the unsteady flow over a blunt plate held normal to a uniform stream has been carried out to study the physics of unsteady separation and reattachment. A finite‐difference procedure is used with 32 spanwise grid cells. In comparison with previous two‐dimensional results, it is observed that the inclusion of spanwise variations significantly improves the calculations and provides superior comparisons with experimental data. Mean turbulent quantities are calculated and found to be in good agreement with experiments. Instantaneous as well as statistical quantities describing the characteristic length and time scales of the large‐scale structures are also presented. The calculations have also been able to capture the experimentally observed low‐frequency unsteadiness of the separation bubble. In addition, a selective high‐frequency shedding from the separated shear layer was found to occur with a period equal to that of the low‐frequency unsteadiness.

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47.27.N-	Wall-bounded shear flow turbulence
47.27.W-	Boundary-free shear flow turbulence
02.70.-c	Computational techniques; simulations

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On the nonlinear stability of a high‐speed, axisymmetric boundary layer

C. David Pruett, Lian L. Ng, and Gordon Erlebacher

Phys. Fluids A 3, 2910 (1991); http://dx.doi.org/10.1063/1.857834 (17 pages) | Cited 6 times

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The stability of a high‐speed, axisymmetric boundary‐layer flow is investigated by means of secondary instability theory and direct numerical simulation. Parametric studies based on temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a hollow cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical solution of the compressible Navier–Stokes equations. Initial perturbations for the temporal direct numerical simulation consist of an axisymmetric ‘‘second‐mode’’ primary disturbance and a subharmonic secondary disturbance comprised of four oblique wave components. At small initial amplitudes of the secondary disturbance, growth rates obtained from the spectrally accurate numerical simulation agree to several significant digits with linear growth rates predicted by secondary instability theory. Qualitative agreement persists to relatively large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric ‘‘second‐mode’’ disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect, but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for peaks in the Reynolds stress components near the critical layer.

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47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.40.Ki	Supersonic and hypersonic flows
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.27.Cn	Transition to turbulence

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Enhancement of stability in uniformly elongating plastic jets with electromagnetic fields

David L. Littlefield

Phys. Fluids A 3, 2927 (1991); http://dx.doi.org/10.1063/1.857835 (9 pages) | Cited 3 times

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The stability of rapidly stretching, perfectly plastic jets when subjected to axial magnetic fields is studied in this analysis. The jet is assumed to be uniformly elongating, infinitely long, and isothermal. An axial magnetic field, assumed to be provided by a solenoid in the surrounding vacuum, is initiated at time t=0. Linear perturbation theory is employed to calculate the time evolution of small disturbances in the jet. Results of the calculations indicate that imposed axial magnetic fields inhibit the growth rates of instabilities in the jet. Entrained magnetic fields, however, are present after the jet leaves the solenoid, and increase the growth rates of disturbances. As a consequence, the overall growth rates are strongly dependent on the magnetic Reynolds number. This result is explained in terms of the applicable magnetohydrodynamic (MHD) stability mechanisms in the jet.

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47.20.-k	Flow instabilities
47.50.-d	Non-Newtonian fluid flows
47.65.-d	Magnetohydrodynamics and electrohydrodynamics
52.30.-q	Plasma dynamics and flow

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On the genesis of droplet stream microspeed dispersions

Melissa Orme

Phys. Fluids A 3, 2936 (1991); http://dx.doi.org/10.1063/1.857836 (12 pages) | Cited 11 times

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Mechanisms that govern uniform droplet generation have been investigated. Droplet formation of viscous low vapor pressure fluids has been achieved by imposing sinusoidal pressure disturbances on a capillary stream. The capillary stream breakup and subsequent droplet propagation took place in a vacuum so that there were no significant interactions with the surrounding atmosphere. Microfluctuations of the droplet speeds have been examined after the droplets have traveled approximately 30 000 droplet diameters, and can vary from 1×10⁻⁶ to 1×10⁻⁴ times the average droplet speed depending on forcing conditions. Growth rate measurements were made of the streams radial disturbance prior to breakup, and were found to be intrinsically related to the measurements of the droplet stream’s speed microfluctuations. From this relation, it is suggested that studies of the characteristics of the droplet stream gives information about the capillary wave instabilities, which lead to droplet formation. A model that describes the microfluctuations is developed and is in excellent agreement with the experimentally obtained values. The model suggests that the source of droplet stream microspeed dispersions is the growth of a noise disturbance that modulates the otherwise controlled periodic pressure perturbation, which initiates droplet breakup.

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47.27.wg	Turbulent jets
47.60.Kz	Flows and jets through nozzles
47.55.Kf	Particle-laden flows

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Microbubble skin friction reduction on an axisymmetric body under the influence of applied axial pressure gradients

H. Clark and S. Deutsch

Phys. Fluids A 3, 2948 (1991); http://dx.doi.org/10.1063/1.857837 (7 pages) | Cited 5 times

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The influence of both a favorable and an adverse applied axial pressure gradient on microbubble‐induced skin friction reduction was examined. An 87 mm diameter, 632 mm long model equipped with a 273 mm long cylindrical force balance was employed. Experiments were carried out in a 305 mm diameter water tunnel, at free‐stream speeds of 4.6, 7.6, 10.7, 13.7, and 16.8 m/sec. Air was injected at rates as high as 12×10⁻³ m³/sec. Measurement of the static pressure along the body with gas injection demonstrated that gas injection did not alter the pressure gradient and that the flow remained axisymmetric. Reductions in skin friction for the zero pressure gradient case agreed well with the earlier results of Deutsch and Castano [Phys. Fluids 29, 3590 (1986)]. The adverse‐gradient‐induced separation of the boundary layer for speeds at and above 7.6 m/sec, for air injection rates in excess of 5.0×10⁻³ m³/sec. The favorable gradient strongly inhibited the drag reduction mechanism [47].

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47.27.N-

Wall-bounded shear flow turbulence

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The added mass, Basset, and viscous drag coefficients in nondilute bubbly liquids undergoing small‐amplitude oscillatory motion

A. S. Sangani, D. Z. Zhang, and A. Prosperetti

Phys. Fluids A 3, 2955 (1991); http://dx.doi.org/10.1063/1.857838 (16 pages) | Cited 20 times

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The motion of bubbles dispersed in a liquid when a small‐amplitude oscillatory motion is imposed on the mixture is examined in the limit of small frequency and viscosity. Under these conditions, for bubbles with a stress‐free surface, the motion can be described in terms of added mass and viscous force coefficients. For bubbles contaminated with surface‐active impurities, the introduction of a further coefficient to parametrize the Basset force is necessary. These coefficients are calculated numerically for random configurations of bubbles by solving the appropriate multibubble interaction problem exactly using a method of multipole expansion. Results obtained by averaging over several configurations are presented. Comparison of the results with those for periodic arrays of bubbles shows that these coefficients are, in general, relatively insensitive to the detailed spatial arrangement of the bubbles. On the basis of this observation, it is possible to estimate them via simple formulas derived analytically for dilute periodic arrays. The effect of surface tension and density of bubbles (or rigid particles in the case where the no‐slip boundary condition is applicable) is also examined and found to be rather small.

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47.55.Kf	Particle-laden flows
47.55.-t	Multiphase and stratified flows

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Dynamic behavior of liquid sheets

Adel Mansour and Norman Chigier

Phys. Fluids A 3, 2971 (1991); http://dx.doi.org/10.1063/1.857839 (10 pages) | Cited 24 times

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An experiment was conducted to study the aerodynamic instability of liquid sheets issuing from a two‐dimensional air‐assisted nozzle. Detailed measurements of the frequency of oscillation of the liquid sheet have been made. The measured vibrational frequencies were then correlated with the resulting spray angle. It was shown that the liquid sheet oscillations are dynamically similar to that of hard spring systems. For each air pressure, three distinct modes of breakup are distinguished. At low liquid flow rates, the sinusoidal mode of breakup is dominant. At intermediate liquid flow rates, both the sinusoidal and the dilational modes are superimposed on the liquid sheet. With a further increase in liquid flow rate, the liquid sheet oscillations mainly become of the dilational type. It was also shown that the effect of introducing air in the nozzle is similar to the effect of inducing forced vibrations on the nozzle jaws. Thus, for each air flow rate, there is a specific vibration frequency for the nozzle. The frequency of these vibrations is proportional to the air velocity. As the liquid sheet natural frequency approaches that of the nozzle, resonance is established. At resonance, the maximum spray angle is achieved.

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68.03.-g	Gas-liquid and vacuum-liquid interfaces
68.05.-n	Liquid-liquid interfaces
47.35.-i	Hydrodynamic waves
47.27.W-	Boundary-free shear flow turbulence
47.55.Kf	Particle-laden flows

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Impinging jets atomization

E. A. Ibrahim and A. J. Przekwas

Phys. Fluids A 3, 2981 (1991); http://dx.doi.org/10.1063/1.857840 (7 pages) | Cited 15 times

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An analysis of the characteristics of the spray produced by an impinging‐jet injector is presented. Predictions of the spray droplet size and distribution are obtained through studying the formation and disintegration of the liquid sheet formed by the impact of two cylindrical jets of the same diameter and momentum. Two breakup regimes of the sheet are considered depending on Weber number, with transition occurring at Weber numbers between 500 and 2000. In the lower Weber number regime, the breakup is due to Taylor cardioidal waves, while at Weber number higher than 2000, the sheet disintegration is by the growth of Kelvin–Helmholtz instability waves. Theoretical expressions to predict the sheet thickness and shape are derived for the low Weber number breakup regime. An existing mathematical analysis of Kelvin–Helmholtz instability of radially moving liquid sheets is adopted in the predictions of resultant drop sizes by sheet breakup at Weber numbers greater than 2000. Comparisons of present theoretical results with experimental measurements and empirical correlations reported in the literature reveal favorable agreement.

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47.20.Dr	Surface-tension-driven instability
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.35.-i	Hydrodynamic waves
47.32.Ef	Rotating and swirling flows

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Secondary fluid flow in a rotating narrow cylindrical annulus heated from the side

M. Kropp and F. H. Busse

Phys. Fluids A 3, 2988 (1991); http://dx.doi.org/10.1063/1.857841 (7 pages) | Cited 3 times

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The problem of bifurcations in the manifold of solutions for fluid flow in the narrow gap between two corotating coaxial vertical cylinders is considered in the case when one of the cylindrical walls is heated, the other is cooled. This problem can be regarded as an extension to the rotating case of the well‐known problem of the flow between two parallel vertical walls kept at different temperatures. The influence of rotation modifies the mechanisms of monotonic and oscillatory instabilities and introduces a new instability. Spiraling rolls instead of axisymmetric motions describe the onset of secondary flows. The Coriolis force leads to a strong reduction of the critical Grashof number. Linear and weakly nonlinear properties of the instabilities are discussed in dependence on the rotation parameter, the Grashof number, and the Prandtl number.

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47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.27.T-	Turbulent transport processes
47.35.-i	Hydrodynamic waves

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Nonlinear free‐surface flows past a submerged inclined flat plate

J.‐M. Vanden‐Broeck and Frédéric Dias

Phys. Fluids A 3, 2995 (1991); http://dx.doi.org/10.1063/1.857842 (6 pages)

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Steady two‐dimensional free‐surface flows past an inclined flat plate submerged in a channel of finite depth are calculated numerically. The flow is assumed to be supercritical. The numerical scheme is based on finite differences. It is shown that there are families of solutions for which there is no force exerted on the plate. In addition, solutions for a horizontal semi‐infinite plate are calculated by series truncation.

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47.35.-i

Hydrodynamic waves

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Nonlinear waves traveling upon a front of solitons

M. Z. Pesenson

Phys. Fluids A 3, 3001 (1991); http://dx.doi.org/10.1063/1.857843 (6 pages) | Cited 1 time

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The equation for perturbations with finite amplitude and finite wavelength traveling on a front of exponential solitons has been derived by means of an asymptotic procedure. The shock waves traveling on a front of exponentially decaying solitons, like the ‘‘shock–shocks’’ of Whitham, have been described. Stability conditions of solitons relative to the multidimensional perturbations have also been obtained. The spectrum of the soliton vibrations in the stable case, the stability threshold, and the growth rate in the unstable case have been calculated. The resulting equation is a generalization of the nonlinear quasioptics for the modulation of solitons with finite front width, in this case, the nonlinearity and diffusion of the perturbations are not independent.

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47.35.-i	Hydrodynamic waves
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.55.Hd	Stratified flows
47.90.+a	Other topics in fluid dynamics (restricted to new topics in section 47)

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Fourth‐order Lagrangian of short waves riding on long waves

Jun Zhang

Phys. Fluids A 3, 3007 (1991); http://dx.doi.org/10.1063/1.857844 (7 pages) | Cited 1 time

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Applying the variational principle, a fourth‐order wave‐action conservation and second‐order dispersion relation of a short‐wave train riding on a long wave are derived from its fourth‐order Lagrangian. The modulated nonlinear Schrödinger equation describing the evolution of short waves on long waves is obtained through the combination of the wave‐action conservation and dispersion relation, and is identical to the previous derivation through a WKB perturbation method. The relationship between a Schrödinger equation and a Lagrangian is explored, revealing that their solutions for a steady short‐wave train are generally different in accuracy except for the leading order.

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47.35.-i	Hydrodynamic waves
41.20.Jb	Electromagnetic wave propagation; radiowave propagation

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On the interaction between first‐ and second‐mode waves in a supersonic boundary layer

L. Maestrello, A. Bayliss, and R. Krishnan

Phys. Fluids A 3, 3014 (1991); http://dx.doi.org/10.1063/1.857845 (7 pages) | Cited 3 times

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Linear stability theory predicts two or more types of unstable disturbances in a sufficiently high‐speed boundary layer. These include the first mode, which is similar to the Tollmien–Schlichting waves found in low‐speed flows, and the second mode, which does not depend strongly on the viscosity. Generally the most unstable first mode is three dimensional while the most unstable second mode is two dimensional. The interaction between these two spatially unstable modes are studied by direct solution of the three‐dimensional Navier–Stokes equations. It is found that the two‐dimensional second mode causes a significant increase in the nonlinearity and in the three‐dimensionality of the flow field. The results suggest that this interaction may accelerate transition for flows where the second mode has a significant growth rate.

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47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.40.Ki	Supersonic and hypersonic flows
43.28.Py	Interaction of fluid motion and sound, Doppler effect, and sound in flow ducts

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Fourth‐order nonlinear evolution equation for two Stokes wave trains in deep water

A. K. Dhar and K. P. Das

Phys. Fluids A 3, 3021 (1991); http://dx.doi.org/10.1063/1.858209 (6 pages) | Cited 11 times

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Fourth‐order nonlinear evolution equations, which are a good starting point for the study of nonlinear water waves as first pointed out by Dysthe [Proc. R. Soc. London Ser. A 369, 105 (1979)] and later elaborated by Janssen [J. Fluid Mech. 126, 1 (1983)], are derived for a deep‐water surface gravity wave packet in the presence of a second wave packet. Here it is assumed that the space variation of the amplitude takes place only in a direction along which the group velocity projection of the two waves overlap. Stability analysis is made for a uniform Stokes wave train in the presence of a second wave train. Graphs are plotted for maximum growth rate of instability and for wave number at marginal stability against wave steepness. Significant deviations are noticed from the results obtained from the third‐order evolution equations which consist of two coupled nonlinear Schrödinger equations.

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47.35.-i

Hydrodynamic waves

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A point vortex dipole model of an isolated modon

Dana D. Hobson

Phys. Fluids A 3, 3027 (1991); http://dx.doi.org/10.1063/1.857846 (7 pages) | Cited 15 times

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A point vortex dipole model for an isolated modon governed by the Charney–Hasegawa–Mima (CHM) equation is developed, building on the point vortex formulation of Zabusky and McWilliams [Phys. Fluids 25, 2175 (1982)]. The model dipole is compared to the exact modon solution in order to determine parameter values for which the model dipole matches the modon’s speed and far‐field behavior. The model allows one to study nonuniform motions analytically. It predicts that right‐moving modons in uniform motion should be stable in the sense that their paths exhibit small‐amplitude oscillations in response to small perturbations of their initial orientation. It also predicts that left‐moving modons in uniform motion should be unstable, being pushed into finite‐amplitude motions by arbitrarily small perturbations. These predictions are confirmed by direct numerical simulation of modons evolving under the CHM equation. It is noted that although the distribution of vorticity within modons may be Lyapunov stable in nearly uniform motions, the paths of modons may be unstable to asymmetric perturbations.

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47.15.ki	Inviscid flows with vorticity
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking

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A binomial Langevin model for turbulent mixing

L. Valiño and C. Dopazo

Phys. Fluids A 3, 3034 (1991); http://dx.doi.org/10.1063/1.857847 (4 pages) | Cited 39 times

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A Langevin model with binomial random diffusion replacing the classical Wiener process is proposed to model the turbulent mixing of a scalar convected by a field of statistically homogeneous turbulence. A Monte Carlo simulation is performed. The results display an excellent agreement with existing data from the numerical experiment of Eswaran and Pope [Phys. Fluids 31, 506 (1988)].

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.32.Ef	Rotating and swirling flows

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Comparison of velocity distribution functions in an argon shock wave between experiments and Monte Carlo calculations for Lennard‐Jones potential

Hiroaki Matsumoto and Katsuhisa Koura

Phys. Fluids A 3, 3038 (1991); http://dx.doi.org/10.1063/1.857848 (8 pages) | Cited 2 times

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The velocity distribution functions (VDF’s) in an argon normal shock wave at an upstream high Mach number 7.183 and low temperature 16 K are calculated using the null‐collision direct‐simulation Monte Carlo method for the Lennard‐Jones (LJ) potential to compare with the experimental results of Holtz and Muntz [Phys. Fluids 26, 2425 (1983)]. The convolved VDF’s for the LJ potential are in reasonable agreement with the measured data in early and late regions of the shock wave but significantly different in the middle region. This discrepancy cannot be explained by a possible uncertainty in the potential well depth. Moreover, the difference in the convolved VDF’s between the LJ potential and the softest and hardest unrealistic molecular models with no attractive force, i.e., the Maxwell molecule and hard sphere, is much smaller than the discrepancy between the experiments and Monte Carlo calculations.

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47.40.-x	Compressible flows; shock waves
34.50.-s	Scattering of atoms and molecules
02.50.Ng	Distribution theory and Monte Carlo studies
47.45.-n	Rarefied gas dynamics

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On the shock enhancement of confined supersonic mixing flows

P. J. Lu and K. C. Wu

Phys. Fluids A 3, 3046 (1991); http://dx.doi.org/10.1063/1.857849 (17 pages) | Cited 1 time

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Direct numerical simulations using high‐resolution total variation diminishing (TVD) scheme are performed for studying the shock enhancement of two‐dimensional confined (spatially growing) supersonic mixing flows. Several specially designed mixing enhancement schemes are examined with emphasis placed on the study of the fundamental aspects involved in the shock‐induced mixing enhancement process. The merits associated with these mixing enhancement schemes are evaluated based on a cost/effectiveness criterion, in which the cost paid for the total pressure loss encountered and the improvement in mixing gained are considered together. The results suggest that mixing enhancement using shock waves can only be effective if the stimulation is spatially persistent, and begins from the very upstream. Being motivated by this observation, an idea of using wavy‐wall configuration to generate the desirable periodic shock stimulation is proposed and investigated. The computed results show that, by an appropriate manipulation of the parameters including wall wavelength, relative phase shift between the top and bottom walls, as well as the amplitude of the waviness, considerable improvement in mixing efficiency can be achieved.

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