摘要:

The method of energy is used to study the stability of transport in a drop which is characterized by an impulsive change in boundary temperature or concentration. Instabilities driven by interfacial‐tension gradients are considered for diffusive base states in which a spherical drop is either stagnant or has an internal circulation at high Peclet number. Two stability criteria are considered for the stagnant drop; strong stability, for which an exponential decay of the disturbance energy is guaranteed; and marginal stability, for which the disturbance energy is less than or equal to its initial value. The strong stability criterion is obtained for the circulating drop. In this latter case, properties of the solution to the dynamic equations are used to constrain the class of admissible functions in the energy theory. Stability curves generated in the Marangoni number‐time plane clearly show the presence of both an onset time and a decay time for the disturbances. Comparison with limited available experimental data shows that predictions based upon the theory are observed qualitatively.

ISSN:0031-9171    

DOI:10.1063/1.863421

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

A spatial stability study of the developing flow in a pipe shows that the critical frequency and wavenumber for the Hornbeck profile are larger than those for the Sparrow profile, but the critical Reynolds number is smaller. Results for the Hornbeck profile are found to be closer to the experimental data.

ISSN:0031-9171    

DOI:10.1063/1.863422

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The problems of Stokes’ flow through corrugated pipes are considered. The corrugations are of small amplitude e and are modeled by stationary random noises. A perturbation solution [up toO(e2)] is developed showing that the pressure drop enhancement is an orderO(e2) effect and is always positive. Furthermore, for slowly varying corrugations, the pressure drop enhancement depends on the statistics of the corrugations em(z) only through its mean square e2<m2≳ and can be predicted by the simpler lubrication approach.

ISSN:0031-9171    

DOI:10.1063/1.863423

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The rotational distribution and collision numberZrof para‐H2in the He shock wave are studied using the master equation and the quantum mechanical rate constant obtained by Rabitz and Zarur. For high Mach number, at the initial stage, the rotational distribution indicates a merging pattern of two Boltzmann distributions at the lower and higher rotational levels corresponding to the pre‐shock temperatureT1and the reduced temperatureT2Tc/(T2+Tc), whereT2andTcare the post‐shock and rate‐constant temperatures, respectively. The rotational distribution at the final stage indicates a non‐Boltzmann distribution with underpopulation at the higher levels, which is also observed for low Mach number. The rotational collision numberZrover the period of the rotational relaxation is found to show a step pattern with the plateaus corresponding to the rotational collision numberZjj′of the two‐level systems (jj′) = (02), (24), (46),....

ISSN:0031-9171    

DOI:10.1063/1.863424

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The transport equation for the joint probability density function of velocity and scalars is shown to provide a good basis for modeling turbulent reactive flows. As in the equation for the probability density function of the scalars alone, nonlinear reaction schemes can be treated without approximation. The advantage of considering the joint probability density function equation is that convection (by both the mean and fluctuating velocities) appears in closed form. Consequently, the gradient‐diffusion assumption for turbulent transport is avoided. Closure approximations are presented for the terms involving the fluctuating pressure and viscous and diffusive mixing. These models can be expected to be reliable since they are compatible with accurate and proven Reynolds‐stress models. The resulting modeled transport equation for the joint probability density function can be solved by the Monte‐Carlo method for inhomogeneous flows with complex reactions.

ISSN:0031-9171    

DOI:10.1063/1.863425

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

Additional experimental results relative to the temperature in the thermal mixing layer downstream of a partially heated turbulence grid are given. Comparison is made of the distributions of mean temperature and temperature intensity with previous data. New results correspond to the characteristics of the higher moments, to the probability density functions at various points within the mixing layer, and the thickness of the temperature interface on the cold side of the layer. The present inability to predict the peak value of the temperature intensity is discussed.

ISSN:0031-9171    

DOI:10.1063/1.863426

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

A method of matching is applied to the energy spectrum equations in the modified cumulant expansion theory for Burgers and two‐ and three‐dimensional Navier–Stokes turbulence, in order to investigate the asymptotic behavior of the energy spectrum in the limit of large Reynolds number and time. It is shown analytically that the spectrum has a similar structure with respect to both Reynolds number and time, and that there is no single similarity law which is valid throughout the wavenumbers, but instead there are several subranges of the wavenumbers which have different similarity laws.

ISSN:0031-9171    

DOI:10.1063/1.863427

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

Many of the equations encountered in fluid dynamics and plasma physics are cubically nonlinear. The properties of a relatively simple statistical theory of cubically nonlinear equations, analogous to Kraichnan’s direct interaction approximation for quadratically nonlinear equations, are explored. Its predictions are compared with the numerical solution of a set of equations called the random‐coupling model; good agreement is found.

ISSN:0031-9171    

DOI:10.1063/1.863428

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The stability of an electrostatic Bernstein–Greene–Kruskal equilibrium by Lewis and Symon’s general linear stability analysis for spatially inhomogeneous Vlasov equilibria, which employs eigenfunctions and eigenvalues of the equilibrium Liouville operator and the modified Poisson operator, is considered. Analytic expressions for the Liouville eigenfuctions and eigenvalues have already been given; approximate analytic expressions for the dominant eigenfunction and eigenvalue of the modified Poisson operator are given. In the kinetic limit three methods are given: (i) the perturbation method, (ii) the Rayleigh–Ritz method, and (iii) a method based on a Hill’s equation. In the fluid limit the Rayleigh–Ritz method is used. The dominant eigenfunction and eigenvalue are then substituted in the dispersion relation and the growth rate calculated. The growth rate agrees very well with previous results found by numerical simulation and by modified Poisson eigenfunctions calculated numerically.

ISSN:0031-9171    

DOI:10.1063/1.863429

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

Energy transport from weak electrostatic microfluctuations, driven unstable by density and temperature gradients perpendicular to a uniform magnetic field in a Vlasov plasma, is calculated. Using the local approximation and assuming resonance broadening as the saturation mechanism, a consistent procedure is used to evaluate and compare the cross‐field energy transport due to enhanced microfluctuations from the universal, lower hybrid, and ion‐acoustic density drift, and the ion, electron, and lower hybrid temperature drift instabilities. If a temperature gradient is the primary source of free energy, the resultant enhanced fluctuations cause a cross‐field thermal energy loss rate which is much greater than the energy loss rate associated with cross‐field particle transport.

ISSN:0031-9171    

DOI:10.1063/1.863417

出版商:AIP    

年代:1981

数据来源: AIP