摘要:

An analysis is made of the stability of the interface between two compressible fluids in a gravity field when the fluids have translational velocities parallel to the interface. The effects of viscosity and surface tension are not included. The general dispersion relation is found to involve Whittaker functions and their first derivatives. Appropriate limits for these functions correspond to various physical conditions. The familiar Rayleigh‐Taylor and Kelvin‐Helmholtz criterions for stability are obtained in the incompressible limit. It is found that compressibility in the subsonic case decreases the range of stability. In the supersonic case, the stability found by Landau holds for only one disturbance mode. In general, stratification leads to instability of the interface for the supersonic case. A simple physical discussion of the Kelvin‐Helmholtz stability problem for incompressible or compressible flow concludes the paper.

ISSN:0031-9171    

DOI:10.1063/1.1711348

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

An investigation is made of some questions pertaining to the stability of potential flow. A formalism due to Eckart is adapted to obtain equations for the perturbations of a known steady potential flow, in a coordinate system defined by the potential function and the stream function. Eigensolutions having a time dependencee−i&ohgr;tare investigated for stability. It is shown that there exist no such stable solutions which are quadratically integrable in an unbounded space, or periodic in a closed space. A subclass of stable solutions is found, belonging to a continuous frequency spectrum. These are not quadratically integrable. The question of the existence of unstable but quadratically integrable solutions is not treated.

ISSN:0031-9171    

DOI:10.1063/1.1711349

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The variational principle which describes the stability problem of superposed fluids can be written in a form which is free of any ambiguities and allows a very simple physical interpretation.

ISSN:0031-9171    

DOI:10.1063/1.1711350

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The fundamental solution of the gravity waves due to a two‐dimensional point singularity submerged in a steady free‐surface flow of a stratified fluid is investigated. A linearized theory is formulated by using Love's equations. The effect of density stratification &rgr;0(y) and the gravity effect are characterized by two flow parameters &sgr; = −(d&rgr;0/dy)/&rgr;0and &lgr; =gL/U2, where &lgr;−½may be regarded as the internal Froude number ifLassumes a characteristic value of &sgr;−1. Two special cases of &sgr; and &lgr; are treated in this paper. In the first case of constant &sgr; (and arbitrary &lgr;) an exact mathematical analysis is carried out. It is shown that the flow is subcritical or supercritical according as &lgr;> or <½, in analogy to the corresponding states of channel flows. In addition to a potential surface wave, which exists only for &lgr;>½, there arises an internal wave which is attenuated at large distances for &lgr;>¼ and decays exponentially for &lgr;<¼. In the second example an asymptotic theory for large &lgr; is developed while &sgr;(y) may assume the profile roughly resembling the actual situation in an ocean where a pronounced maximum called a seasonal thermocline occurs. Internal waves are now propagated to the downstream infinity in a manner analogous to the channel propagation of sound in an inhomogeneous medium.

ISSN:0031-9171    

DOI:10.1063/1.1711351

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A ``natural time'' is defined in terms of the viscometric functions of a simple fluid. Its magnitude is a measure of the relative importance of normal‐stress effects. Such a time is shown to be an ordering parameter for departures from the theory of linear viscosity in fluids with fading memory. The frequency dependence of the absorption and phase shift in the diffusion of forced sinusoidal shearing at the boundary of a semi‐infinite mass of fluid are shown to depend critically upon the natural time.

ISSN:0031-9171    

DOI:10.1063/1.1711352

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

In the oscillating motion of an incompressible viscoelastic fluid in a pipe, at high Reynolds number the root‐mean‐square axial velocity has its maximum value in a boundary layer at the wall of the tube. The elasticity of the fluid can make this annular effect much more pronounced than it is in the case of a Newtonian viscous fluid. The analysis is carried out for small‐amplitude oscillations of a general viscoelastic fluid, and the exact solution for this case is compared with the solution obtained by the boundary‐layer approximation. The solution in the case of slow motion of arbitrary amplitude is also considered, and it is shown that no annular effect occurs in this case.

ISSN:0031-9171    

DOI:10.1063/1.1711353

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A numerical method has been used to solve completely the full equations for the motion of a viscous, heat‐conducting, incompressible fluid flowing through a channel past a rectangular cylinder. The dynamics of the unsteady flow were made visible by means of a number of different types of contour plots, and selected ones are presented and discussed to illustrate various newly discovered features of the von Ka´rma´n vortex street. In addition, the heat transfer was measured from the heated rear of the cylinder to the colder fluid, with data presented in the form of Nusselt number correlated with Reynolds number. Corrections are derived for blockage, and Prandtl number scaling is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1711354

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

Onsager's conservative cascade model used to deduce the turbulent energy spectrum in the isotropic ``inertial range,'' is generalized in three different ways, with examples taken from the turbulent mixing problem. (a) Extension to a nonconservative cascade, mixing with a first‐order isothermal chemical reaction, is presented more compactly than an earlier treatment and is applied to a new case. (b) Application to mixing at wavenumbers in the viscous range is indicated briefly. (c) Extension is made to a dual cascade, a model for turbulent mixing with a second‐order isothermal reaction. The nonlinearity of the reaction causes spectral transfer.

ISSN:0031-9171    

DOI:10.1063/1.1711355

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A quantity is defined which measures the degree of complication of a turbulent flow. It indicates the amount of information necessary per unit volume to describe the turbulence with an accuracy comparable to thermal agitation. It represents a small supplement to the entropy of the fluid. It is also found that maximum intricacy corresponds to a maximum rate of energy dissipation.

ISSN:0031-9171    

DOI:10.1063/1.1711356

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The direct‐interaction approximation for turbulence maintained by stationary, isotropic, random stirring forces is formulated in the wavenumber‐frequency domain. Further, simplifying approximations are made. The final equations involve the wavenumber energy‐spectrum, a characteristic correlation frequency for each wavenumber, and a characteristic response frequency for each wavenumber. A relation is exhibited between the simplified equations and a Fokker‐Planck type approximation recently proposed by Edwards.

ISSN:0031-9171    

DOI:10.1063/1.1711357

出版商:AIP    

年代:1964

数据来源: AIP