摘要:

The problem of determining the development with time of the flow of a viscous incompressible fluid outside a rotating sphere is considered. The sphere is started impulsively from rest to rotate with constant angular velocity about a diameter. The motion is governed by a coupled set of three nonlinear time‐dependent partial differential equations which are solved by first employing the semi‐analytical method of series truncation to reduce the number of independent variables by one and then solving numerically a finite set of partial differential equations in one space variable and the time. The calculations have been carried out on the assumption that the Reynolds number is very large. The physical properties of the flow are calculated as functions of the time and compared with existing solutions for large and small times. A radial jet is found to develop with time near the equator of the sphere as a consequence of the collision of the boundary layers.

ISSN:0031-9171    

DOI:10.1063/1.862466

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

For a one‐dimensional flow situation involving a source, a simple closed form solution for the mass density is obtained for the mass continuity equation by introducing a change in variable. Instead of functionalizing the flow in terms of the velocity, the starting time or transit time is used. This type of functionalization allows the individual trajectories to be obtained by algebraic or geometric means, avoiding the nonclosed form solution associated with integrating the velocity. For a time varying system, the integrals of mass, momentum, and energy all involve the mass density expression. By eliminating the mass density expression from these integrals and expressing the velocity in terms of one of the new time parameters, a set of equations is obtained which may be easier to solve than the original set of equations.

ISSN:0031-9171    

DOI:10.1063/1.862446

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

The evolution of an initially binary (zero unity) scalar field undergoing turbulent and molecular mixing is studied in terms of conservation equations for the probability density function of the scalar property. Attention is focused on the relaxation of the dynamic system to a state independent of the intial conditions. A few existing methods are discussed and evaluated and a new mechanistic model is proposed. Classical iteration techniques are used to obtain an equation for the single point probability density and the unperturbed Green’s function. It is suggested that use of the true Green’s function or perturbed propagator of the system might be necessary in order to obtain the correct evolution of the probability density function.

ISSN:0031-9171    

DOI:10.1063/1.862431

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

An experimental determination of statistical properties of the interface separating turbulent fluid and contiguous nonturbulent fluid in a slightly heated plane wake, subjected to a uniform and constant rate of strain, has been made by means of digital sampling and processing techniques. The results, which comprise intermittency factor and burst rate distributions, root‐mean‐square interface slopes and probability density functions of the durations of turbulent and nonturbulent fluid, indicate that, as in the case of the unstrained wake, the interface position may be regarded as a stationary Gaussian random variable.

ISSN:0031-9171    

DOI:10.1063/1.862432

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

The fundamental triad‐interaction system is the building block of the nonlinear interaction of the three‐dimensional Navier–Stokes equations. It satisfies incompressibility, conserves energy and helicity, preserves measure under the time evolution, and involves an arbitrary parameter taking any value in [0,2&pgr;]. Under several values of this parameter, it is found that the fundamental triad‐interaction system cannot be ergodic on the constant energy‐helicity surface because of the extraneous constants of motion other than energy and helicity. This at once implies that isotropy is not possible for the spectral tensor, for isotropy calls for mixing which is a stronger requirement than ergodicity. Although the dynamics of a single triad‐interaction system is not directly relevant to real homogeneous turbulence, a theoretical framework to investigate ergodicity and mixing and isotropy of the three‐dimensional turbulence model by consistently including many fundamental triad‐interaction systems is provided.

ISSN:0031-9171    

DOI:10.1063/1.862433

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

The stability of nonisothermal flow through porous media is investigated, when both density and viscosity variations with temperature are present. The instability phenomena are due to the buoyancy effect of a density gradient directed upward, and to the fingering effect of the displacement of a more viscous fluid by a less viscous one. Small perturbations are superimposed on the basic flow, and their development is investigated in order to establish the criteria of flow stability. The flow variables are expanded in a series of eigenfunctions, and the ensuing system of ordinary differential equations is solved numerically. Criteria of flow stability and parameters affecting flow conditions are studied.

ISSN:0031-9171    

DOI:10.1063/1.862434

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

Solitary waves and cnoidal waves have been found in an adiabatic compressible atmosphere which, under ambient conditions, has winds, and is isothermal. The theory is illustrated with an example for which the background wind is linearly increasing. It is found that the number of possible critical speeds of the flow depends crucially on whether the Richardson number is greater or less than one‐fourth.

ISSN:0031-9171    

DOI:10.1063/1.862435

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

The dynamics of a rotating, cylindrical liquid shell (liner) adiabatically compressing a trapped medium (the payload) is investigated analytically and numerically. The state variables at minimum radius (turnaround) are computed as functions ofpf, the peak payload pressure andu∞, the velocity the liner would attain if allowed to expand without restraint. For each choice ofpfandu∞, the rotational speed is chosen to just stabilize the Rayleigh–Taylor modes at the liner‐payload interface. The acceleration of the inner surface is largest immediately prior to turnaround, so that the initial rotational speed required for stabilization is close to that for an equivalent incompressible liner. Near turnaround the inner portion of the liner becomes significantly compressed, making the efficiency with which liner kinetic energy is transfered to the payload considerably less than that for an incompressible liner. The liner compression provided at turnaround alters the implosion dynamics and creates a pressure pulse propagating outward, analogous to a ’’water hammer’’. An additional result of compression is a slower rebound speed after turnaround, compared with the implosion speed.

ISSN:0031-9171    

DOI:10.1063/1.862436

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

A soluble model of the development of the linear pertubations about a time‐varying state of a compressible medium is presented. A Lagrangian description is employed to rederive the equations for the self‐similar motion of an ideal fluid and to obtain the linearized equations of motion for pertubations about a general time‐varying basic state. The resulting formalism is applied in cylindrical geometry to calculate the growth of flute‐like modes associated with a similarity solution modeling the implosion and expansion of a fluid liner. A complete solution is obtained for the perturbed motion. The only modes for which the perturbation amplitudes grow faster than the unperturbed liner radius during both implosion and expansion are divergence‐ and curl‐free. Numerical and analytical results are obtained for these and shown to reduce, in the short‐wavelength limit, to the Rayleigh–Taylor instability found previously for incompressible time‐independent basic states. In addition, a new kind of instability is found: a class of overstable internal modes (sound waves), which are ’’pumped up’’ in amplitude during implosion, but decay during the expansion phase.

ISSN:0031-9171    

DOI:10.1063/1.862437

出版商:AIP    

年代:1979

数据来源: AIP

摘要:

The effect of flow shear on the stability of rotating ideal magnetohydrodynamic equilibria is investigated. It is found that a large enough shear can sometimes completely stabilize the flute(k=0) modes. The most notable result is a theorem which provides for an analytical determination of the exact number of unstable modes. A weaker sufficient condition for stability is also derived.

ISSN:0031-9171    

DOI:10.1063/1.862438

出版商:AIP    

年代:1979

数据来源: AIP